Anomalous Temperature Dependence of the Band Gap in Black Phosphorus

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 ab-initio calculations, we present an explanation

Unraveling the Peculiarities in the Temperature-Dependent Structural Evolution of Black Phosphorus

“…In a recent study, Wang et al [26] suggested that anisotropy in the thermal transport properties of bulk BP might be of particular interest in the fabrication of thermoelectric/optoelectronic devices. Recently, the temperature dependence of the band-gap of BP studied by ab initio calculations shed some light on the anomalous band-gap opening with the increasing volume [27]. The calculated temperature dependence of the lattice parameters along the armchair, zigzag and stacking directions had a good correspondence with the data shown in Figure 5a.…”

Evolution of electronic structure of few-layer phosphorene from angle-resolved photoemission spectroscopy of black phosphorous

“…7). This anomalous temperature dependence has been recently explained considering the coupling of the electrons with low-frequency transverse optical modes [50]. We underline that this same temperature dependence of the gap must also be taken into account when performing temperature-dependent transport measurements to extract the value of the gap [25].…”

“…The remaining differences are ascribed to a combination of several effects such as intrinsic doping by impurities, weak interaction with lithium ions, the total energy resolution of the experiment (20 meV), and the fact that the transport gap was extracted by temperature dependent measurements. However, as was shown recently by Villegas and collaborators [50], the band gap has a strong and anomalous temperature dependence which could affect the transport results.…”

Giant exciton-phonon coupling and zero-point renormalization in hexagonal monolayer boron nitride

“…The lattice anharmonic contribution causes the lattice thermal expansion, constraining the band-gap to reduce further. However, we do not intend to compute this using a standard quasi-harmonic approximation approach [47], as it is well-known that unless there is no portion of the real part of the Eliashberg function difference taken between the lowest conduction and the top valence band (i.e, ℜ g 2 F C1 (ω) − g 2 F V1 (ω) ) that acquires a positive value, E g (T ) will always be much larger than E LT E g [18,48,49]. This is also an indirect proof to predict whether the gap decreases with T or not.…”