First-principles calculations on the intrinsic resistivity of borophene: anisotropy and temperature dependence

Abstract

The intrinsic resistivity arising from electron–phonon scattering is an important property of metals, especially at room temperature. Borophene, a kind of successfully synthesized two-dimensional (2D) boron sheet, exhibits metallic electronic transport behavior. In this paper, we report first-principles calculations on the intrinsic resistivity of two borophene allotropes, called β₁₂ and χ₃. At first, we find that the intrinsic resistivity of the two structures shows non-trivial anisotropy which amounts to at least 28%. In addition, our calculations indicate that the intrinsic resistivity of β₁₂ and χ₃ are both proportional to temperature in the high-temperature region (>160 K). However, in the low-temperature region (<70 K), the T⁴-law of the intrinsic resistivity predicted by the Bloch–Grüneisen theory for 2D metals holds true for β₁₂ but breaks down for χ₃. Based on a detailed analysis, we find that the two borophenes have complicated Fermi surfaces with multiple branches. Optical phonon modes in β₁₂ and the Umklapp process in χ₃ play non-trivial roles in the low-temperature region. All of these factors influencing the intrinsic resistivity of borophene are beyond the simplifications adopted in the Bloch–Grüneisen theory. Therefore, we conclude that the Bloch–Grüneisen theory is inapplicable to explain the temperature dependence of the intrinsic resistivity of β₁₂ and χ₃, two experimentally available 2D metals.