Living on the edge: Topology, electrostatics, and disorder

Abstract

We address the co-existence of massless and massive topological edge states at the interface between two materials with different topological phases. We modify the well known Bernevig-Hughes-Zhang model to introduce a smooth function describing the band inversion and the band bending due to electrostatic effects between the bulk of the quantum well and the vacuum. Within this minimal model we identify distinct parameter sets that can lead to the co-existence of the two types of edge states, and that determine their number and characteristics. We propose several experimental setups that could demonstrate their presence in two-dimensional topological systems, as well as ways to regulate or tune the contribution of the massive edge states to the conductance of associated electronic devices. Our results suggest that such states may also be present in novel two-dimensional Van der Waals topological materials. * Tineke L. van den Berg: tineke vandenberg001@ehu.eus † Dario Bercioux: dario.bercioux@dipc.org

Volkov-Pankratov states in topological graphene nanoribbons

“…Such massive edge states were first described by Volkov and Pankratov [26][27][28], and are therefore refered to as Volkov-Pankratov (VP) states. Recently, VP states have attracted attention again in the context of topological insulators (TIs) [29][30][31][32][33] and topological superconductors [34]. Although VP states in TIs are not topologically protected, they are of topological origin, because they result from the band inversion between a topological and a trivial material [30].…”

“…Threedimensional TIs with band inversion at the Γ-point were investigated both theoretically, within an effective linear in momentum model [30,32], as well as experimentally, in HgTe/CdTe heterojunctions [29,31]. Other studies focused on two-dimensional quantum wells within the Bernevig-Hughes-Zhang model [33]. In these works the VP states appeared due to the smooth modulations in the band structure near the edges.…”

Dirac quantum well engineering on the surface of topological insulator

“…Theoretical studies by Tchoumakov et al showed that the occurrence of such states is generic in what is now called a topological heterojunction [14], i.e., a smooth interface between a topological material and a trivial insulator. Indeed, they have been shown to arise not only in TIs [12][13][14][15], but also in interfaces of Weyl semimetals [16][17][18], topological graphene nanoribbons [19] and topological superconductors [20]. Furthermore, the magneto-optical properties of smooth topolog-ical interfaces have been studied both in the context of TIs [15,21] and Weyl semimetals [18] in the prospect of a, to the best of our knowledge yet missing, direct spectroscopic identification of massive VP states.…”

Robustness of Helical Edge States Under Edge Reconstruction

“…Introduction: There has been much interest in understanding the physics of the quantum spin hall (QSH) phase motivated by theoretical predictions [1][2][3][4][5][6][7][8][9][10][11] and experimental discovery [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] due to the possibility of realizing topologically protected helical edge states. Initially, it was suggested that the QSH phase could be realized in graphene [1], with the hallmark of this topologically non-trivial phase being its protection by time-reversal symmetry (TRS).…”