I am using the Chebyshev KPM implementation in pybinding to study electronic transport in a disordered tight-binding model. While analyzing the conductivity and mobility, I encountered a few behaviors that I would like to ask about.
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Mobility behavior at low carrier density
At low carrier densities (near the band edge), I observe that for some parameter ranges the mobility at larger disorder strength can be higher than at smaller disorder.
When examined in more detail, the mobility as a function of disorder (especially between intermediate values, e.g. W ≈ 1–2) shows oscillatory or non-monotonic behavior (high–low–high–low), particularly for small broadening.
I have verified that the carrier density is fixed accurately and that the Fermi level varies smoothly with disorder.
I would like to ask whether this behavior is expected from KPM conductivity calculations in this regime, and what strategies you would recommend to reduce or stabilize such fluctuations (e.g. choice of broadening, averaging schemes, or convergence parameters).
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Negative conductivity values
In some cases, especially for certain broadening values, the calculated conductivity becomes slightly negative.
Since negative longitudinal conductivity is unphysical, I am wondering whether this originates from numerical artifacts of the KPM approximation (e.g. finite moments, kernel effects, or insufficient averaging), and whether there are known guidelines to avoid this issue.
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Physical meaning of broadening in the Lorentz kernel
In the documentation and examples, the Lorentz kernel is often motivated by its connection to Green’s functions.
I would like to clarify whether the broadening parameter in the Lorentz kernel should be interpreted as having a physical meaning (e.g. related to lifetime or scattering rate), or whether it should be regarded purely as a numerical resolution parameter in KPM transport calculations.
Thank you very much for developing and maintaining pybinding. It has been extremely helpful for my research, and I would appreciate any guidance or clarification on these points.
I am using the Chebyshev KPM implementation in pybinding to study electronic transport in a disordered tight-binding model. While analyzing the conductivity and mobility, I encountered a few behaviors that I would like to ask about.
Mobility behavior at low carrier density
At low carrier densities (near the band edge), I observe that for some parameter ranges the mobility at larger disorder strength can be higher than at smaller disorder.
When examined in more detail, the mobility as a function of disorder (especially between intermediate values, e.g. W ≈ 1–2) shows oscillatory or non-monotonic behavior (high–low–high–low), particularly for small broadening.
I have verified that the carrier density is fixed accurately and that the Fermi level varies smoothly with disorder.
I would like to ask whether this behavior is expected from KPM conductivity calculations in this regime, and what strategies you would recommend to reduce or stabilize such fluctuations (e.g. choice of broadening, averaging schemes, or convergence parameters).
Negative conductivity values
In some cases, especially for certain broadening values, the calculated conductivity becomes slightly negative.
Since negative longitudinal conductivity is unphysical, I am wondering whether this originates from numerical artifacts of the KPM approximation (e.g. finite moments, kernel effects, or insufficient averaging), and whether there are known guidelines to avoid this issue.
Physical meaning of broadening in the Lorentz kernel
In the documentation and examples, the Lorentz kernel is often motivated by its connection to Green’s functions.
I would like to clarify whether the broadening parameter in the Lorentz kernel should be interpreted as having a physical meaning (e.g. related to lifetime or scattering rate), or whether it should be regarded purely as a numerical resolution parameter in KPM transport calculations.
Thank you very much for developing and maintaining pybinding. It has been extremely helpful for my research, and I would appreciate any guidance or clarification on these points.