Nontrivial topology and topological phase transition in two-dimensional monolayer Tl

Abstract

Topological insulating material with dissipationless edge states is a rising star in spintronics. While most two-dimensional (2D) topological insulators belong to group-IV or -V elements in a honeycomb lattice, herein, we propose a new topological phase in the 2D hexagonal group-III crystal, h-Tl, based on a tight-binding model and density-functional theory calculation. Analysis of band dispersion reveals a Dirac nodal-ring near the Fermi level, which is attributed to px,y/pz band crossing. Upon inclusion of spin-orbit coupling (SOC), h-Tl turns into a quantum spin Hall insulator under 21% biaxial strain, confirmed by integrating spin Berry curvature in the Brillouin zone and spin-polarized edge states. A prominent feature of its electronic properties is that the effect of SOC plays two essential roles of both topological gap opening and band inversion between px,y/pz orbitals, which is the first observed phenomenon in 2D materials. This study extends the scope of 2D elemental topological insulators and presents a platform to design new 2D topotronics materials.

Large-band-gap non-Dirac quantum spin Hall states and strong Rashba effect in functionalized thallene films

“…The positions of the atoms in the unit cells for the two monolayers are given in the Supplementary Material as Table SI . Compared to the Tl–Tl bond length ( ) in pristine thallene (3.01 Å 18 and 3.03 Å 19 ), the Tl-Tl bond lengths in Tl 2 H (3.04 Å) and Tl 2 H 2 (3.05 Å) are increased slightly by the hydrogenation. The trend is reasonable because the repulsive force between the H–H and Tl–H ions appears in the monolayer with H adsorbed.…”

“…Different from other heavy element monolayers, the thallene monolayer is a fully flat 2D honeycomb lattice without buckling 18 , 19 . In other words, the Tl atoms in thallene are aligned in the same plane, with two Tl atoms in each unit cell.…”

“…Besides the groups IVA Pb and VA Bi, group IIIA Tl can also be regarded as a heavy element, whose graphene-like monolayer structure is called thallene 18 , 19 . The pristine 2D honeycomb-like thallene is a topological trivial semiconductor.…”

“…The pristine 2D honeycomb-like thallene is a topological trivial semiconductor. The phase transition from a semiconductor to a QSH insulator can be achieved under the application of large biaxial strain and its nontrivial topology comes from a band inversion between p x/y and p z orbitals induced by SOC 18 . The thallene monolayer has been successfully prepared in experiments by cooling the 2/3 monolayer of mobile Tl atoms on a single-layer NiSi 2 atop a Si(111) substrate below ~ 150 K 19 .…”

Electrical conductivity of statically perturbed topological crystalline insulators

“…The topological property originates from the coexistence of bulk gapped bands and surface/edge metallic gapless bands for twodimensional/three-dimensional materials, which is so-called non-trivial band structures [1,[3][4][5]. Following this discovery, researchers started exploring the novel quantum materials with such features and band structures [6][7][8][9][10][11][12][13][14]. One of these materials is topological insulator (TI) in which the surface/edge gapless states are protected by particle-hole symmetry, chiral symmetry and Z 2 time-reversal symmetry [6-9, 15, 16].…”