Spontaneous layer polarization and conducting domain walls in the quantum Hall regime of bilayer graphene (original) (raw)
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Distinguishing Spontaneous Quantum Hall States in Bilayer Graphene
Physical Review Letters, 2012
Chirally stacked N-layer graphene with N ≥ 2 is susceptible to a variety of distinct broken symmetry states in which each spin-valley flavor spontaneously transfers charge between layers. In mean-field theory one of the likely candidate ground states for a neutral bilayer is the layer antiferromagnet (LAF) that has opposite spin-polarizations in opposite layers. In this Letter we analyze how the LAF and other competing states are influenced by Zeeman fields that couple to spin and by interlayer electric fields that couple to layer pseudospin, and comment on the possibility of using Zeeman response and edge state signatures to identify the character of the bilayer ground state experimentally.
Emergence of helical edge conduction in graphene at the ν = 0 quantum Hall state
Physical Review B, 2016
The conductance of graphene subject to a strong, tilted magnetic field exhibits a dramatic change from insulating to conducting behavior with tilt-angle, regarded as evidence for the transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) ν = 0 quantum Hall state. We develop a theory for the electric transport in this system based on the spin-charge connection, whereby the evolution in the nature of collective spin excitations is reflected in the charge-carrying modes. To this end, we derive an effective field theoretical description of the low-energy excitations, associated with quantum fluctuations of the spin-valley domain wall ground-state configuration which characterizes the two-dimensional (2D) system with an edge. This analysis yields a model describing a onedimensional charged edge mode coupled to charge-neutral spin-wave excitations in the 2D bulk. Focusing particularly on the FM phase, naively expected to exhibit perfect conductance, we study a mechanism whereby the coupling to these bulk excitations assists in generating back-scattering. Our theory yields the conductance as a function of temperature and the Zeeman energy-the parameter that tunes the transition between the FM and CAF phases-with behavior in qualitative agreement with experiment.
Broken-symmetry states and phase diagram of the lowest Landau level in bilayer graphene
Physical Review B, 2011
Broken-symmetry quantum Hall (QH) states with filling factors ν = 0, ±1, ±2, ±3 in the lowest Landau level in bilayer graphene are analyzed by solving the gap equation in the random phase approximation. It is shown that in the plane of electric and magnetic fields, the critical line, which separates the spin and layer polarized phases at ν = 0, extends to the ν = ±1 QH states. The amplitudes of the gaps in the ν = ±1, ±3, and ν = ±2 QH states are significantly smaller than the amplitude of the ν = 0 gap, due to the separate filling of the n = 0 and n = 1 orbital Landau levels and the negative contribution of the Hartree term, respectively. It is shown that those values of the external electric field where the conductance is not quantized correspond to the minima of the gaps.
Competing ordered states with filling factor two in bilayer graphene
The quantum Hall effect, in which a two-dimensional sample's Hall conductivities become quantized, is a remarkable transport anomaly commonly observed at strong magnetic fields. However, it may also appear at zero magnetic field if time-reversal symmetry is broken. Charge-neutral bilayer graphene is unstable to a variety of competing and closely related broken symmetry states, some of which have non-zero quantized Hall conductivities. Here we explore those states by stabilizing them with external fields. Transport spectroscopy measurements reveal two distinct states that have two quantum units of Hall conductivity, stabilized by large magnetic and electric fields, respectively. The majority spins of both phases form a quantum anomalous Hall state, and the minority spins constitute a Kekulé state with spontaneous valley coherence for phase I and a quantum valley Hall state for phase II. Our results shed light on the rich set of competing ordered states in bilayer graphene.
Spin-valley coherent phases of the ν=0 quantum Hall state in bilayer graphene
Physical Review B
Bilayer graphene (BLG) offers a rich platform for broken symmetry states stabilized by interactions. In this work we study the phase diagram of BLG in the quantum Hall regime at filling factor ν = 0 within the Hartree-Fock approximation. In the simplest non-interacting situation this system has eight (nearly) degenerate Landau levels near the Fermi energy, characterized by spin, valley, and orbital quantum numbers. We incorporate in our study two effects not previously considered: (i) the nonperturbative effect of trigonal warping in the single-particle Hamiltonian, and (ii) short-range SU(4) symmetry-breaking interactions that distinguish the energetics of the orbitals. We find within this model a rich set of phases, including ferromagnetic, layer-polarized, canted antiferromagnetic, Kekulé, a "spin-valley entangled" state, and a "broken U(1) × U(1)" phase. This last state involves independent spontaneous symmetry breaking in the layer and valley degrees of freedom, and has not been previously identified. We present phase diagrams as a function of interlayer bias D and perpendicular magnetic field B ⊥ for various interaction and Zeeman couplings, and discuss which are likely to be relevant to BLG in recent measurements. Experimental properties of the various phases and transitions among them are also discussed.
Physical Review B, 2012
For bilayer graphene in a magnetic field at the neutral point, we derive and solve a full set of gap equations including all Landau levels and taking into account the dynamically screened Coulomb interaction. There are two types of the solutions for the filling factor ν = 0: (i) a spin-polarized type solution, which is the ground state at small values of perpendicular electric field E ⊥ , and (ii) a layer-polarized solution, which is the ground state at large values of E ⊥ . The critical value of E ⊥ that determines the transition point is a linear function of the magnetic field, i.e., E ⊥,cr = E off ⊥ +aB, where E off ⊥ is the offset electric field and a is the slope. The offset electric field and energy gaps substantially increase with the inclusion of dynamical screening compared to the case of static screening. The obtained values for the offset and the energy gaps are comparable with experimental ones. The interaction with dynamical screening can be strong enough for reordering the levels in the quasiparticle spectrum (the n = 2 Landau level sinks below the n = 0 and n = 1 ones).
Edge states of bilayer graphene in the quantum Hall regime
Physical Review B, 2011
We study the low-energy edge states of bilayer graphene in a strong perpendicular magnetic field. Several possible simple boundary geometries related to zigzag edges are considered. Tight-binding calculations reveal three types of edge-state behaviors: weakly, strongly, and nondispersive edge states. These three behaviors may all be understood within a continuum model, and related by nonlinear transformations to the spectra of
Impurity states in the quantum spin Hall phase in graphene
Physical Review B, 2012
Two-dimensional insulators with time-reversal symmetry can have two topologically different phases, the quantum spin Hall and the normal phase. The former is revealed by the existence of conducting edge states that are topologically protected. Here we show that the reaction to impurity, in bulk, is radically different in the two phases and can be used as a marker for the topological phase. Within the context of the Kane-Mele model for graphene, we find that strictly normalizable in-gap impurity states only occur in the quantum spin Hall phase and carry a dissipationless current whose chirality is determined by the spin and pseudospin of the residing electron.
Valley-kink in bilayer graphene at ν=0: A charge density signature for quantum Hall ferromagnetism
Physical Review B, 2012
We investigate interaction-induced valley domain walls in bilayer graphene in the ν = 0 quantum Hall state, subject to a perpendicular electric field that is antisymmetric across a line in the sample. Such a state can be realized in a double-gated suspended sample, where the electric field changes sign across a line in the middle. The noninteracting energy spectrum of the ground state is characterized by a sharp domain wall between two valley-polarized regions. Using the Hartree-Fock approximation, we find that the Coulomb interaction opens a gap between the two lowest-lying states near the Fermi level, yielding a smooth domain wall with a kink configuration in the valley index. Our results suggest the possibility to visualize the domain wall via measuring the charge density difference between the two graphene layers, which we find exhibits a characteristic pattern. The width of the kink and the resulting pattern can be tuned by the interplay between the magnetic field and the gate electric fields.
Broken Symmetry Quantum Hall States in Dual-Gated ABA Trilayer Graphene
ABA-stacked trilayer graphene is a unique 2D electron system with mirror reflection symmetry and unconventional quantum Hall effect. We present low-temperature transport measurements on dual-gated suspended trilayer graphene in the quantum Hall (QH) regime. We observe QH plateaus at filling factors ν = −8, −2, 2, 6, and 10, which is in agreement with the full-parameter tight binding calculations. In high magnetic fields, odd-integer plateaus are also resolved, indicating almost complete lifting of the 12-fold degeneracy of the lowest Landau level (LL). Under an out-ofplane electric field E ⊥ , we observe degeneracy breaking and transitions between QH plateaus. Interestingly, depending on its direction, E ⊥ selectively breaks the LL degeneracies in the electron-doped or holedoped regimes. Our results underscore the rich interaction-induced phenomena in trilayer graphene. . Low-energy band structure of ABA-stacked TLG calculating (left panel) using only γ 0 and γ 1 , (right panel) using γ 0 −γ 5 . Inset: ABA-stacked TLG lattice with hopping parameters γ 1 −γ 5 . (b). SEM image of a dual-gated suspended TLG device. (c) G(V bg ) before (blue) and after (red) current annealing.