Temperature dependence of electronic conductivity from ab initio thermal simulation

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.

💡 Research Summary

This paper introduces a computationally inexpensive method for estimating the temperature dependence of electronic conductivity by extending the classic Hindley‑Mott approximation (σ ∝ N²(E_F)) to incorporate thermal fluctuations obtained from ab‑initio molecular dynamics (AIMD). The authors call the approach the thermally‑averaged Hindley‑Mott (TAHM) method. In practice, they run AIMD simulations at a series of fixed temperatures, extract the Kohn‑Sham eigenvalues at each Born‑Oppenheimer snapshot, and construct a Gaussian‑broadened density of states D(E, t). The quantity N²(E_F, t) is defined as the square of the DOS integrated over a narrow window around the Fermi level, using a Gaussian width h that is tuned to the electronic character of each material (metallic, semiconducting, or amorphous). By averaging N² over a sufficiently long, equilibrated trajectory (⟨N²⟩_t), they obtain a temperature‑dependent scalar that is proportional to the DC conductivity. A single experimental data point is used to calibrate the proportionality constant η; thereafter σ(T) = η ⟨N²⟩_t for any temperature.

Five representative systems are examined: crystalline aluminum (c‑Al), aluminum with a grain boundary (Al‑GB), a four‑layer AB‑stacked “worm‑like” graphene‑aluminum composite (Al‑Gr), amorphous silicon (a‑Si), and amorphous germanium‑antimony‑telluride (a‑GST). All simulations are performed with VASP using PAW‑PBE potentials; Γ‑point sampling is employed, and trajectory lengths range from 2.5 ps (c‑Al) to up to 10 ps (a‑GST) with time steps between 0.5 fs and 2 fs. The authors verify convergence of ⟨N²⟩_t by monitoring the running average and require less than a 5 % change over successive steps.

For the metallic systems (c‑Al and Al‑GB) the averaged N² decreases with temperature, reproducing the Bloch‑Grüneisen (BG) trend: σ drops roughly 10 % between 100 K and 700 K, in line with experimental resistivity data and with more rigorous Kubo‑Greenwood (KGF) calculations. The grain‑boundary sample shows a slightly larger resistivity increase, reflecting additional scattering at the interface, yet the overall temperature dependence remains consistent with the BG model.

In contrast, the Al‑Gr composite exhibits a monotonic increase of ⟨N²⟩_t with temperature, leading to a linear rise in conductivity (slope ≈ 1.49 × 10⁴ S m⁻¹ K⁻¹). This semiconducting‑like response is attributed to the undulating multilayer graphene morphology, which creates thermally activated interfacial conduction channels that become more populated as temperature rises. The result differs from prior simulations of flat, few‑layer Al‑Gr interfaces that displayed metallic behavior, highlighting the importance of realistic microstructural features.

Amorphous silicon shows a pronounced temperature‑induced widening of the electronic gap; consequently N²(E_F) diminishes with temperature, and the predicted conductivity decreases, matching both KGF benchmarks and experimental measurements. Amorphous GST displays a milder trend, with modest changes in N² and a relatively flat conductivity curve, consistent with its mixed metallic‑amorphous character.

The authors discuss the methodological assumptions: (1) an adiabatic Born‑Oppenheimer treatment that neglects explicit electron‑phonon coupling, (2) classical nuclear dynamics that ignore phonon quantization, (3) the use of Kohn‑Sham eigenvalues as proxies for true quasiparticle energies, (4) omission of the matrix element D(E_F) in the conductivity expression, and (5) applicability primarily to homogeneous or weakly anisotropic systems. Despite these approximations, the TAHM method captures the correct qualitative trends across a diverse set of materials while requiring orders of magnitude less computational effort than full KGF or Boltzmann‑transport calculations.

In summary, the thermally‑averaged Hindley‑Mott approach provides a simple, scalable route to link time‑dependent electronic structure from AIMD to temperature‑dependent transport properties. By leveraging the readily available N²(E_F) from standard DFT‑MD workflows, researchers can quickly screen complex, disordered, or nanostructured materials for conductivity trends, calibrate against a single experimental datum, and obtain quantitative predictions. Future extensions could incorporate quantum nuclear effects, more accurate treatment of the matrix element, or tensorial conductivity extraction, further broadening the method’s applicability to emerging functional materials.