Topological Edge States at a Tilt Boundary in Gated Multilayer Graphene

Abstract

Despite much interest in engineering new topological surface (edge) states using structural defects, such topological surface states have not been observed yet. We show that recently imaged tilt boundaries in gated multilayer graphene should support topologically protected gapless edge states. We approach the problem from two perspectives: the microscopic perspective of a tight-binding model and an ab initio calculation on a bilayer, and the symmetry-protected topological (SPT) state perspective for a general multilayer. Hence, we establish the tilt-boundary edge states as the first concrete example of the edge states of symmetry-protected Z-type SPT, protected by no-valley mixing, electron-number conservation, and time-reversal T symmetries. Further, we discuss possible phase transitions between distinct SPTs upon symmetry changes. Combined with a recently imaged tilt-boundary network, our findings may explain the long-standing puzzle of subgap conductance in gated bilayer graphene. This proposal can be tested through future transport experiments on tilt boundaries. In particular, the tilt boundaries offer an opportunity for the in situ imaging of topological edge transport.

Colloquium: Topological band theory

“…Th : Kane 2005a, Beenakker 2008, Peres 2010, Lau 2013, Wunsch 2008, Kotov 2012, Goerbig 2011, Sarma 2011, Weeks 2011, Diniz 2013, Maher 2013, Park 2009, Pesin 2012, Neto 2009, Vaezi 2013, Hu 2012Exp: Beenakker 2008, Peres 2010, Kotov 2012, Goerbig 2011, Sarma 2011, Maher 2013, Neto 2009, Gomes 2012, Kravets 2013, Ju 2015, Young 2014, Gorbachev 2014germanene Th: Liu 2011, Tabert 2013, Kikutake 2013, Drummond 2012, Ezawa 2012, Tahir 2013, Gupta 2014, Padilha 2013, Pan 2014GaAs/Ge/GaAs Th: Zhang 2013 GaBi; InBi; TlBi Th: Bi4Br4 Th: GeX;SnX;PbX;BiX(X= H, I, Br, Cl, F or OH)…”

Gate-controlled topological conducting channels in bilayer graphene

“…However the use of light is not always desirable in electronics and device proposals using bulk valley polarization often put stringent requirements on the size and edge orientation of the active area 3 . Alternatively, electrically created, valley-polarized topological conducting channels in high-mobility bilayer graphene may offer a robust, scalable platform to realize valleytronic operations 1,6,[8][9][10][11][12][13][14][15] . Figure 1a illustrates the dual-split-gating scheme proposed by Martin et al 6 , where an AB-stacked bilayer graphene (BLG) sheet is controlled by two pairs of top and bottom gates separated by a line junction.…”

Critical behavior of four-terminal conductance of bilayer graphene domain walls

“…In the presence of an interlayer electric field, when the field direction is reversed across a line [15][16][17][18][19][20][21] or when the field is uniform and the layer stacking switches from AB to BA 16,22,23 , the valley-projected Chern number changes by 2 (−2) across the domain wall in valley K (K ). As a result, both types of domain walls host two chiral edge states in each valley with chirality (direction) locked to valley index K or K , as shown in Fig.…”