[Wannier] BoltzWann module for thermoelectric study

Fri Jun 27 15:46:20 CEST 2025

Dear Prof. Giovanni Pizzi and Wannier90 community,

Kindly let me explain what I am attempting to do. Using the BoltzWann
module, I want to reproduce the result computed by BoltzTraP code by
varying carrier concentration n (cm-3) at constant temperature T (example
<https://pubs.acs.org/cms/10.1021/cm504244b/asset/images/large/cm-2014-04244b_0004.jpeg>).
However, in the Wannier90 input file, we can only input the chemical
potential μ instead of n (cm-3). So, I need to convert the desired n (cm-3)
into μ, for which I have come up with the below python code. Please excuse
my coding inaccuracies as I am a beginner at it and kindly fix any
mathematical mistakes (possibly in bisection algorithm) and coding errors.
If it's all correct, it fails to give converged μ at higher n (e.g. 10^24
cm-3).  I have also attached DOS output computed using quantum espresso
code for reference.

Code:

import numpy as np
from scipy import constants

# Constants
T = 300  # Temperature in Kelvin
k_B = constants.k / constants.e  # Boltzmann constant in eV/K (≈8.617333e-5)

# --- Convert unit cell volume to cm³ ---
V_cell_au3 = 1805.5096  # Unit cell volume in (a.u.)³
bohr_to_angstrom = 0.52917721
V_cell_A3 = V_cell_au3 * (bohr_to_angstrom ** 3)
V_cell_cm3 = V_cell_A3 * 1e-24

print(f"Unit cell volume = {V_cell_cm3:.4e} cm³")

# Fermi-Dirac function
def fermi_dirac(E, mu, T):
    kT = k_B * T
    x = (E - mu) / kT

    # Handle large values to prevent overflow
    return np.piecewise(x,
                       [x < -100, x > 100],
                       [1.0, 0.0, lambda x: 1/(1 + np.exp(x))])

# Load DOS data
data = np.loadtxt('case_dos.dat')
energy = data[:, 0]  # Energy in eV
dos = data[:, 1]     # DOS in states/eV/unit cell

# Compute carrier concentration using trapezoid rule
def carrier_concentration(mu, energy, dos, T, V_cm3):
    product = dos * fermi_dirac(energy, mu, T)
    n_unit_cell = np.trapezoid(product, energy)
    n_cm3 = n_unit_cell / V_cm3
    return n_cm3

# Bisection algorithm with auto-bound detection
def find_mu(target_n, energy, dos, T, V_cm3, tol=1e-3, max_iter=100):
    # Auto-detect proper bounds
    mu_low, mu_high = -100, 100  # Start with wide range
    n_low = carrier_concentration(mu_low, energy, dos, T, V_cm3)
    n_high = carrier_concentration(mu_high, energy, dos, T, V_cm3)

    # adjust lower bound
    while n_low > target_n:
        mu_low -= 50
        n_low = carrier_concentration(mu_low, energy, dos, T, V_cm3)
        print(f"Expanding lower bound to μ = {mu_low} eV, n = {n_low:.4e}
cm⁻³")

    # adjustupper bound
    while n_high < target_n:
        mu_high += 50
        n_high = carrier_concentration(mu_high, energy, dos, T, V_cm3)
        print(f"Expanding upper bound to μ = {mu_high} eV, n = {n_high:.4e}
cm⁻³")

    print(f"\nStarting bisection with bounds: μ = [{mu_low}, {mu_high}] eV")
    print(f"Initial concentrations: n_low = {n_low:.4e} cm⁻³, n_high =
{n_high:.4e} cm⁻³")

    # Bisection loop
    for i in range(max_iter):
        mu_mid = (mu_low + mu_high) / 2
        n_mid = carrier_concentration(mu_mid, energy, dos, T, V_cm3)

        rel_error = abs(n_mid - target_n) / target_n
        print(f"Iter {i+1}: μ = {mu_mid:.6f} eV, n = {n_mid:.4e} cm⁻³,
error = {rel_error:.2%}")

        if rel_error < tol:
            print("\nConverged!")
            return mu_mid

        if n_mid < target_n:
            mu_low = mu_mid
        else:
            mu_high = mu_mid

    print(f"Warning: Max iterations reached ({max_iter})")
    return mu_mid

if __name__ == "__main__":
    # Target carrier concentration (cm⁻³)
    target_n = 1e18

    # Find chemical potential
    print(f"\nSearching for μ for n = {target_n:.1e} cm⁻³")
    mu_target = find_mu(target_n, energy, dos, T, V_cell_cm3)

    # Final verification
    n_final = carrier_concentration(mu_target, energy, dos, T, V_cell_cm3)
    print(f"\nResult: μ = {mu_target:.6f} eV gives n = {n_final:.4e} cm⁻³")

On Mon, Jun 23, 2025 at 4:02 PM Abhijeet Jaysingrao kale ic39253 <
ic39253 at imail.iitm.ac.in> wrote:

> Dear Prof. Giovanni Pizzi,
>
> Thank you very much for the information. I tried obtaining a Fermi-Dirac
> distribution but did not succeed. Can I get further help regarding how to
> obtain Fermi-Dirac distribution function from Wannier output and then
> finally compute carrier concentration?
>
> Regards,
> Abhijeet.
>
> On Thu, Jun 19, 2025 at 8:26 PM Giovanni Pizzi <giovanni.pizzi at epfl.ch>
> wrote:
>
>> Hi,
>>
>> 1. You should convert the carrier concentration into a chemical potential
>> by integrating the product of the Fermi-Dirac distribution function and of
>> the DOS, and looking for the chemical potential that gives you the expected
>> number of electrons (e.g. with a bisection algorithm).
>>
>> 2. Internally it should work, but indeed the code only prints the upper
>> triangle for sigma, Sigma*S and kappa (electronic contribution) to thermal
>> conductivity. If you want to check if there is a non-symmetric part, you
>> need to adapt the code to print all coordinates.
>> (Note that for the Seebeck coefficient, all 9 components are reported
>> instead).
>>
>> Best,
>> Giovanni Pizzi
>>
>>
>> *Group leader, Materials Software and Data Group, PSI *
>> https://www.psi.ch/en/lms/people/giovanni-pizzi
>>
>>
>>
>>
>> On 18 Jun 2025, at 12:23, Abhijeet Jaysingrao kale ic39253 <
>> ic39253 at imail.iitm.ac.in> wrote:
>>
>> Dear Wannier90 community,
>>
>> I am Abhijeet from IIT Madras (India). I am using the BoltzWann module to
>> compute thermoelectric properties of monolayer systems. I'd be grateful if
>> anyone could suggest me on following questions:
>>
>> 1. How to input carrier concentration range like chemical potential and
>> temperature?
>> 2. Can we use BoltzWann for thermoelectric properties of magnetic
>> materials even though it outputs 6 components of electrical conductivity
>> when it requires all 9?
>>
>> Thanks in advance.
>> Regards,
>> Abhijeet.
>>
>> _______________________________________________
>> Wannier mailing list
>> Wannier at lists.quantum-espresso.org
>> https://lists.quantum-espresso.org/mailman/listinfo/wannier
>>
>>
>>
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