Superfluid-insulator transition of quantum Hall domain walls in bilayer graphene

Abstract

We consider the zero-filled quantum-Hall ferromagnetic state of bilayer graphene subject to a kink-like perpendicular electric field, which generates domain walls in the electronic state and lowenergy collective modes confined to move along them. In particular, it is shown that two pairs of collective helical modes are formed at opposite sides of the kink, each pair consisting of modes with identical helicities. We derive an effective field-theoretical model of these modes in terms of two weakly coupled anisotropic quantum spin-ladders, with parameters tunable through control of the electric and magnetic fields. This yields a rich phase diagram, where due to the helical nature of the modes, distinct phases possess very different charge conduction properties. Most notably, this system can potentially exhibit a transition from a superfluid to an insulating phase.PACS numbers: 73.22.Gk, 73.43.Lp, 72.80.Vp, 75.10.Pq, 75.10.Jm Among the most intriguing electronic properties of graphene is the emergence of novel collective states in the quantum Hall (QH) regime [1]. In particular, the peculiar ν = 0 QH states in both monolayer graphene (MLG) [2][3][4] and bilayer graphene (BLG) [5] suggest that Coulomb interactions lift the degeneracies of the half-filled zero energy Landau level. The multitude of discrete degrees of freedom (two valleys (K,K ) and two spin states in MLG, and an additional layer index in BLG) dictates a rich variety of possible exchange-induced broken symmetry states [6][7][8], as generalizations of the spontaneously polarized ferromagnetic state of an ordinary two-dimensional (2D) electron gas [9]. These can be controlled by external fields: in MLG, primarily by tuning the Zeeman energy via a strong parallel magnetic field [10]; in BLG, the orbital isospin degeneracies can be lifted by applying a perpendicular electric field [11].The unique features of the broken symmetry ν = 0 QH states are most prominently manifested by the nature of their collective excitations. While in the standard QH ferromagnet the elementary charge excitations are Skyrmions [9], more complex forms of spin-textures have been predicted in graphene, e.g. charge-2e Skyrmions in BLG [12]. Yet more remarkably, the particle-hole symmetry of the bulk spectrum allows the formation of charge conducting edge modes associated with kinks in the effective Zeeman field, where it changes sign across a line. These can be realized near physical edges of the graphene ribbon [13][14][15], or in the interior of a BLG sheet subject to non-uniform gating [16][17][18].The coherent domain wall (DW) forming in the spin/isospin configuration near such a kink supports a gapless collective mode, which possesses a onedimensional (1D) dynamics along the kink of a helical character. The latter arises from the constraint relating a spin/isospin texture to the charge degree of freedom [9]. This yields a mapping to a helical Luttinger liquid (HLL), with a single flavor encoding spin and charge related by duality, in analogy with the edge states of 2D topol...

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