Fig. 3: Electronic states at the Fermi level are localized in regions with lower amounts of Peierls-like distortions.
From: Effect of Peierls-like distortions on transport in amorphous phase change devices
a Density of states (gray line) and inverse participation ratio of each state (red dots) at a temperature of approximately 150 K. The insets at the top visualize the spatial distribution of selected electronic states around the Fermi level. They are ordered by their value of the inverse participation ratio (IPR) from high values (left) to low values (right). Light and dark colors indicate high and low wavefunction amplitudes of a specific state, respectively. We observe localization in regions with low amounts of distortions. Compared to the inset at the bottom left, which shows again the distribution of the ratio r2/r1 of long to short bonds at low temperatures with low (light colors) and high (dark colors) amounts of distortion (Fig. 1c). In the dark, distorted region at the front center, we observe no wavefunction amplitude for any of the localized states shown at the top, but some amplitude for the delocalized state (top right). The rightmost inset at the top shows a delocalized state for comparison, where the distribution of amplitudes is homogeneous. Isosurface plots of the same states are shown in Supplementary Fig. 15. b Ratio of long to short bonds (r2/r1) averaged for each electronic state in dependence of energy (details in the Methods section). The results are shown for four different temperatures. Horizontal lines indicate the average value of r2/r1 at the respective temperature. The localized states observed in (a) show lower amounts of Peierls-like distortions than the average. This is true in particular for states around the Fermi level. As also described in the Methods section, additional reference calculations of the density of states (DOS) and IPR using the more accurate TB09 exchange-correlation functional are shown in Supplementary Fig. 2.
