Abstract
Our density functional theory calculations show that tiny-gap semiconductor SiGe monolayer is a quantum valley Hall insulator with a spontaneous electric polarization and, under a small biaxial strain, undergoes a topological phase transition between the states with opposite valley Chern numbers. The topological phase transition entails abrupt inversion of the in-plane electric polarization corresponding to inversion of the sublattice pseudospin polarization, while the out-of-plane electric polarization shows a linear response to the biaxial strain as well as to the perpendicular electric field regardless of the phase transition. Thus, the quantum valley Hall state entails in-plane ferroelectricity corresponding to a sublattice pseudospin ferromagnetism.
Highlights
Our density functional theory calculations show that tiny-gap semiconductor SiGe monolayer is a quantum valley Hall insulator with a spontaneous electric polarization and, under a small biaxial strain, undergoes a topological phase transition between the states with opposite valley Chern numbers
Under a small biaxial strain that can be induced by a lattice constant mismatch with the substrate, monatomic 2D group IV materials such as graphene, silicene and germanene show no significant changes in the band structure and the linear energy dispersion near the K point remains almost intact, because the biaxial strain maintains all crystal symmetries.[14, 15]
Uniaxial strain further destroys the symmetry and some conflicting results were reported for the band gap of the uniaxially strained monatomic 2D materials of group IV elements.[16,17,18,19]
Summary
We can see that the band gap closes at the critical strain ac = 0.38% corresponding to a = 0.396 nm, indicating a quantum phase transition. Ezc linearly decreases with increasing lattice constant and is nearly zero at the critical strain, indicating that an intrinsic potential difference between the two sublattices corresponds to the quantum valley Hall states and the strain-induced topological phase transition. We found that the SiGe monolayer is a quantum valley Hall insulator with spontaneous electric polarization, undergoing a topological phase transition under a small biaxial strain. The quantum valley Hall state described by a two-dimensional Dirac Hamiltonian with mass gap entails in-plane ferroelectricity corresponding to a sublattice pseudospin ferromagnetism
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