Phase diagram for theν=0quantum Hall state in monolayer graphene

Abstract

The ν = 0 quantum Hall state in a defect-free graphene sample is studied within the framework of quantum Hall ferromagnetism. We perform a systematic analysis of the "isospin" anisotropies, which arise from the valley and sublattice asymmetric short-range electron-electron (e-e) and electron-phonon (e-ph) interactions. The phase diagram, obtained in the presence of generic isospin anisotropy and the Zeeman effect, consists of four phases characterized by the following orders: spinpolarized ferromagnetic, canted antiferromagnetic, charge density wave, and Kekulé distortion. We take into account the Landau level mixing effects and show that they result in the key renormalizations of parameters. First, the absolute values of the anisotropy energies become greatly enhanced and can significantly exceed the Zeeman energy. Second, the signs of the anisotropy energies due to e-e interactions can change upon renormalization. A crucial consequence of the latter is that the short-range e-e interactions alone could favor any state on the phase diagram, depending on the details of interactions at the lattice scale. On the other hand, the leading e-ph interactions always favor the Kekulé distortion order. The possibility of inducing phase transitions by tilting the magnetic field is discussed.

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

“…In fact, a canted antiferromagnetic state (Fig. 3b) that spontaneously breaks this symmetry is among the theoretically allowed ν = 0 states [12][13][14] . Within this scenario, the canting angle is controlled by the ratio of the Zeeman energy, gµ B B T , and the antiferromagnetic exchange coupling, which depends only on B ⊥ .…”

“…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 .…”

“…c, Conductance under the same conditions. The absence of a detectable change in capacitance, even as the two-terminal conductance undergoes a transition from an insulating to a metallic state suggests that the conductance transition is due to the emergence of gapless edge states.but the sublattice structure of the zLL adds additional interaction anisotropies 22 that can favor spin unpolarized ground states characterized by lattice scale spin-or charge-density wave order [12][13][14]23 . This interplay can be probed experimentally by changing the in-plane component of magnetic field, which changes the Zeeman energy but does not affect orbital energies, and previous observations indeed confirm that the state responsible for the ν=0 insulator is spin unpolarized 24 .…”

“…but the sublattice structure of the zLL adds additional interaction anisotropies 22 that can favor spin unpolarized ground states characterized by lattice scale spin-or charge-density wave order [12][13][14]23 . This interplay can be probed experimentally by changing the in-plane component of magnetic field, which changes the Zeeman energy but does not affect orbital energies, and previous observations indeed confirm that the state responsible for the ν=0 insulator is spin unpolarized 24 .…”

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

“…A variety of approaches have been used to estimate these short-range corrections to the Coulomb interaction [14][15][16][17][18][19][20] . In this paper, we adopt a two-parameter phenomenological model motivated by crystal momentum conservation and by the expectation that corrections to the Coulomb interaction are significant only at distances shorter than a magnetic length 20 l B = c/eB ⊥ .…”