Spontaneous layer polarization and conducting domain walls in the quantum Hall regime of bilayer graphene

Abstract

Bilayer graphene subjected to perpendicular magnetic and electric fields displays a subtle competition between different symmetry broken phases, resulting from an interplay between the internal spin and valley degrees of freedom. The transition between different phases is often identified by an enhancement of the conductance. Here, we propose that the enhanced conductance at the transition is due to the appearance of robust conducting edge states at domain walls between the two phases. We formulate a criterion for the existence of such conducting edge states at the domain walls. For example, for a spontaneously layer polarized state at filling factor ν = 2, domains walls between regions of opposite polarization carry conducting edge modes. A microscopic analysis shows that lattice-scale interactions can favor such a layer polarized state.

Emergence of helical edge conduction in graphene at theν=0quantum Hall state

“…is a ferromagnet (FM). Such a bulk phase supports a gapless collective edge mode associated with a domain wall in the spin configuration, which can be modeled as a helical Luttinger liquid [18][19][20][21] . Insulating behavior therefore suggests that the true ground state is not a FM.…”

Wess-Zumino-Witten Terms in Graphene Landau Levels

“…A number of recent experimental [1][2][3][4][5][6][7] and theoretical [8][9][10][11][12][13][14][15][16][17][18][19] works have focused on the presence of antiferromagnetism (AF) in neutral monolayer and bilayer graphene in an applied magnetic field. It has also been argued that a non-magnetic state with lattice symmetry breaking in the Kekulé valence bond solid (VBS) pattern (see Fig.…”

Metallic Phase and Temperature Dependence of the ν=0 Quantum Hall State in Bilayer Graphene

“…Effective short-ranged interactions, for example, is shown to stabilize a canted spin anti-ferromagnetic (CAF), layer coherent ground state at small D, which transitions to a fully layer (FLP), spin unpolarized state at large D [9,10]. Experiments to date support this scenario, where a conductance peak is commonly associated with the putative CAF/ FLP phase boundary [18,20,[23][24][25]. This line boundary further splits into two branches at high perpendicular magnetic field B > 12 T, with the phase region in between thought to be partially polarized in all indices [20,23,26,27].Even at a moderate B, calculations including more hopping terms and other symmetryallowed electron-electron interaction terms have uncovered a more nuanced picture [11,17,26].…”

“…In the "standard" devices, the conductance peak at the first-order CAF/ FLP transition (D * ) in Fig. 2(a) is attributed to a microscopic network of CAF and FLP phases [18,20,[23][24][25]. Applied to the M phase, this network model would imply that the CAF/ FLP phase transition occur over an extended range of D-field, which seems highly unusual for first-order transitions.…”