Conductance of quantum spin Hall edge states from first principles: The critical role of magnetic impurities and inter-edge scattering

Abstract

The outstanding transport properties expected at the edge of two-dimensional time-reversal invariant topological insulators have proven to be challenging to realize experimentally, and have so far only been demonstrated in very short devices. In search for an explanation to this puzzling observation, we here report a full first-principles calculation of topologically protected transport at the edge of novel quantum spin Hall insulators -specifically, Bismuth and Antimony halidesbased on the non-equilibrium Green's functions formalism. Our calculations unravel two different scattering mechanisms that may affect two-dimensional topological insulators, namely time-reversal symmetry breaking at vacancy defects and inter-edge scattering mediated by multiple co-operating impurities, possibly non-magnetic. We discuss their drastic consequences for typical non-local transport measurements as well as strategies to mitigate their negative impact. Finally, we provide an instructive comparison of the transport properties of topologically protected edge states to those of the trivial edge states in MoS2 ribbons. Although we focus on a few specific cases (in terms of materials and defect types) our results should be representative for the general case and thus have significance beyond the systems studied here.

Dual Topological Insulator Device with Disorder Robustness

“…There is no net magnetic moment resulting from these defects, preserving TRS. The presence of defects on TIs can cause interference on edge states as a result of small ribbon widths 57 or high vacancy concentration 58 , where the defects mediate the coupling between the states on opposite edges leading to backscattering. The ribbons used in our calculations are almost 86 Å wide, therefore, the defects studied at concentrations of about 0.4 % are not enough to disturb the correspondence with the bulk and they do not interfere with the topological states, remaining with a closed bandgap.…”

Helical Liquids in Semiconductors

“…For a nanoribbon or stripe-like geometry in which the interchannel coupling becomes nonnegligible, the stability of multiple parallel helical liquids has been investigated (Xu & Moore 2006, Santos et al 2019). In addition, there is a first-principle study on interedge scattering due to a single nonmagnetic bulk impurity, a relevant backscattering source for narrow ribbons (Vannucci et al 2020), as well as theoretical works on Coulomb drag in two parallel interacting helical edge modes (Zyuzin & Fiete 2010, Chou et al 2015, Kainaris et al 2017. Furthermore, (Hou et al 2009) proposed corner junctions as a probe of 2DTI helical edge states.…”

“…Finally, we note that a full first-principle study of edge transport was carried out (Vannucci et al 2020), particularly focusing on several recently proposed quantum spin Hall materials with large bulk gaps (bismuth and antimony halides, binary compounds BiX and SbX with X ∈ {F, Cl, Br, I}). As expected, magnetic impurities trapped at the vacancy defects were identified as crucial backscattering sources which break the time-reversal symmetry and, in general, lead to the conductance quantization breakdown.…”

Robustness of quantized transport through edge states of finite length: Imaging current density in Floquet topological versus quantum spin and anomalous Hall insulators

“…Note that in the case of vacancies at the edges of QSHI, our tight-binding Hamiltonian in Eq. (22) does not capture possibility of formation of a localized magnetic moment at the vacancy site which requires first-principles Hamiltonians [73]. This opens a possibility of backscattering involving spin flip which will disrupt [73] (nearly) quantized conductance in Fig.…”