Spin-Polarized to Valley-Polarized Transition in Graphene Bilayers atν=0in High Magnetic Fields

Abstract

We investigate the transverse electric field (E) dependence of the ν=0 quantum Hall state (QHS) in dual-gated graphene bilayers in high magnetic fields. The longitudinal resistivity (ρxx) measured at ν=0 shows an insulating behavior which is strongest in the vicinity of E=0, and at large E-fields. At a fixed perpendicular magnetic field (B), the ν=0 QHS undergoes a transition as a function of E, marked by a minimum, temperature-independent ρxx. This observation is explained by a transition from a spin polarized ν=0 QHS at small E-fields, to a valley (layer) polarized ν=0 QHS at large E-fields. The E-field value at which the transition occurs has a linear dependence on B. We investigate dual-gated graphene bilayers, a device geometry which allows independent control of the total density and transverse electric field. At a fixed perpendicular magnetic field (B), we observe the emergence of a quantum Hall state (QHS) at filling factor ν = 0 in the presence of a transverse electric field (E), evinced by a large longitudinal resistivity (ρ xx ) with an insulating behavior, consistent with the opening of a gap between the electron and hole bands. Interestingly, as the B-field is increased we observe a developing ν = 0 QHS at E=0, explained by the Zeeman splitting of the Landau levels at zero energy. As a function of E, the ν = 0 QHS undergoes a transition from spin polarized at small E-fields, to valley (layer) polarized at large E-fields.Our samples consist of natural graphite mechanically exfoliated on a 300 nm SiO 2 dielectric layer, thermally grown on a highly doped n-type Si substrate, with an As doping concentration of ∼ 10 20 cm −3 . Optical inspection and Raman spectroscopy are used to identify graphene bilayer flakes for device fabrication. We define metal contacts using electron beam (e-beam) lithography followed by 50 nm Ni deposition and lift-off [ Fig. 1(a)].A second e-beam lithography step followed by O 2 plasma etching are used to pattern a Hall bar on the graphene bilayer flake. To deposit the top gate dielectric, we first deposit a ∼ 20Å thin Al layer as a nucleation layer for the atomic layer deposition (ALD) of Al 2 O 3 . The sample is then transferred ex-situ to an ALD chamber. X-ray photoelectron spectroscopy and electrical measurements confirm the Al layer is fully oxidized in the presence of residual O 2 during evaporation, and the exposure to ambient O 2 [10]. Next, a 15 nm-thick Al 2 O 3 film is deposited using trimethyl aluminum as the Al source and H 2 O as oxidizer [11], followed by the Ni top gate deposition [ Fig. 1(a)]. Longitudinal (ρ xx ) and Hall (ρ xy ) resistivity measurements are performed down to a temperature of T = 0.3 K, and using standard low-current, low-frequency lock-in techniques. Three samples, labeled as A, B, and C, with mobilities of 1500 − 2400 cm 2 /Vs were investigated in this study, all with similar results.We use Hall measurements to determine the total carrier density (n tot ) as a function of top (V T G ) and back (V BG ) gate voltages, and the corresponding cap...

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

“…The graphene analog of the chemical potential µ term which tunes transitions between antiferromagnetic and d-wave superconducting states in the HTS case, is a sublatticestaggered potential v . Interestingly this field is easily tunable experimentally [34][35][36][37] in the bilayer graphene case. SO(5) symmetry in HTS is conjectured to emerge in low-energy effective theory 21 , and can be exactly realized in extended Hubbard model with artificial longrange interactions 38,39 ; however, it never becomes exact for commonly used models like t − J or Hubbard model.…”

Evidence for a spin phase transition at charge neutrality in bilayer graphene

“…In particular, a quantum spin Hall analogue has been predicted at ν = 0 in bilayer graphene if the ground state is a spin ferromagnet 8,9 . Previous studies have demonstrated that the bilayer ν = 0 state is an insulator in a perpendicular magnetic field [10][11][12][13][14][15][16] , though the exact nature of this state has not been identified. Here we present measurements of the ν = 0 state in a dual-gated bilayer graphene device in tilted magnetic field.…”

“…Transport studies in a dual-gated geometry [12][13][14] indicate that this gapped state results from an interaction-driven spontaneous symmetry breaking in the valley-spin space 17 . However, the exact order of the resulting ground state remains controversial.…”

“…The application of an in-plane magnetic field and perpendicular electric field allows us to map out a full phase diagram of the ν = 0 state as a function of experimentally tunable parameters. At large in-plane magnetic field we observe a quantum phase transition to a metallic state with conductance of order 4e 2 /h, consistent with predictions for the ferromagnet.Under a strong perpendicular magnetic field, bilayer graphene (BLG) develops a ν = 0 quantum Hall (QH) state at the charge neutrality point (CNP) which displays anomalous insulating behavior [10][11][12][13][14][15][16] . Transport studies in a dual-gated geometry 12-14 indicate that this gapped state results from an interaction-driven spontaneous symmetry breaking in the valley-spin space 17 .…”

“…Under a strong perpendicular magnetic field, bilayer graphene (BLG) develops a ν = 0 quantum Hall (QH) state at the charge neutrality point (CNP) which displays anomalous insulating behavior [10][11][12][13][14][15][16] . Transport studies in a dual-gated geometry [12][13][14] indicate that this gapped state results from an interaction-driven spontaneous symmetry breaking in the valley-spin space 17 .…”