Quantum spin Hall effect on germanene nanorod embedded in completely hydrogenated germanene

Abstract

We show that germanene nanoroads embedded in a completely hydrogenated germanene (germanane) exhibits a Quantum Spin Hall Effect (QSHE). These nanoroads can be obtained experimentally by local hydrogen dissociation from germanane. Using first principle calculations we predict that germanene nanoroads with zigzag interfaces show dissipationless conducting channels with in-plane and out-of-plane spin textures.The search for topological quantum phases of matter led condensed matter scientists to inspect, under a different point of view, materials known as Topological Insulators (TI). Those materials exhibit different properties and physical phenomena, like the quantum spin Hall effect (QSHE) [1], axion electrodynamics [2] and Majorana fermions [3]. The QSHE in two dimensional (2D) materials was proposed by Kane and Mele for graphene [1], followed by an independent proposal by Bernevig, Hughes and Zhang for the CdTe/HgTe/CdTe quantum well [4]. The latter has been confirmed experimentally [5], but for graphene due to the small spin-orbit bandgap, the observation of the QSHE would apply only at unaffordable experimental conditions [6,7].New candidate materials has been proposed to overcome the issue presented by graphene for the observation of the QSHE. Among some of these materials are the silicene [8][9][10][11][12][13], germanene [14], 2D hexagonal Si x Ge 1−x [15], and stanene [16]. They present similar properties to graphene, having some additional features, such as: (i) buckled honeycomb lattice; (ii) relatively large spin-orbit coupling (SOC), with bandgap of the order of meV and topological invariant Z 2 = 1 [14,15]. Such characteristics makes these 2D TI good candidates for the observation of the QSHE.From the experimental point of view, the pursuit of 2D materials that could display the QSHE was intensified by the synthesization of silicene. Silicene is mostly grown on metal surfaces, [8][9][10][11][12][17][18][19][20] that introduces some difficulties to isolate this single layer material and construct devices that will allow the measurement of the QSHE. Also the SOC bandgap in silicene is small, around 1.9 meV, so that the temperature to observe the QSHE will also be very low.A recent work of Bianco et al.[21] reported synthesis of germanane, a completely hydrogenated germanene structure. This opens up a new route to the experimental observation of the QSHE at higher temperatures. The formation and stability of this material, as well as the study of the QSHE may play an important role in nanoelectronics [21].In this work we propose a feasible setup for the observation of QSHE that is based on germanane [21]. The system is a germanene nanoroad embedded in germanane. We find that the germanene nanoroads with zigzag interfaces presents dissipationless conducting channels with in-plane and out-of-plane spin texture. We also show that with a small perturbation at the edge is possible to lift the degeneracy between interfaces, allowing a single-interface conduction. The electronic structure simulations were perf...

Topological phases in two-dimensional materials: a review

“…the states between fluorinated stanene and stanane. Similar results have also been reported for germanene and the 2D counterpart of lead [100,181,182] as well as the dumbbell stanene [180].…”

Quantum spin Hall states in graphene interacting with WS2 or WSe2

“…22 It should be noted that the bands above and below the Fermi level have opposite spin in agreement with the signature of the QSH phase. A similar picture appears in germanene nanorods embedded in fully Hpassivated germanene 23 and in two-dimensional Sn, 24 for which the gap can be strongly enhanced by the application of strain such that devices can operate at room temperature.…”

First-principles study of the stability of free-standing germanene in oxygen atmosphere

“…The corresponding DOS shows the semimetallic or zerogap semiconducting character of germanene, in agreement with the previous report. 7 To simulate the Ge-O ratio dependance of the O 2 molecule adsorption on germanene, one O 2 molecule is put on unit cells with different sizes from 1×1×1 to 4×4×1. Results show that for all the unit cell sizes applied, if the interaction between O 2 molecule and germanene is strong enough, O 2 molecule dissociates into two O atoms that bond tightly with Ge atoms after relaxation, which indicates that the process of dissociation is independent of the size of unit cell.…”

“…8 Furthermore, phonon calculations demonstrate the stability of silicene and germanene in their ground states. 9,10 In addition, recent studies predict that SOC effect can open a 1.5 meV band gap in silicene as well as 25 meV in germanene, 7,11 useful to the topological insulators.…”

“…Theoretically, density functional theory (DFT) studies of silicene or germanene have illustrated that silicon or germanium prefers sp 3 hybridization instead of sp 2 , thus, silicene or germanene is energetically favorable as a low-buckled (LB) structure with an amplitude of about 0.44Å and 0.69 A. 6,7 Moreover, the band structures in the LB configurations of silicene and germanene are ambipolar, and their charge carrier can behave like a massless Dirac fermion at the K point because of the π and π * bands that linearly cross at the Fermi level. It is also found that the electronic and magnetic properties of silicene and germanene nanoribbons show size and geometry dependence.…”