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Parameters

Introduction

The wannier90.x code described in Part wannier90.x calculates the maximally-localized Wannier functions.

The postw90.x executable contains instead a series of modules that take the Wannier functions calculated by wannier90.x and use them to calculate different properties. This executable is parallel (by means of MPI libraries), so it can be run on multiple CPUs. The information on the calculated Wannier functions is read from the checkpoint seedname.chk file. Note that this is written in an unformatted machine-dependent format. If you need to use this file on a different machine, or you want to use a version of postw90.x compiled with a different compiler, refer to Sec. w90chk2chk in the Appendices for a description of how to export/import this file.

Usage

postw90.x can be run in parallel using MPI libraries to reduce the computation time.

For serial execution use: postw90.x [seedname]

  • seedname: If a seedname string is given the code will read its input from a file seedname.win. The default value is wannier. One can also equivalently provide the string seedname.win instead of seedname.

For parallel execution use: mpirun -np NUMPROCS postw90.x [seedname]

  • NUMPROCS: substitute with the number of processors that you want to use.

Note that the mpirun command and command-line flags may be different in your MPI implementation: read your MPI manual or ask your computer administrator.

Note also that this requires that the postw90.x executable has been compiled in its parallel version (follow the instructions in the file README.install in the main directory of the wannier90 distribution) and that the MPI libraries and binaries are installed and correctly configured on your machine.

seedname.win File

The postw90.x uses the same seedname.win input file of wannier90.x. The input keywords of postw90.x must thus be added to this file, using the same syntax described in Sec. wannier90.x.

Note that wannier90.x checks if the syntax of the input file is correct, but then ignores the value of the flags that refer only to modules of postw90.x, so one can safely run wannier90.x on a file that contains also postw90.x flags.

Similarly, postw90.x ignores flags that refer only to wannier90.x (as number of iterations, restart flags, ...). However, some parts of the input file must be there, as for instance the number of Wannier functions, etc.

The easiest thing to do is therefore to simply add the postw90 input keywords to the seedname.win file that was used to obtain the Wannier functions.

List of available modules

The currently available modules in postw90.x are:

  • dos: Calculation of the density of states (DOS), projected density of states (PDOS), net spin etc.

  • kpath: Calculation of \(k\)-space quantities such as energy bands, Berry curvature and Berry curvature-like term of spin Hall conductivity along a piecewise linear path in the BZ (see tutorials 17, 18 and 29 of the tutorial).

  • kslice: Calculation of \(k\)-space quantities on a planar slice of the BZ (see tutorials 17, 18 and 29 of the tutorial).

  • berry: Calculation of properties related to the BZ integral of the Berry curvature, Berry connection and Berry curvature-like term of spin Hall conductivity, including anomalous Hall conductivity, orbital magnetisation, optical conductivity, nonlinear shift current and spin Hall conductivity (see Chap. Berry and tutorials 18, 19, 25, 29 and 30 of the tutorial). It also includes an option to compute \(k\cdot p\) expansion coefficients (see Sec. kdotp and tutorial 33 of the tutorial).

  • gyrotropic: Calculation of gyrotropic properties, including natural and current0induced optical rotation, and the current-induced magnetization (see Chap. Gyrotropic and tutorial 24 of the tutorial).

  • BoltzWann: Calculation of electronic transport properties for bulk materials using the semiclassical Boltzmann transport equation (see Chap. BoltzWann and tutorial 16 of the tutorial).

  • geninterp (Generic Band Interpolation): Calculation band energies (and band derivatives) on a generic list of \(k\) points (see Chap. Geninterp).

Keyword List

On the next pages the list of available  input keywords is reported. In particular, Table Global Parameters of postw90 reports keywords that affect the generic behavior of all modules of . Often, these are "global" variables that can be overridden by module-specific keywords (as for instance the kmesh flag). The subsequent tables describe the input parameters for each specific module. A description of the behaviour of the global flags is described Sec. Global variables; the description of the flags specific to the modules can be found in the following sections.

Global Parameters of postw90

Keyword Type Description
kmesh I Dimensions of the uniform interpolation \(k\)-mesh (one or three integers)
kmesh_spacing R Minimum spacing between \(k\) points in Å\(^{-1}\)
adpt_smr L Use adaptive smearing
adpt_smr_fac R Adaptive smearing prefactor
adpt_smr_max P Maximum allowed value for the adaptive energy smearing (eV)
smr_type S Analytical form used for the broadened delta function
smr_fixed_en_width P Energy smearing (if non-adaptive)
num_elec_per_state I Number of electrons per state
scissors_shift P Scissors shift applied to the conduction bands (eV) (deprecated)
num_valence_bands I Number of valence bands
spin_decomp L Decompose various properties into up-spin, down-spin, and possibly spin-flip parts
spin_axis_polar P Polar angle of the spin quantization axis (deg)
spin_axis_azimuth P Azimuthal angle of the spin quantization axis (deg)
spin_moment\(^*\) L Determines whether to evaluate the spin magnetic moment per cell
uHu_formatted L Read a formatted seedname.uHu file
spn_formatted L Read a formatted seedname.spn file
berry_curv_unit S Unit of Berry curvature

seedname.win file keywords controlling the general behaviour of the modules in postw90. Argument types are represented by, I for a integer, R for a real number, P for a physical value, L for a logical value and S for a text string.
* The keyword spin_moment does not affect the behavior of the modules in , and does not really belong to any of them. It is listed here for lack of a better place.

berry Parameters

Keyword Type Description
berry L Calculate Berry-type quantities
berry_task S List of properties to compute
[berry_]kmesh I Dimensions of the uniform interpolation \(k\)-mesh (one or three integers)
[berry_]kmesh_spacing R Minimum spacing between \(k\) points in Å\(^{-1}\)
berry_curv_adpt_kmesh I Linear dimension of the adaptively refined \(k\)-mesh used to compute the anomalous/spin Hall conductivity
berry_curv_adpt_kmesh_thresh P Threshold magnitude of the Berry curvature for adaptive refinement
kubo_freq_min P Lower limit of the frequency range for optical spectra, JDOS, shift current and spin Hall conductivity (eV)
kubo_freq_max P Upper limit of the frequency range for optical spectra, JDOS, shift current and spin Hall conductivity (eV)
kubo_freq_step R Step for increasing the optical frequency in the specified range
kubo_eigval_max P Maximum energy eigenvalue included when evaluating the Kubo-Greenwood conductivity, JDOS, shift current and spin Hall conductivity
[kubo_]adpt_smr L Use adaptive energy smearing for the optical conductivity, JDOS, shift current and spin Hall conductivity
[kubo_]adpt_smr_fac R Adaptive smearing prefactor
[kubo_]adpt_smr_max P Maximum allowed value for the adaptive energy smearing (eV)
[kubo_]smr_type S Analytical form used for the broadened delta function when computing the optical conductivity, JDOS, shift current and spin Hall conductivity
[kubo_]smr_fixed_en_width P Energy smearing (if non-adaptive) for the optical conductivity, JDOS, shift current and spin Hall conductivity (eV)
sc_eta R Energy broadening of energy differences in the sum over virtual states when computing shift current
sc_phase_conv I Convention for phase factor of Bloch states when computing shift current
sc_w_thr R Frequency threshold for speeding up delta function integration when computing shift current
sc_use_eta_corr L Use finite-eta correction for computing shift current
shc_freq_scan L Calculate Fermi energy scan or frequency scan of spin Hall conductivity
shc_method S How to obtain the spin current matrix elements for SHC
shc_alpha I The spin current direction of spin Hall conductivity
shc_beta I The direction of applied electrical field of spin Hall conductivity
shc_gamma I The spin direction of the spin current of spin Hall conductivity
shc_bandshift L Rigid bandshift of the conduction bands
shc_bandshift_firstband I Index of the first band to shift
shc_bandshift_energyshift P Energy shift of the conduction bands (eV)
kdotp_kpoint R \(k\) point for \(k\cdot p\) expansion (\(2\pi/a\), with \(a\) lattice constant in Å)
kdotp_num_bands I Number of bands for \(k\cdot p\) expansion
kdotp_bands I Band indexes corresponding to the \(k\cdot p\) bands

seedname.win file keywords controlling the berry module. Argument types are represented by, I for a integer, R for a real number, P for a physical value, L for a logical value and S for a text string.

dos Parameters

Keyword Type Description
dos L Calculate the density of states and related properties
dos_task S List of properties to compute
dos_energy_min P Lower limit of the energy range for computing the DOS (eV)
dos_energy_max P Upper limit of the energy range for computing the DOS (eV)
dos_energy_step R Step for increasing the energy in the specified range (eV)
dos_project I List of WFs onto which the DOS is projected
[dos_]kmesh I Dimensions of the uniform interpolation \(k\)-mesh (one or three integers)
[dos_]kmesh_spacing R Minimum spacing between \(k\) points in Å\(^{-1}\)
[dos_]adpt_smr L Use adaptive smearing for the DOS
[dos_]adpt_smr_fac R Adaptive smearing prefactor
[dos_]adpt_smr_max P Maximum allowed value for the adaptive energy smearing (eV)
[dos_]smr_fixed_en_width P Energy smearing (if non-adaptive) for the DOS (eV)
[dos_]smr_type S Analytical form used for the broadened delta function when computing the DOS.

seedname.win file keywords controlling the dos module. Argument types are represented by, I for a integer, R for a real number, P for a physical value, L for a logical value and S for a text string.

kpath Parameters

Keyword Type Description
kpath L Calculate properties along a piecewise linear path in the BZ
kpath_task L List of properties to evaluate
kpath_num_points I Number of points in the first kpath segment
kpath_bands_colour S Property used to colour the energy bands along the path

seedname.win file keywords controlling the kpath module. Argument types are represented by, I for a integer, R for a real number, P for a physical value, L for a logical value and S for a text string.

kslice Parameters

Keyword Type Description
kslice L Calculate properties on a slice in the BZ
kslice_task S List of properties to evaluate
kslice_corner R Position of the corner of the slice
kslice_b1 R First vector defining the slice
kslice_b2 R Second vector defining the slice
kslice_2dkmesh I Dimensions of the uniform interpolation \(k\)-mesh on the slice (one or two integers)
kslice_fermi_level P This parameter is not used anymore. Use fermi_energy instead.
kslice_fermi_lines_colour S Property used to colour the Fermi lines

seedname.win file keywords controlling the kslice module. Argument types are represented by, I for a integer, R for a real number, P for a physical value, L for a logical value and S for a text string.

gyrotropic Parameters

Keyword Type Description
gyrotropic L Calculate gyrotropic quantities
gyrotropic_task L List of properties to compute
[gyrotropic_]kmesh I Dimensions of the uniform interpolation \(k\)-mesh (one or three integers)
[gyrotropic_]kmesh_spacing R Minimum spacing between \(k\) points in Å\(^{-1}\)
gyrotropic_freq_min P Lower limit of the frequency range for optical rotation (eV)
gyrotropic_freq_max P Upper limit of the frequency range for optical rotation (eV)
gyrotropic_freq_step P Step for increasing the optical frequency in the specified range
gyrotropic_eigval_max P Maximum energy eigenvalue included when evaluating the interband natural optical activity
gyrotropic_degen_thresh P threshold to exclude degenerate bands from the calculation
[gyrotropic_]smr_type S Analytical form used for the broadened delta function
[gyrotropic_]smr_fixed_en_width P Energy smearing (eV)
[gyrotropic_]band_list I list of bands used in the calculation
gyrotropic_box_center
gyrotropic_box_b1
gyrotropic_box_b2
gyrotropic_box_b3		 R
R
R
R		 The center and three basis vectors, defining the box for integration (in reduced coordinates, three real numbers for each vector)

seedname.win file keywords controlling the gyrotropic module. Argument types are represented by, I for a integer, R for a real number, P for a physical value, L for a logical value and S for a text string.

BoltzWann Parameters

Keyword Type Description
boltzwann L Calculate Boltzmann transport coefficients
[boltz_]kmesh I Dimensions of the uniform interpolation \(k\)-mesh (one or three integers)
[boltz_]kmesh_spacing R Minimum spacing between \(k\) points in Å\(^{-1}\)
boltz_2d_dir S Non-periodic direction (for 2D systems only)
boltz_relax_time P Relaxation time in fs
boltz_mu_min P Minimum value of the chemical potential \(\mu\) in eV
boltz_mu_max P Maximum value of the chemical potential \(\mu\) in eV
boltz_mu_step R Step for \(\mu\) in eV
boltz_temp_min P Minimum value of the temperature \(T\) in Kelvin
boltz_temp_max P Maximum value of the temperature \(T\) in Kelvin
boltz_temp_step R Step for \(T\) in Kelvin
boltz_tdf_energy_step R Energy step for the TDF (eV)
boltz_tdf_smr_fixed_en_width P Energy smearing for the TDF (eV)
boltz_tdf_smr_type S Smearing type for the TDF
boltz_calc_also_dos L Calculate also DOS while calculating the TDF
boltz_dos_energy_min P Minimum value of the energy for the DOS in eV
boltz_dos_energy_max P Maximum value of the energy for the DOS in eV
boltz_dos_energy_step R Step for the DOS in eV
[boltz_]smr_type S Smearing type for the DOS
[boltz_]adpt_smr L Use adaptive smearing for the DOS
[boltz_]adpt_smr_fac R Adaptive smearing prefactor
[boltz_]adpt_smr_max P Maximum allowed value for the adaptive energy smearing (eV)
[boltz_]fixed_en_width P Energy smearing (if non-adaptive) for the DOS (eV)
boltz_bandshift L Rigid bandshift of the conduction bands
boltz_bandshift_firstband I Index of the first band to shift
boltz_bandshift_energyshift P Energy shift of the conduction bands (eV)

seedname.win file keywords controlling the BoltzWann module (calculation of the Boltzmann transport coefficients in the Wannier basis). Argument types are represented by, I for a integer, R for a real number, P for a physical value, L for a logical value and S for a text string.

geninterp Parameters

Keyword Type Description
geninterp L Calculate bands for given set of \(k\) points
geninterp_alsofirstder L Calculate also first derivatives
geninterp_single_file L Write a single file or one for each process

seedname.win file keywords controlling the Generic Band Interpolation (geninterp) module. Argument types are represented by, I for a integer, R for a real number, P for a physical value, L for a logical value and S for a text string.

Global variables

integer :: kmesh(:)

Dimensions of the interpolation grid used in postw90.x.

Not to be confused with the mp_grid input flag, which instead specifies the Monkhorst--Pack grid used in the ab-initio calculation!

If three integers \(l\) \(m\) \(n\) are given, the reciprocal-space cell subtended by the three primitive translations is sampled on a uniform \(l\times m\times n\) grid (including \(\Gamma\)). If only one integer \(m\) is given, an \(m\times m\times m\) grid is used.

If you use a module which needs a k-mesh, either kmesh_spacing or kmesh must be defined.

real(kind=dp) :: kmesh_spacing

An alternative way of specifying the interpolation grid. This flag defines the minimum distance for neighboring \(k\) points along each of the three directions in \(k\) space.

The units are Å\(^{-1}\).

If you use a module which needs a k-mesh, either kmesh_spacing or kmesh must be defined.

logical :: adpt_smr

Determines whether to use an adaptive scheme for broadening the DOS and similar quantities defined on the energy axis. If true, the values for the smearing widths are controlled by the flag adpt_smr_fac.

The default value is true.

real(kind=dp) :: adpt_smr_fac

The width \(\eta_{n{\bf k}}\) of the broadened delta function used to determine the contribution to the spectral property (DOS, ...) from band \(n\) at point \({\bf k}\) is calculated as \(\eta_{n{\bf k}}=\alpha\vert \nabla_{\bf k} \varepsilon_{n{\bf k}}\vert \Delta k,\) where \(\varepsilon_{n{\bf k}}\) is the energy eigenvalue and the dimensionless factor \(\alpha\) is given by adpt_smr_fac. \(\Delta k\) is taken to be the largest of the mesh spacings along the three reciprocal lattice vectors \({\bf b_1}\), \({\bf b_2}\), and \({\bf b_3}\). If the calculated value of \(\eta_{n{\bf k}}\) exceeds adpt_smr_max, the latter value is used.

The default value is \(\sqrt{2}\).

real(kind=dp) :: adpt_smr_max

See description given immediately above.

The units are eV. The default value is 1.0.

character(len=120) :: smr_type

Defines the analytical form used for the broadened delta function in the computation of the DOS and similar quantities defined on the energy axis.

  • gauss: Gaussian smearing

  • m-pN: derivative of the \(N\)-th order Methfessel-Paxton function (\(N\geq 0\)). Example: m-p2 for the second-order Methfessel-Paxton function. If only m-p is provided, the first-order function is used, i.e., it is equivalent to m-p1.

  • m-v or cold: derivative of the Marzari--Vanderbilt cold-smearing function

  • f-d: derivative of the Fermi-Dirac distribution function

The default value is gauss.

logical :: smr_fixed_en_width

Energy width for the smearing function for the DOS. Used only if adpt_smr is false.

The units are eV. The default value is 0 eV. Note that if the width is smaller than twice the energy step (e.g. dos_energy_step for the dos module), the DOS will be unsmeared (thus the default is to have an unsmeared properties when adpt_smr is set to false.).

integer :: num_elec_per_state

Number of electrons per state. It can only take the values one or two.

The default value is 1 if spinors=true, 2 otherwise.

real(kind=dp) :: scissors_shift

Scissors shift applied to the conduction bands.

Note

This variable is deprecated and will be removed in future versions of the code. This applies the scissors shift only to the Hamiltonian, but also other matrices might need to be updated if a scissors shift is applied. If you are using BoltzWann, consider using boltz_bandshift instead. If you are calculating spin Hall conductivity, consider using shc_bandshift instead.

The units are eV. The default value is 0 eV (i.e., no scissors shift applied).

integer :: num_valence_bands

Number of valence bands of the system. Used in different modules and for the scissors shift.

No default value.

logical :: spin_decomp

If true, extra columns are added to some output files (such as seedname-dos.dat for the dos module, and analogously for the berry and BoltzWann modules).

For the dos and BoltzWann modules, two further columns are generated, which contain the decomposition of the required property (e.g., total or orbital-projected DOS) of a spinor calculation into up-spin and down-spin parts (relative to the quantization axis defined by the input variables spin_axis_polar and spin_axis_azimuth). For the berry module with berry_task = kubo, three extra columns are added to seedname-jdos.dat, containing the decomposition of the JDOS into up \(\rightarrow\) up, down \(\rightarrow\) down, and spin-flip transitions. In the same way, six extra columns are added to the data files seedname-kubo*.dat where the complex optical conductivity is stored.

The file seedname.spn must be present at input. Furthermore, if this variable is set to true it requires num_elec_per_state = 1.

The default value is false.

real(kind=dp) :: spin_axis_polar

Polar angle of the spin quantization axis.

The units are degrees. The default value is 0.

real(kind=dp) :: spin_axis_azimuth

Azimuthal angle of the spin quantization axis.

The units are degrees. The default value is 0.

logical :: spin_moment

Determines whether to evaluate the spin moment.

The default value is false.

logical :: uHu_formatted

If uHu_formatted=true, then the uHu matrix elements will be read from disk as formatted (ie ASCII) files; otherwise they will be read as unformatted files.

The default value of this parameter is false.

logical :: spn_formatted

If spn_formatted=true, then the spin matrix elements will be read from disk as formatted (ie ASCII) files; otherwise they will be read as unformatted files. Unformatted is generally preferable as the files will take less disk space and I/O is significantly faster. However such files will not be transferable between all machine architectures and formatted files should be used if transferability is required (i.e., for test cases).

The default value is false.

character(len=20) :: berry_curv_unit

Unit in which the Berry curvature is specified at input (in berry_curv_adpt_kmesh_thresh) or written to file (when kpath_task=curv or kpath_task=shc or kslice_task=curv or kslice_task=shc).

  • ang2: Angstrom\(^2\)

  • bohr2: Bohr\(^2\) (atomic units)

The default value is ang2.

logical :: sc_use_eta_corr

If sc_use_eta_corr=true, apply the finite-eta correction of the shift current (Eq. (19) of Ref. 1). Without the correction, the convention of the Bloch sum (determined by sc_phase_conv) can affect the computed shift-current spectra. See Ref. 1 for details.

The default value is true.

DOS

Note that the behavior of the dos module is also influenced by the value of some global flags (listed in Table Global Parameters of postw90), as spin_decomp, spin_axis_polar, spin_axis_azimuth, scissors_shift, etc. Some of the global flags can be possibly overridden by local flags of the DOS module, listed below, which have the same name of the global flag but are prefixed by dos_.

logical :: dos

Determines whether to enter the DOS routines.

The default value is false.

character(len=20) :: dos_task

The quantity to compute when dos=true

The valid options for this parameter are:

  • dos_plot Density of states. An output data file seedname-dos.dat is created, containing the energy values in eV in the first column, and the total DOS per unit cell and unit energy range (in eV\(^{-1}\)) in the second. Two additional columns are present if spin_decomp=true

The default value is dos_plot.

real(kind=dp) :: dos_energy_min

Lower limit of the energy range for computing the DOS. Units are eV.

The default value is the minimum value of the energy eigenvalues stored in seedname.eig, minus 0.6667.

real(kind=dp) :: dos_energy_max

Upper limit of the energy range for computing the DOS. Units are eV.

If an inner energy window was specified, the default value is the upper bound of the innter energy window, plus 0.6667. Otherwise it is the maximum value of the energy eigenvalues stored in seedname.eig, plus 0.6667.

real(kind=dp) :: dos_energy_step

Energy step for the grid of energies used to plot the dos. Units are eV.

The default value is 0.01 eV.

integer :: dos_project(:)

If present postw90 computes, instead of the total DOS, the partial DOS projected onto the WFs listed. The WFs are numbered according to the file seedname.wout.

For example, to project onto WFs 2, 6, 7, 8, and 12:

dos_project : 2, 6-8, 12

The DOS projected onto a set \({\cal S}\) of orbitals is calculated as

\[ \begin{equation} \begin{aligned} \rho_{\cal S}(E)&=\frac{1}{N_k}\sum_{\bf k}\sum_n \langle \psi_{n\bf k}^{({\rm H})}\vert \hat{P}_{\bf k}({\cal S})\vert \psi_{n\bf k}^{({\rm H})}\rangle\delta(\varepsilon_{n\bf k}-E)\\ \hat{P}_{\bf k}({\cal S})&=\sum_{m\in{\cal S}} \vert \psi_{n\bf k}^{({\rm W})}\rangle\langle \psi_{n\bf k}^{({\rm W})}\vert, \end{aligned} \end{equation} \]

where \(N_k\) is the number of mesh points used to sample the BZ, and the superscript (H) and (W) refer to Hamiltonian gauge and Wannier gauge 2.

integer :: dos_kmesh(:)

Overrides the kmesh global variable (see Sec. Global variables).

real(kind=dp) :: dos_kmesh_spacing

Overrides the kmesh_spacing global variable (see Sec. Global variables).

logical :: dos_adpt_smr

Overrides the adpt_smr global variable (see Sec. Global variables).

real(kind=dp) :: dos_adpt_smr_fac

Overrides the adpt_smr_fac global variable (see Sec. Global variables).

real(kind=dp) :: dos_adpt_smr_max

Overrides the adpt_smr_max global variable (see Sec. Global variables).

logical :: dos_smr_fixed_en_width

Overrides the smr_fixed_en_width global variable (see Sec. Global variables).

Note that if the width is smaller than twice the energy step dos_energy_step, the DOS will be unsmeared (thus the default is to have an unsmeared DOS).

character(len=20) :: dos_smr_type

Overrides the smr_type global variable (see Sec. Global variables).

kpath

logical :: kpath

Determines whether to enter the kpath routines.

The default value is false.

character(len=20) :: kpath_task

The quantities to plot when kpath=true

The valid options for this parameter are:

  • bands Energy bands, in eV. The following files are created:

    • seedname-bands.dat (data file)

    • seedname-bands.gnu (gnuplot script)

    • seedname-bands.py (python script)

    • seedname-path.kpt (list of \(k\)-points along the path, written in the pwscf format)

  • curv Minus the Berry curvature given by Berry Eq. [anomalous Hall Conductivity] of Ch. Berry, in units of berry_curv_unit. The following files are created:

    • seedname-curv.dat (data file)

    • seedname-curv_{x,y,z}.gnu (gnuplot scripts)

    • seedname-curv_{x,y,z}.py (python scripts)

  • morb The integrand of the \(k\)-space orbital magnetization formula [Berry Eq. [orbital magnetization] of Ch. Berry] in eV\(\cdot\)Å\(^2\). Four output files are created:

    • seedname-morb.dat (data file)

    • seedname-morb_{x,y,z}.gnu (gnuplot scripts)

    • seedname-morb_{x,y,z}.py (python scripts)

  • shc The band-projected Berry curvature-like term of spin Hall conductivity given by Berry Eq. [spin Hall conductivity] of Ch. Berry, in units of berry_curv_unit. The following files are created:

    • seedname-shc.dat (data file)

    • seedname-shc.gnu (gnuplot scripts)

    • seedname-shc.py (python scripts)

  • Any combination of the above. The following combinations are of special interest

    • kpath_task = bands+curv

    • kpath_task = bands+morb

    • kpath_task = bands+shc

    They generate the following files:

    • seedname-bands.dat (data file)

    • seedname-{curv,morb,shc}.dat (data file)

    • seedname-bands+{curv,morb}_{x,y,z}.py or seedname-bands+shc.py (python scripts)

    Two-panel figures are produced, with the energy bands within \(\pm 0.65\) eV of the Fermi level in the top panel, and the Berry curvature (or \(k\)-space orbital magnetization, or \(k\)-resolved Berry curvature-like term of spin Hall conductivity) in the bottom panel.

The default value is bands.

integer :: kpath_num_points

If kpath=true, then the number of points along the first section of the bandstructure plot given by kpoint_path. Other sections will have the same density of \(k\)-points.

The default value is 100.

character(len=20) :: kpath_bands_colour

When kpath_task=bands, colour code the energy bands according to the specified quantity.

The valid options for this parameter are:

  • spin Spin projection (in units of \(\hbar/2\)) along the quantization axis defined by the variables spin_axis_polar and spin_axis_azimuth, for a spinor calculation

  • shc Band-projected Berry curvature-like term of spin Hall conductivity (in units of berry_curv_unit) defined by the variables shc_alpha, shc_beta and shc_gamma, for a spinor calculation

  • none no colour coding

The default value is none.

kslice

logical :: kslice

Determines whether to enter the kslice routines.

The default value is false.

character(len=20) :: kslice_task

The quantity to plot when kslice=true

The valid options for this parameter are:

  • fermi_lines Lines of intersection between constant-energy surfaces and the slice. The energy level is specified by the keyword fermi_energy. Output files:

    • seedname-kslice-fermi-spn.dat (data file when kslice_fermi_lines_colour = spin)

    • seedname-bnd_n.dat (gnuplot data files when kslice_fermi_lines_colour = none)

    • seedname-kslice-coord.dat (python data files when kslice_fermi_lines_colour = none)

    • seedname-kslice-bands.dat (python data file when kslice_fermi_lines_colour = none)

    • seedname-kslice-fermi_lines.gnu (gnuplot script)

    • seedname-kslice-fermi_lines.py (python script)

  • curv[+fermi_lines] Heatmap of the Berry curvature of the occupied states [together with the constant-energy contours]. The unit of Berry curvature is berry_curv_unit.

    Output files:

    • seedname-kslice-coord.dat (data files)

    • seedname-kslice-curv.dat (data file)

    • [seedname-kslice-bands.dat] (data file)

    • seedname-kslice-curv_{x,y,z}[+fermi_lines].py (python scripts)

  • morb[+fermi_lines] Heatmap of the \(k\)-space orbital magnetization in eV\(\cdot\)Å\(^2\) [together with the constant-energy contours]. Output files:

    • seedname-kslice-coord.dat (data files)

    • seedname-kslice-morb.dat (data file)

    • [seedname-kslice-bands.dat] (data file)

    • seedname-kslice-morb_{x,y,z}[+fermi_lines].py (python scripts)

  • shc[+fermi_lines] Heatmap of the Berry curvature-like term of the occupied states [together with the constant-energy contours]. The unit of Berry curvature-like term is berry_curv_unit.

    Output files:

    • seedname-kslice-coord.dat (data files)

    • seedname-kslice-shc.dat (data file)

    • [seedname-kslice-bands.dat] (data file)

    • seedname-kslice-shc[+fermi_lines].py (python scripts)

The default value is fermi_lines.

Note

When kslice_fermi_lines_colour = none the gnuplot scripts draw the \(k\)-slices with a square shape, even when kslice_b1 and kslice_b2 below are not at right angles, or do not have equal lengths. (The python scripts draw the slices with the correct parallelogram shape.)

real(kind=dp) :: kslice_corner(3)

Reduced coordinates of the lower-left corner of the slice in k-space.

The default value is \((0.0,0.0,0.0)\)

real(kind=dp) :: kslice_b1(3)

Reduced coordinates of the first reciprocal-space vector defining the slice.

The default value is \((1.0,0.0,0.0)\).

real(kind=dp) :: kslice_b2(3)

Reduced coordinates of the second reciprocal-space vector defining the slice.

The default value is \((0.0,1.0,0.0)\).

integer :: kslice_2dkmesh(2)

Dimensions of the \(k\)-point grid covering the slice. If two integers \(m\) \(n\) are given, the slice is sampled on a uniform \(m\times n\) grid. If only one integer \(m\) is given, an \(m\times m\) grid is used.

The default value for kslice_kmesh is 50.

character(len=20) :: kslice_fermi_lines_colour

When kslice_task=fermi_lines (but not when combined with curv or morb), colour code the Fermi lines according to the specified quantity.

The valid options for this parameter are:

  • spin Spin projection (in units of \(\hbar/2\)) along the quantization axis defined by the variables spin_axis_polar and spin_axis_azimuth, for a spinor calculation

  • none no colour coding

The default value is none.

berry

logical :: berry

Determines whether to enter the berry routines.

The default value is false.

character(len=120) :: berry_task

The quantity to compute when berry=true

The valid options for this parameter are:

  • kubo Complex optical conductivity and joint density of states.

    Output files:

    • seedname-kubo-S_{xx,yy,zz,xy,xz,yz}.dat (data files). First column: optical frequency \(\hbar\omega\) in eV. Second and third columns: real and imaginary parts of the symmetric conductivity \(\sigma^{\rm S}_{\alpha\beta}(\hbar\omega)=\sigma^{\rm S}_{\beta\alpha}(\hbar\omega)\) in S/cm. Six additional columns are present if spin_decomp = true.

    • seedname-kubo-A_{yz,zx,xy}.dat (data files). First column: optical frequency \(\hbar\omega\) in eV. Second and third columns: real and imaginary parts of the antisymmetric conductivity \(\sigma^{\rm A}_{\alpha\beta}(\hbar\omega)=-\sigma^{\rm A}_{\beta\alpha}(\hbar\omega)\) in S/cm. Six additional columns are present if spin_decomp = true.

    • seedname-jdos.dat (data file). First column: energy difference \(\hbar\omega\) in eV between conduction (\(c\)) and valence (\(v\)) states with the same crystal momentum \({\bf k}\). Second column: joint density of states \(\rho_{cv}(\hbar\omega)\) (number of states per unit cell per unit energy range, in eV\(^{-1}\)). Three additional columns are present if spin_decomp = true.

  • ahc Anomalous Hall conductivity, in S/cm. The three independent components \(\sigma_x=\sigma_{yz}\), \(\sigma_y=\sigma_{zx}\), and \(\sigma_z=\sigma_{xy}\) are computed.

    Output files:

    • seedname-ahc-fermiscan.dat (data file). The first column contains the Fermi level \(\varepsilon_F\) in eV, and the following three column the values of \(\sigma_{x,y,z}(\varepsilon_F)\). This file is written if a range of Fermi energies is specified via fermi_energy_min and fermi_energy_max. If a single Fermi energy is given, the AHC is printed in seedname.wpout only.

  • morb Orbital magnetisation, in bohr magnetons per cell.

    Output files:

    • seedname-morb-fermiscan.dat (data file). The first column contains the Fermi level \(\varepsilon_F\) in eV, and the following three column the values of \(M^{\rm orb}_{x,y,z}(\varepsilon_F)\). This file is written if a range of Fermi energies is specified via fermi_energy_min and fermi_energy_max. If a single Fermi energy is given, \({\bf M}^{\rm orb}\) is printed in seedname.wpout only.

  • sc Nonlinear shift current.

    Output files:

    • seedname-sc_{xxx,xxy,xxz,...}.dat (data files). The shift current is described by a \(3\times3\times3\) tensor \(\sigma^{abc}\). The program outputs a set of 18 files, and the 9 remaining components can be obtained by taking into account that \(\sigma^{abc}\) is symmetric under \(b\leftrightarrow c\) index exchange. First column: optical frequency \(\hbar\omega\) in eV. Second column: nonlinear shift current \(\sigma^{abc}(\hbar\omega)\) in A/V\(^{2}\).

  • shc Spin Hall conductivity (SHC), in \((\hbar/e)\)S/cm.

    Output files:

    • seedname-shc-fermiscan.dat (data file). The first column is the number of entries in the list, the second column contains the Fermi level \(\varepsilon_F\) in eV, and the last column contains the values of \(\sigma_{\alpha\beta}^{\text{spin}\gamma}(\varepsilon_F)\). This file is written if a range of Fermi energies is specified via fermi_energy_min and fermi_energy_max. If a single Fermi energy is given, the file will contain SHC at this specific energy.

    • seedname-shc-freqscan.dat (data file). The first column is the number of the entry in the list, the second column contains the frequency \(\hbar\omega\) in eV, and the following two columns contain the values of the real part \(\Re[\sigma_{\alpha\beta}^{\text{spin}\gamma}(\omega)]\) and imaginary part \(\Im[\sigma_{\alpha\beta}^{\text{spin}\gamma}(\omega)]\) of ac SHC. This file is written if a range of frequencies is specified via kubo_freq_min and kubo_freq_max.

  • kdotp \(k\cdot p\) expansion coefficients.

    Output files:

    • seedname-kdotp_{0,1,2}.dat (data files); respectively, the zeroth, first and second order \(k\cdot p\) expansion coefficients, in units of eV, eV\(\cdot\)Å, and eV\(\cdot\)Å\(^{2}\).

There is no default value.

integer :: berry_kmesh(:)

Overrides the kmesh global variable (see Sec. Global variables).

real(kind=dp) :: berry_kmesh_spacing

Overrides the kmesh_spacing global variable (see Sec. Global variables).

integer :: berry_curv_adpt_kmesh

If a positive integer \(n\) is given and berry_task=ahc[or berry_task=shc], an \(n\times n\times n\) mesh is placed around points on the uniform mesh (defined by either berry_kmesh or berry_kmesh_spacing) where the magnitude of the \(k\)-space Berry curvature[\(k\)-space Berry curvature-like term of SHC] exceeds the threshold value specified in berry_curv_adpt_kmesh_thresh. This can be used to densify the BZ integration mesh around spikes in the Berry curvature[Berry curvature-like term of SHC].

The default value is 1.

real(kind=dp) :: berry_curv_adpt_kmesh_thresh

Magnitude of the Berry curvature[Berry curvature-like term of SHC] (in units of berry_curv_unit) that triggers adaptive mesh refinement when berry_task=ahc[berry_task=shc].

The default value is 100.0.

real(kind=dp) :: kubo_freq_min

Lower limit of the frequency range for computing the optical conductivity, JDOS and ac SHC. Units are eV.

The default value 0.0.

real(kind=dp) :: kubo_freq_max

Upper limit of the frequency range for computing the optical conductivity, JDOS and ac SHC. Units are eV.

If an inner energy window was specified, the default value is dis_froz_max-fermi_energy+0.6667. Otherwise it is the difference between the maximum and the minimum energy eigenvalue stored in seedname.eig, plus 0.6667.

real(kind=dp) :: kubo_freq_step

Difference between consecutive values of the optical frequency between kubo_freq_min and kubo_freq_max. Units are eV.

The default value is 0.01.

real(kind=dp) :: kubo_eigval_max

Maximum energy eigenvalue of the eigenstates to be included in the evaluation of the optical conductivity, JDOS and ac SHC. Units are eV.

If an inner energy window was specified, the default value is the upper bound of the inner energy window plus 0.6667. Otherwise it is the maximum energy eigenvalue stored in seedname.eig plus 0.6667.

logical :: kubo_adpt_smr

Overrides the adpt_smr global variable (see Sec. Global variables).

real(kind=dp) :: kubo_adpt_smr_fac

Overrides the adpt_smr_fac global variable (see Sec. Global variables).

real(kind=dp) :: kubo_adpt_smr_max

Overrides the adpt_smr_max global variable (see Sec. Global variables).

logical :: kubo_smr_fixed_en_width

Overrides the smr_fixed_en_width global variable (see Sec. Global variables).

character(len=120) :: kubo_smr_type

Overrides the smr_type global variable (see Sec. Global variables).

logical :: shc_freq_scan

Determines whether to calculate the frequency scan (i.e. the ac SHC) or the Fermi energy scan (i.e. the dc SHC) of the spin Hall conductivity.

The default value is false, which means dc SHC is calculated.

character(len=120) :: shc_method

If it is qiao/ryoo, the ac or dc SHC is calculated using Junfeng Qiao's/Jihoon Ryoo's method. To calculate the Kubo formula, the spin current matrix elements are required, and the two methods differ in the degree of approximation. For details, see the section shc.

integer :: shc_alpha

The \(\alpha\) index of spin Hall conductivity \(\sigma_{\alpha\beta}^{\text{spin}\gamma}\), i.e. the direction of spin current. Possible values are 1, 2 and 3, representing the x, y and z directions respectively.

The default value is 1.

integer :: shc_beta

The \(\beta\) index of spin Hall conductivity \(\sigma_{\alpha\beta}^{\text{spin}\gamma}\), i.e. the direction of applied electric field. Possible values are 1, 2 and 3, representing the x, y and z directions respectively.

The default value is 2.

integer :: shc_gamma

The \(\gamma\) index of spin Hall conductivity \(\sigma_{\alpha\beta}^{\text{spin}\gamma}\), i.e. the spin direction of spin current. Possible values are 1, 2 and 3, representing the x, y and z directions respectively.

The default value is 3.

If all the shc_alpha, shc_beta and shc_gamma are set as default values, the \(\sigma_{xy}^{\text{spin}z}\) is computed.

logical :: shc_bandshift

Shift all conduction bands by a given amount (defined by shc_bandshift_energyshift).

Note

this flag slightly differs from the global scissors_shift flag: with shc_bandshift, an exact rigid shift is applied after interpolation; scissors_shift applies instead the shift before interpolation. As a consequence, results may slightly differ (and this is why we provide both possibilities). Note also that with scissors_shift you have to provide the number of valence bands num_valence_bands, while with shc_bandshift you should provide the first band to shift shc_bandshift_firstband = num_valence_bands\(+1\).

The default value is false.

integer :: shc_bandshift_firstband

Index of the first conduction band to shift.

That means that all bands with index \(i\ge {\tt shc\_bandshift\_firstband}\) will be shifted by shc_bandshift_energyshift, if shc_bandshift is true.

The units are eV. No default value; if shc_bandshift is true, this flag must be provided.

real(kind=dp) :: shc_bandshift_energyshift

Energy shift of the conduction bands.

The units are eV. No default value; if shc_bandshift is true, this flag must be provided.

real(kind=dp) :: sc_eta

The width \(\eta\) used to broaden energy differences in denominators of the form

\[ \begin{equation} \frac{1}{\varepsilon_{n\bf{k}}-\varepsilon_{m\bf{k}}}\rightarrow \text{Re}\frac{1}{\varepsilon_{n\bf{k}}-\varepsilon_{m\bf{k}}+i\eta}. \end{equation} \]

The above is needed in shift-current calculations in order to avoid numerical problems caused by near-degeneracies in the sum over virtual states.

The units are eV. The default value is 0.4.

integer :: sc_phase_conv

Convention for the expansion of the Bloch states in shift-current calculations. It can only take the values one or two. We follow the convention of Ref. 3:

  • 1: Include Wannier centre \({\bm \tau}_{n}=\langle w_{n{\bf 0}}|{\bf r}| w_{n{\bf 0}} \rangle\) in the phase factor (so-called tight-binding convention):

    \[ \begin{equation} |u_{n\bf{k}}\rangle = \sum_{\bf{R}} e^{-i{\bf k}({\bf r}-{\bf R} -{\bm \tau}_{n})}| w_{n\bf{R}} \rangle \end{equation} \]

  • 2: Do not include Wannier centre in the phase factor (usual Wannier90 convention):

    \[ \begin{equation} |u_{n\bf{k}}\rangle = \sum_{\bf{R}} e^{-i\bf{k}(\bf{r}-\bf{R})}| w_{n\bf{R}} \rangle \end{equation} \]

If sc_use_eta_corr=true, the convention does not affect the full shift-current matrix element, but it does affect the weights of the internal components that compose it (see Ref. 4). If sc_use_eta_corr=false, the convention can affect the full shift-current matrix element (see Ref. 1).

The default value is 1.

real(kind=dp) :: sc_w_thr

Parameter \(\alpha_{t}\) for speeding up the frequency integration in shift-current calculations. It settles the frequency threshold \(\omega_{t}=\alpha_{t}\eta_{n{\bf k}}\) (a factor times the broadening) beyond which the delta functions are taken as zero.

The default value is 5.0.

real(kind=dp) :: kdotp_kpoint(3)

Defines the \(k\) point around which the \(k\cdot p\) expansion is performed.

The default value is 0.0 0.0 0.0 (\(\Gamma\)).

integer :: kdotp_num_bands

Number of bands forming the \(k\cdot p\) basis set.

No default value.

integer :: kdotp_bands(kdotp_num_bands)

Band indexes of bands belonging to \(k\cdot p\) basis. Number of entries must be equal to the integer defined in kdotp_num_bands. The band labelling follows that of "wannierised" bands.

No default value.

Gyrotropic

logical :: gyrotropic

Determines whether to enter the gyrotropic routines.

The default value is false.

character(len=120) :: gyrotropic_task

The quantity to compute when gyrotropic=true

May contain one or more of the following valid options (note that each option starts with a '-'):

  • -D0 The Berry-curvature dipole tensor (dimensionless)

    Output file: seedname-gyrotropic-D.dat ( see Sec. output data format for file format description)

  • -Dw The finite-frequency Berry-curvature dipole tensor (dimensionless)

    Output file: seedname-gyrotropic-tildeD.dat ( see Sec. output data format for file format description)

  • -C The ohmic conductivity tensor (Ampere/cm)

    Output file: seedname-gyrotropic-C.dat ( see Sec. output data format for file format description)

  • -K The orbital contribution to the kME tensor (Ampere)

    Output file: seedname-gyrotropic-K_orb.dat ( see Sec. output data format for file format description)

    • -spin : if this task is present, compute also the spin contribution.

      Output file: seedname-gyrotropic-K_spin.dat

  • -NOA The orbital contribution to the NOA (Å)

    Output file: seedname-gyrotropic-NOA_orb.dat ( see Sec. output data format for file format description)

    • -spin : if this task is present, compute also the spin contribution.

      Output file: seedname-gyrotropic-NOA_spin.dat

  • -dos the density of states

    Output file: seedname-gyrotropic-DOS.dat. First column - energy (eV), second column - DOS (\(1/(\mathrm{eV}\times\mathring{A}^3)\))

There is no default value.

output data format

The calculated tensors are written as functions of Fermi level \(E_F\) (first column) and frequency \(\omega\) (second column). If the tensor does not denend on \(\omega\), the second column is filled by zeros. Data is grouped in blocks of the same \(\omega\) separated by two blank lines. In case of natural optical activity the columns 3 to 11 contain the independent components of \(\gamma_{abc}\) (antisymmetric in \(ab\)): \(yzx\), \(zxy\) ,\(xyz\), \(yzy\), \(yzz\), \(zxz\), \(xyy\), \(yzz\) and \(zxx\). For tensors \(C_{ab}\), \(D_{ab}\), \(\widetilde D_{ab}\), \(K_{ab}\) the symmetric and antisymmetric components are writted. Thus, the columns 3 to 11 are marked as \(xx\), \(yy\), \(zz\), \(xy\), \(xz\), \(yz\), \(x\), \(y\), \(z\), wich correspond ,e.g., for \(D_{ab}\) to \(D_{xx}\), \(D_{yy}\), \(D_{zz}\), \((D_{xy}+D_{yx})/2\), \((D_{xz}+D_{zx})/2\), \((D_{yz}+D_{zy})/2\), \((D_{yz}-D_{zy})/2\), \((D_{zx}-D_{xz})/2\), \((D_{xy}-D_{yx})/2\)

integer :: gyrotropic_kmesh(:)

Overrides the kmesh global variable (see Sec. Global variables).

real(kind=dp) :: gyrotropic_kmesh_spacing

Overrides the kmesh_spacing global variable (see Sec. Global variables).

real(kind=dp) :: gyrotropic_freq_min

Lower limit of the frequency range for computing the optical activity.

Units are eV. The default value 0.0.

real(kind=dp) :: gyrotropic_freq_max

Upper limit of the frequency range for computing the optical activity. Units are eV.

If an inner energy window was specified, the default value is dis_froz_max-fermi_energy+0.6667. Otherwise it is the difference between the maximum and the minimum energy eigenvalue stored in seedname.eig, plus 0.6667.

real(kind=dp) :: gyrotropic_freq_step

Difference between consecutive values of the optical frequency between gyrotropic_freq_min and gyrotropic_freq_max.

Units are eV. The default value is 0.01.

real(kind=dp) :: gyrotropic_eigval_max

Maximum energy eigenvalue of the eigenstates to be included in the evaluation of the Natural optical activity. Units are eV.

If an inner energy window was specified, the default value is the upper bound of the inner energy window plus 0.6667. Otherwise it is the maximum energy eigenvalue stored in seedname.eig plus 0.6667.

logical :: gyrotropic_smr_fixed_en_width

Overrides the smr_fixed_en_width global variable (see Sec. Global variables).

character(len=120) :: gyrotropic_smr_type

Overrides the smr_type global variable (see Sec. Global variables).

character(len=120) :: gyrotropic_degen_thresh

The threshould to eliminate degenerate bands from the calculation in order to avoid divergences.

Units are eV. The dfault value is 0.

character(len=120) :: gyrotropic_box_center

- three real numbers. Optionally the integration may be restricted to a parallelogram, centered at gyrotropic_box_center and defined by vectors gyrotropic_box_b{1,2,3}

In reduced coordinates. Default value is 0.5 0.5 0.5

character(len=120) :: gyrotropic_box_b1

- three real numbers. In reduced coordinates. Default value is 1.0 0.0 0.0

character(len=120) :: gyrotropic_box_b2

- three real numbers. In reduced coordinates. Default value is 0.0 1.0 0.0

character(len=120) :: gyrotropic_box_b3

- three real numbers. In reduced coordinates. Default value is 0.0 0.0 1.0

BoltzWann

logical :: boltzwann

Determines whether to enter the  routines.

The default value is false.

integer :: boltz_kmesh(:)

It determines the interpolation \(k\) mesh used to calculate the TDF (from which the transport coefficient are calculated). If boltz_calc_also_dos is true, the same \(k\) mesh is used also for the DOS. Overrides the kmesh global variable (see Sec. Global variables).

real(kind=dp) :: boltz_kmesh_spacing

Overrides the kmesh_spacing global variable (see Sec. Global variables).

character(len=4) :: boltz_2d_dir

For two-dimensional systems, the direction along which the system is non-periodic. It can assume the following values: x for a 2D system on the \(yz\) plane, y for a 2D system on the \(xz\) plane, z for a 2D system on the \(xy\) plane, or no for a 3D system with periodicity along all threee directions.

This value is used when calculating the Seebeck coefficient, where the electrical conductivity tensor needs to be inverted. If the value is different from zero, only the relevant \(2\times 2\) sub-block of the electrical conductivity is inverted.

The default value is no.

real(kind=dp) :: boltz_relax_time

The relaxation time to be used for the calculation of the TDF and the transport coefficients.

The units are fs. The default value is 10 fs.

real(kind=dp) :: boltz_mu_min

Minimum value for the chemical potential \(\mu\) for which we want to calculate the transport coefficients.

The units are eV. No default value.

real(kind=dp) :: boltz_mu_max

Maximum value for the chemical potential \(\mu\) for which we want to calculate the transport coefficients.

The units are eV. No default value.

real(kind=dp) :: boltz_mu_step

Energy step for the grid of chemical potentials \(\mu\) for which we want to calculate the transport coefficients.

The units are eV. No default value.

real(kind=dp) :: boltz_temp_min

Minimum value for the temperature \(T\) for which we want to calculate the transport coefficients.

The units are K. No default value.

real(kind=dp) :: boltz_temp_max

Maximum value for the temperature \(T\) for which we want to calculate the transport coefficients.

The units are K. No default value.

real(kind=dp) :: boltz_temp_step

Energy step for the grid of temperatures \(T\) for which we want to calculate the transport coefficients.

The units are K. No default value.

real(kind=dp) :: boltz_tdf_energy_step

Energy step for the grid of energies for the TDF.

The units are eV. The default value is 0.001 eV.

character(len=120) :: boltz_tdf_smr_type

The type of smearing function to be used for the TDF. The available strings are the same of the global smr_type input flag.

The default value is the one given via the smr_type input flag (if defined).

real(kind=dp) :: boltz_tdf_smr_fixed_en_width

Energy width for the smearing function. Note that for the TDF, a standard (non-adaptive) smearing scheme is used.

The units are eV. The default value is 0 eV. Note that if the width is smaller than twice the energy step boltz_tdf_energy_step, the TDF will be unsmeared (thus the default is to have an unsmeared TDF).

logical :: boltz_calc_also_dos

Whether to calculate also the DOS while calculating the TDF.

If one needs also the DOS, it is faster to calculate the DOS using this flag instead of using independently the routines of the dos module, since in this way the interpolation on the \(k\) points will be performed only once.

The default value is false.

real(kind=dp) :: boltz_dos_energy_min

The minimum value for the energy grid for the calculation of the DOS.

The units are eV. The default value is minval(eigval)-0.6667, where minval(eigval) i s the minimum eigenvalue returned by the ab-initio code on the ab-initio \(q\) me sh.

real(kind=dp) :: boltz_dos_energy_max

The maximum value for the energy grid for the calculation of the DOS.

The units are eV. The default value is maxval(eigval)+0.6667, where maxval(eigval) i s the maximum eigenvalue returned by the ab-initio code on the ab-initio \(q\) me sh.

real(kind=dp) :: boltz_dos_energy_step

Energy step for the grid of energies for the DOS.

The units are eV. The default value is 0.001 eV.

character(len=120) :: boltz_dos_smr_type

Overrides the smr_type global variable (see Sec. Global variables).

logical :: boltz_dos_adpt_smr

Overrides the adpt_smr global variable (see Sec. Global variables).

real(kind=dp) :: boltz_dos_adpt_smr_fac

Overrides the adpt_smr_fac global variable (see Sec. Global variables).

real(kind=dp) :: boltz_dos_adpt_smr_max

Overrides the adpt_smr_max global variable (see Sec. Global variables).

logical :: boltz_dos_smr_fixed_en_width

Overrides the smr_fixed_en_width global variable (see Sec. Global variables).

logical :: boltz_bandshift

Shift all conduction bands by a given amount (defined by boltz_bandshift_energyshift).

Note

this flag slightly differs from the global scissors_shift flag: with boltz_bandshift, an exact rigid shift is applied after interpolation; scissors_shift applies instead the shift before interpolation. As a consequence, results may slightly differ (and this is why we provide both possibilities). Note also that with scissors_shift you have to provide the number of valence bands num_valence_bands, while with boltz_bandshift you should provide the first band to shift boltz_bandshift_firstband = num_valence_bands\(+1\).

The default value is false.

integer :: boltz_bandshift_firstband

Index of the first conduction band to shift.

That means that all bands with index \(i\ge {\tt boltz\_bandshift\_firstband}\) will be shifted by boltz_bandshift_energyshift, if boltz_bandshift is true.

The units are eV. No default value; if boltz_bandshift is true, this flag must be provided.

real(kind=dp) :: boltz_bandshift_energyshift

Energy shift of the conduction bands.

The units are eV. No default value; if boltz_bandshift is true, this flag must be provided.

Generic Band Interpolation

logical :: geninterp

Determines whether to enter the Generic Band Interpolation routines.

The default value is false.

logical :: geninterp_alsofirstder

Whether to calculate also the first derivatives of the bands at the given \(k\) points.

The default value is false.

logical :: geninterp_single_file

Whether to write a single seedname_geninterp.dat file (all I/O is done by the root node); or instead multiple files (one for each node) with names seedname_geninterp_NNNNN.dat, where NNNNN is the node number. See also the discussion in Sec. seedname_geninterp.dat or seedname_geninterp_NNNNN.dat.

The default value is true.

  1. Jae-Mo Lihm. Comment on “ab initio calculation of the shift photocurrent by wannier interpolation”. Phys. Rev. B, 103:247101, Jun 2021. URL: https://link.aps.org/doi/10.1103/PhysRevB.103.247101, doi:10.1103/PhysRevB.103.247101. ↩↩↩

  2. X. Wang, J. R. Yates, I. Souza, and D. Vanderbilt. Ab initio calculation of the anomalous hall conductivity by wannier interpolation. Phys. Rev. B, 74:195118, 2006. ↩

  3. T. Yusufaly, D. Vanderbilt, and S. Coh. Tight-Binding Formalism in the Context of the PythTB Package. \url http://physics.rutgers.edu/pythtb/formalism.html. ↩

  4. Julen Ibañez-Azpiroz, Stepan S. Tsirkin, and Ivo Souza. Ab initio calculation of the shift photocurrent by wannier interpolation. Phys. Rev. B, 97:245143, Jun 2018. URL: https://link.aps.org/doi/10.1103/PhysRevB.97.245143, doi:10.1103/PhysRevB.97.245143. ↩