Anomalous temperature dependence of the band-gap in Black Phosphorus

TL;DR

This paper explains the unusual increase in black phosphorus's band-gap with temperature by analyzing atomic vibrations and thermal expansion effects through ab-initio calculations.

Contribution

It provides a detailed ab-initio explanation for the anomalous temperature dependence of BP's band-gap, linking atomic vibrations and thermal expansion.

Findings

Band-gap increases with temperature in BP.

Atomic vibrations drive the gap opening.

Thermal expansion contributes to the anomaly.

Abstract

Black Phosphorus (BP) has gained renewed attention due to its singular anisotropic electronic and optical properties that might be exploited for a wide range of technological applications. In this respect, the thermal properties are particularly important both to predict its room temperature operation and to determine its thermoelectric potential. From this point of view, one of the most spectacular and poorly understood phenomena is, indeed, the BP temperature-induced band-gap opening: when temperature is increased the fundamental band-gap increases instead of decreasing. This anomalous thermal dependence has also been observed, recently, in its monolayer counterpart. In this work, based on \textit{ab-initio} calculations, we present an explanation for this long known, and yet not fully explained, effect. We show that it arises from a combination of harmonic and lattice thermal expansion contributions, which are, in fact, highly interwined. We clearly narrow down the mechanisms that cause this gap opening by identifying the peculiar atomic vibrations that drive the anomaly. The final picture we give explains both the BP anomalous band-gap opening and the frequency increase with increasing volume (tension effect).