Uniaxial negative thermal expansion and band renormalization in monolayer Td−MoTe2 at low temperature

Abstract

The temperature-induced structure variation and its effect on physical properties is pivotal in material preparation for devices application. Motivated by surface scanning tunnel microscope (STM) measurement of ${T}_{d}\ensuremath{-}{\mathrm{MoTe}}_{2}$ single crystal at low temperature, temperature dependent electronic structure, lattice dynamics, and topological properties are explored to understand the microscopic origin of the observed anisotropic negative thermal expansion and abnormal STM images below 70 K. Remarkably, we find that the nonequivalent Te atoms in ${T}_{d}\ensuremath{-}{\mathrm{MoTe}}_{2}$ have qualitatively different contributions to both phonon spectra and electronic structures. The in-plane longitudinal acoustic mode and the ${\mathrm{Te}}_{(2)}$ atoms are found to play an important role in uniaxial negative thermal expansion and the temperature dependent electronic phase transition, respectively. Interestingly, under the scalar relativistic approximation, a band renormalization occurs, accompanied by a Dirac phase transition from type II to type I, upon cooling below 70 K. Introducing spin-orbit coupling induces a temperature dependent semimetal--semiconductor transition. Our results explain the experimental phenomena very well: abnormal surface STM image below 70 K does not originate from the displacement of the Te atoms but the band renormalization owing to strong electron-lattice coupling.