Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state

Abstract

Low-dimensional electronic systems have traditionally been obtained by electrostatically confining electrons, either in heterostructures or in intrinsically nanoscale materials such as single molecules, nanowires, and graphene. Recently, a new paradigm has emerged with the advent of symmetry-protected surface states on the boundary of topological insulators, enabling the creation of electronic systems with novel properties. For example, time reversal symmetry (TRS) endows the massless charge carriers on the surface of a three-dimensional topological insulator with helicity, locking the orientation of their spin relative to their momentum 1,2 . Weakly breaking this symmetry generates a gap on the surface, 3 resulting in charge carriers with finite effective mass and exotic spin textures 4 . Analogous manipulations of the one-dimensional boundary states of a two-dimensional topological insulator are also possible, but have yet to be observed in the leading candidate materials 5,6 . Here, we demonstrate experimentally that charge neutral monolayer graphene displays a new type of quantum spin Hall (QSH) effect 7,8 , previously thought to exist only in time reversal invariant topological insulators 5,9-11 , when it is subjected to a very large magnetic field angled with respect to the graphene plane. Unlike in the TRS case 5,9,10 , the QSH presented here is protected by a spin-rotation symmetry that emerges as electron spins in a half-filled Landau level are polarized by the large in-plane magnetic field. The properties of the resulting helical edge states can be modulated by balancing the applied field against an intrinsic antiferromagnetic instability [12][13][14] , which tends to spontaneously break the spin-rotation symmetry. In the resulting canted antiferromagnetic (CAF) state, we observe transport signatures of gapped edge states, which constitute a new kind of one-dimensional electronic system with tunable band gap and associated spin-texture 15 .In the integer quantum Hall effect, the topology of the bulk Landau level (LL) energy bands 16 requires the existence of gapless edge states at any interface with the vacuum. The metrological precision of the Hall quantization can be traced to the inability of these edge states to backscatter due to the physical separation of modes with opposite momentum by the insulating sample bulk 17 . In contrast, counterpropagating boundary states in a symmetry-protected topological (SPT) insulator coexist spatially but are prevented from backscattering by a symmetry of the experimental system 1,2 . The local symmetry that protects transport in SPT surface states is unlikely to be as robust as the inherently nonlocal physical separation that protects the quantum Hall effect. However, it enables the creation of new electronic systems in which momentum and some quantum number such as spin are coupled, potentially leading to devices with new functionality. Most experimentally realized SPT phases are based on TRS, with counterpropagating states protected from intermixing by the Kram...

Edge states in graphene-like systems

“…Interestingly, there is very strong experimental evidence that this interaction driven QSH phase has been observed in the experiments, where the ferromagnetic order is favored by applying a quite large in-plane magnetic field 94 . At half filling, the experiments show how two terminal conductance of graphene is tuned from 0, corresponding to a gapped quantum Hall phase to 1.8 e 2…”

“…Young and coworkers. They verified, by means of local capacitance measurements, the opening of a band-gap in bulk and the edge nature of the transport by means of a floating gate technique 94 . The edge conductance in the QSH-like phase was G = 1.8G 0 , below the ideal case of G = 2G 0 which suggest that some sort of spin-flip backscattering mechanism is present in the sample.…”

“…94 Two different scenarios are possible to understand the large field needed to overcome a the fully gapped phase. The first one consists on hav- ing an AF ground state at zero in-plane field, turning it into ferromagnetic above the critical field.…”

SO(5) symmetry in the quantum Hall effect in graphene

“…When lattice corrections to the continuum Dirac model's Coulomb interactions are ignored the ground state at neutrality (ν = 0) is a Slater determinant 7 with all the N = 0 single-particle states of two arbitrarily chosen flavors occupied and, because the Hamiltonian is SU(4) invariant, has four independent degenerate Goldstone modes. The rich flavor physics of graphene in the quantum Hall regime has already been established by experiments which demonstrate that phase transitions between distinct many-electron states with the same filling factor ν can be driven by tuning magnetic field strength or tilt-angle [8][9][10][11][12] .…”

“…The quantum Hall state of graphene at neutrality is believed to be a canted antiferromagnet, as indicated by the behaviour of the edge conductance in experiments with tilted magnetic fields 10 . However, as we argue below, these experiments are not sufficient to determine the proximity of graphene to the ideal SO(5) symmetric state.…”