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 \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).

Published in Nano Letters

References in corpus (10)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• The Renaissance of Black Phosphorus
• Broadband Linear-Dichroic Photodetector in a Black Phosphorus Vertical p-n Junction
• Enhanced Thermoelectric Efficiency via Orthogonal Electrical and Thermal Conductances in Phosphorene
• Giant Anharmonic Phonon Scattering in PbTe
• Quasiparticle band structure and tight-binding model for single- and bilayer black phosphorus
• Hinge-like structure induced unusual properties of black phosphorus and new strategies to improve the thermoelectric performance
• Observation of Low-frequency Interlayer Breathing Modes in Few-layer Black Phosphorus
• The temperature dependence of electronic eigenenergies in the adiabatic harmonic approximation
• Edge phonons in black phosphorus

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