Quantum spin Hall phase in multilayer graphene

Abstract

The so-called quantum spin Hall phase is a topologically nontrivial insulating phase that is predicted to appear in graphene and graphenelike systems. In this paper we address the question of whether this topological property persists in multilayered systems. We consider two situations: purely multilayer graphene and heterostructures where graphene is encapsulated by trivial insulators with a strong spin-orbit coupling. We use a four-orbital tight-binding model that includes full atomic spin-orbit coupling and we calculate the Z 2 topological invariant of the bulk states as well as the edge states of semi-infinite crystals with armchair termination. For homogeneous multilayers we find that even when the spin-orbit interaction opens a gap for all possible stackings, only those with an odd number of layers host gapless edge states while those with an even number of layers are trivial insulators. For heterostructures where graphene is encapsulated by trivial insulators, it turns out that interlayer coupling is able to induce a topological gap whose size is controlled by the spin-orbit coupling of the encapsulating materials, indicating that the quantum spin Hall phase can be induced by proximity to trivial insulators.

h-BN-layer-induced chiral decomposition in the electronic properties of multilayer graphene

“…However, theoretical and experimental works on chiral electron transport in multilayer systems have received less attention than in the case of mono-, bi-and tri-layer graphene. On the other hand, there is a generic interest in the possibility of engineering the electronic properties of two-dimensional crystals by combining them into multilayers [28], [34] ÷ [35]. In this context, it is interesting to see how the transport properties of graphene multilayers change by proximity to an insulator, so that the conducting channels would be only through graphene bands.…”

“…The case of bilayer systems has been widely studied both theoretically [1][2][3][4][5][6][7][8][9][10][11][12][13] and exper imentally [14][15][16][17][18][19][20][21][22]. For systems with three or more mono layers, electronic structures are also investigated theoretically [23][24][25][26][27][28][29] and experimentally [30][31][32][33], showing that multilayer graphene has a number of intriguing properties, including a tunable band gap opening and antiKlein tunnelling, arising from the chiral characteristics of charge carriers.…”

Electrical spin manipulation in graphene nanostructures

“…In order to estimate the contact interaction we adopt a tightbinding model that permits computing how the π orbitals of graphene hybridize with the s orbital of hydrogen. This can be performed using the TB model with four orbitals per carbon atom [64,65] and one orbital per hydrogen atom. Within this model, the midgap states are, in principle, a linear combination of p z , p x , p y , and s orbitals of the carbon atoms and the s orbital of the edge hydrogen atoms.…”

Quantum spin Hall effect in rutile-based oxide multilayers

“…The gapless nature of these edge states is not totally protected against perturbations even when they respect time-reversal symmetry, because perturbations mixing the two families, such as chemical edge reconstruction, will be able to open up an edge gap This topological crystalline insulating phase is analogous to two coupled non-trivial quantum spin Hall states, as in bilayer graphene with spin-orbit coupling. 29,30 Importantly, topological insulating states, even if they are not protected against symmetry mixing perturbations, have been shown to be robust [31][32][33][34][35][36] against edge perturbations.…”