Strain driven topological phase transitions in atomically thin films of group IV and V elements in the honeycomb structures

Abstract

We have investigated topological electronic properties of freestanding bilayers of group IV (C, Si, Ge, Sn, and, Pb) and V (As, Sb, and, Bi) elements of the periodic table in the buckled and planar honeycomb structures under isotropic strain using first-principles calculations. Our focus is on mapping strain driven phase diagrams and identifying topological phase transitions therein as a pathway for guiding search for suitable substrates to grow two-dimensional (2D) topological insulators (TIs) films. Bilayers of group IV elements, excepting Pb, generally transform from trivial metal → topological metal → TI → topological metal → trivial metal phase with increasing strain from negative (compressive) to positive (tensile) values. Similarly, among the group V elements, As and Sb bilayers transform from trivial metal → trivial insulator → TI phase, while Bi transforms from a topological metal to TI phase. The band gap of 0.5 eV in the TI phase of Bi is the largest we found among all bilayers studied, with the band gap increasing further under tensile strain. Differences in the topological Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. characteristics of bilayers of group V elements reflect associated differences in the strength of the spin-orbit coupling (SOC). We show, in particular, that the topological band structure of Sb bilayer becomes similar to that of a Bi bilayer when the strength of the SOC in Sb is artificially enhanced by a factor of 4. This study provides the first report that As can be a 2D TI under tensile strain. Notably, we found the existence of TI phases in all elemental bilayers we studied, except Pb.

Topological phases in two-dimensional materials: a review

“…In addition, although the low-buckled structure naturally breaks the mirror symmetry about the plane leading to an intrinsic Rashba-type spin-orbit coupling, this is not detrimental to the 2D Z 2 TIs since the intrinsic Rashba spin-orbit coupling is momentum-dependent and vanishes at the Dirac K/K ′ points [94]. Another striking property of the low-buckled structure is the external tunability when an electric field [95][96][97][98] or strain [99,100] is applied.…”

The nontrivial electronic structure of Bi/Sb honeycombs on SiC(0001)

“…Recent theoretical work has predicted that a number of organic compounds [9][10][11] as well as many atomically thin films of elements of groups IV and V as well III-V compounds assume a 2D-TI phase in the honeycomb structure. Beyond carbon [12], the predicted 2D-TIs include films of silicon, germanium [13], tin [14], and bismuth [15], and InBi, GaBi, and TlBi [16] alloys at their equilibrium honeycomb structures, while arsenic [17], antimony [18], BBi, and AlBi [16] transition to a 2D TI phase under strain. Several of the newly predicted 2D-TIs exhibit band gaps large enough to exceed thermal excitation energy at room temperature [15,16,[18][19][20].…”

Quantum spin hall insulators in strain-modified arsenene

“…19 Ma et al also successfully predicted the large-bulk-gap topological phases in the methyl-functionalized Bi, Sb and Pb thin bilayer films. 34 Furthermore, Winterfeld et al demonstrated that HgSe can be tuned into a 3D topological insulator via proper strain engineering. For example, by applying a perpendicular electric field on few-layer black phosphorous, a normal-totopological phase transition in this multilayer stack of phosphorene can be achieved, in which the topological band inversion entirely originates from the electric-field-induced Stark effect, whereas the effect of SOC is to open a band gap at the Dirac-like band crossing, rendering the system a 2D TI.…”