Temperature dependence of electronic conductivity from ab initio thermal simulation

TL;DR

This work addresses the challenge of predicting how electronic conductivity changes with temperature in metals, semiconductors, and disordered materials. It introduces the thermally averaged Hindley-Mott (TAHM) method, which estimates $\sigma(T)$ by averaging the squared near-$E_F$ electronic density of states, $N^2(E_F)$, along ab initio MD trajectories and calibrating with a single experimental data point via $\sigma_{N^2}(T)=\eta\langle N^2(T)\rangle_t$. Applied to five systems—crystalline Al, Al with a grain boundary, Al–Gr graphene composite, amorphous Si, and amorphous GST—the method reproduces Bloch–Grüneisen trends for metals, semiconducting-like increases for interfaces and amorphous materials, and captures microstructure-induced conduction pathways, all while remaining computationally efficient. The results demonstrate TA HM as a simple, transferable descriptor for temperature-dependent electronic transport, offering a practical complement to more rigorous Kubo–Greenwood calculations for rapid screening of complex materials.

Abstract

We present a temperature-dependent extension of the approximate electronic conductivity formula of Hindley and Mott that leverages time-averaged fluctuations of the electronic density of states obtained from ab initio molecular dynamics. By thermally averaging the square of the density of states near the Fermi level, we obtain an estimate of the temperature dependence of the conductivity. This approach termed the thermally-averaged Hindley-Mott (TAHM) method was applied to five representative systems: crystalline aluminum (c-Al), aluminum with a grain boundary (AlGB), a four-layer graphene-aluminum composite (Al-Gr), amorphous silicon (a-Si) and amorphous germanium-antimony-telluride (a-GST). The method reproduces the expected Bloch-Gruneisen decrease in conductivity for c-Al and AlGB. Generally, the reduction (increase) in conductivity for metallic (semiconducting) materials are reproduced. It captures microstructure-induced, thermally activated conduction in multilayer Al-Gr, a-Si and a-GST. Overall, the approach provides a computationally efficient link between time-dependent electronic structure and temperature-dependent transport, offering a simple and approximate tool for exploring electronic conductivity trends in complex and disordered materials.

Figures (7)

• Figure 1: Structural representation of (a) aluminum with grain boundary (AB stacking fault represented by the red dashed line), (b) aluminum-graphene composite formed with the worm-like 4-layer (AB-stacked) graphene (gray), (c) amorphous silicon, and (d) amorphous germanium (teal)-antimony (purple)-telluride (brown) .
• Figure 2: The electronic density of states near the Fermi level obtained from the MD simulations at different instantaneous Born-Oppenheimer snapshots, showing for (a) Crystalline aluminum, (b) Aluminum with a grain boundary, (c) Aluminum-graphene composite, (d) amorphous silicon, and relaxed (e) amorphous germanium–antimony–telluride.
• Figure 3: Analysis for crystalline aluminum (c-Al) and aluminum with a grain boundary (Al$_\text{GB}$) . (a) Instantaneous $N_t^2$ from the EDOS at different temperatures and (b) the convergence of the running time-average of $N_t^2$ for c-Al (similar plots for Al$_\text{GB}$ are provided in Figure S3a and b). Converged $\langle N^2 \rangle_t$ versus temperature with quadratic fit for (c) c-Al and (d) Al$_\text{GB}$. (e) Experimental resistivity chowdhury2013experimental compared with values from $N^2(E_F)$ for c-Al and Al$_\text{GB}$; Bloch–Grüneisen (BG) predictions are included. (f) Temperature-dependent resistivity for c-Al and Al$_\text{GB}$; from $\langle N^2 \rangle_t$, with error bars from MD time averaging.
• Figure 4: Analysis for aluminum-graphene composite structure.The running time-average of $N_t^2$ illustrating convergence.(b) Temperature dependent $\langle N^2 \rangle_t$ conductivity extrapolated from experimental conductivity at 300 K from Reference Smyrak2025.
• Figure 5: Spatial projection of $N^2$ electronic activity in the Al-graphene composite. (a) 2D colormap of normalized $N^2$ on a (100) plane slice at $x \approx 6.0$ Å. (b) Radial ($\rho$) profiles of $N^2$ extracted along the colored traces in (a) at the indicated projection angles $\theta$.