Coexistence of Canted Antiferromagnetism and Bond Order in ν=0 Graphene.

Motivated by experimental studies of graphene in the quantum Hall regime, we revisit the phase diagram of a single sheet of graphene at charge neutrality. Because of spin and valley degeneracies, interactions play a crucial role in determining the nature of the ground state. We show that, generically within the Hartree-Fock approximation, in the regime of interest there is a region of coexistence between magnetic and bond orders in the phase diagram. We demonstrate this result both in continuum and lattice models, and argue that the coexistence phase naturally provides a possible explanation for unreconciled experimental observations on the quantum Hall effect in graphene.

Weyl Semimetal Path to Valley Filtering in Graphene.

We propose a device in which a sheet of graphene is coupled to a Weyl semimetal, allowing for the physical access to the study of tunneling from two- to three-dimensional massless Dirac fermions. Because of the reconstructed band structure, we find that this device acts as a robust valley filter for electrons in the graphene sheet. We show that, by appropriate alignment, the Weyl semimetal draws away current in one of the two graphene valleys, while allowing current in the other to pass unimpeded. In contrast to other proposed valley filters, the mechanism of our proposed device occurs in the bulk of the graphene sheet, obviating the need for carefully shaped edges or dimensions.

Helical Edge States and Quantum Phase Transitions in Tetralayer Graphene.

Helical conductors with spin-momentum locking are promising platforms for Majorana fermions. Here we report observation of two topologically distinct phases supporting helical edge states in charge neutral Bernal-stacked tetralayer graphene in Hall bar and Corbino geometries. As the magnetic field B_{⊥} and out-of-plane displacement field D are varied, we observe a phase diagram consisting of an insulating phase and two metallic phases, with 0, 1, and 2 helical edge states, respectively. These phases are accounted for by a theoretical model that relates their conductance to spin-polarization plateaus. Transitions between them arise from a competition among interlayer hopping, electrostatic and exchange interaction energies. Our work highlights the complex competing symmetries and the rich quantum phases in few-layer graphene.

Spin Mode Switching at the Edge of a Quantum Hall System.

Quantum Hall states can be characterized by their chiral edge modes. Upon softening the edge potential, the edge has long been known to undergo spontaneous reconstruction driven by charging effects. In this Letter we demonstrate a qualitatively distinct phenomenon driven by exchange effects, in which the ordering of the edge modes at ν=3 switches abruptly as the edge potential is made softer, while the ordering in the bulk remains intact. We demonstrate that this phenomenon is robust, and has many verifiable experimental signatures in transport.

Interaction-Induced Dirac Fermions from Quadratic Band Touching in Bilayer Graphene.

We revisit the effect of local interactions on the quadratic band touching (QBT) of the Bernal honeycomb bilayer model using renormalization group (RG) arguments and quantum Monte Carlo (QMC) simulations. We present a RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead, they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased QMC simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a finite U/t despite the U=0 hopping problem having a QBT. The onset of antiferromagnetism takes place at a continuous transition which is consistent with (2+1)D Gross-Neveu criticality. We conclude that generically in models of bilayer graphene, even if the free dispersion has a QBT, small local interactions generate a Dirac phase with no symmetry breaking and that there is a finite-coupling transition out of this phase to a symmetry-broken state.

Compact z = 2 electrodynamics in 2 + 1 dimensions: confinement with gapless modes.

We consider 2+1-dimensional compact U(1) gauge theory at the Lifshitz point with a dynamical critical exponent z=2. As in the usual z=1 theory, monopoles proliferate the vacuum for any value of the coupling, generating a mass scale. The theory of the dilute monopole gas is written in terms of a nonrelativistic sine-Gordon model with two real fields. While monopoles remove some of the massless poles of the perturbative field strength propagator, a gapless mode representing the incomplete screening of monopoles remains, and is protected by a shift invariance of the original theory. Timelike Wilson loops still obey area laws, implying that minimal charges are confined, but the action of spacelike Wilson loops of linear size L goes instead as L(3).

Critical behavior in graphene with Coulomb interactions.

We demonstrate that, in the presence of Coulomb interactions, electrons in graphene behave like a critical system, supporting power law correlations with interaction-dependent exponents. An asymptotic analysis shows that the origin of this behavior lies in particle-hole scattering, for which the Coulomb interaction induces anomalously close approaches. With increasing interaction strength the relevant power law changes from real to complex, leading to an unusual instability characterized by a complex-valued susceptibility in the thermodynamic limit. Measurable quantities, as well as the connection to classical two-dimensional systems, are discussed.

Hamiltonian theory of disorder at nu = 1/3.

The Hamiltonian theory of the fractional quantum Hall regime provides a simple and tractable approach to calculating gaps, polarizations, and many other physical quantities. In this Letter we include disorder in our treatment and show that a simple model with minimal assumptions produces results consistent with a range of experiments. In particular, the interplay between disorder and interactions can result in experimental signatures which mimic those of spin textures.

Quantum Hall to insulator transition in the bilayer quantum Hall ferromagnet.

We describe a phase transition of the bilayer quantum Hall ferromagnet at nu=1. In the presence of static disorder (modeled by a periodic potential), bosonic S=1/2 spinons undergo a superfluid-insulator transition while preserving ferromagnetism. The Mott insulating phase has an emergent U(1) photon, and the transition is between Higgs and Coulomb phases of this photon. Consequences for charge and counterflow conductivity and for interlayer tunneling conductance are discussed.

Interplay between the mesoscopic Stoner and Kondo effects in quantum dots.

We consider electrons confined to a quantum dot interacting antiferromagnetically with a spin-1 / 2 Kondo impurity. The electrons also interact among themselves ferromagnetically with a dimensionless coupling J , where J =1 denotes the bulk Stoner transition. We show that as J approaches 1 there is a regime with enhanced Kondo correlations, followed by one where the Kondo effect is destroyed and impurity is spin polarized opposite to the dot electrons. The most striking signature of the first, Stoner-enhanced Kondo regime is that a Zeeman field increases the Kondo scale, in contrast to the case for noninteracting dot electrons. Implications for experiments are discussed.

Coherence network in the quantum Hall bilayer.

Recent experiments on quantum Hall bilayers near total filling factor 1 have demonstrated that they support an imperfect two-dimensional superfluidity, in which there is nearly dissipationless transport at nonvanishing temperature observed both in counterflow resistance and interlayer tunneling. We argue that this behavior may be understood in terms of a coherence network induced in the bilayer by disorder, in which an incompressible, coherent state exists in narrow regions separating puddles of dense vortex-antivortex pairs. A renormalization group analysis shows that it is appropriate to describe the system as a vortex liquid. We demonstrate that the dynamics of the nodes of the network leads to a power law temperature dependence of the tunneling resistance, whereas thermally activated hops of vortices across the links control the counterflow resistance.

Quantum dots with disorder and interactions: a solvable large-g limit.

We analyze the problem of interacting electrons on a ballistic quantum dot with chaotic boundary conditions, where the effective interactions at low energies are characterized by Landau parameters. When the dimensionless conductance g of the dot is large, the disordered interacting problem can be solved in a saddle-point approximation which becomes exact as g --> infinity (as in a large-N theory), leading to a phase transition in each Landau interaction channel. In the weak-coupling phase constant charging and exchange interactions dominate the low-energy physics, while the strong-coupling phase displays a spontaneous distortion of the Fermi surface, smeared out by disorder.

Interactions and disorder in quantum dots: instabilities and phase transitions.

Using a fermionic renormalization group approach, we analyze a model where the electrons diffusing on a quantum dot interact via Fermi-liquid interactions. Describing the single-particle states by random matrix theory, we find that interactions can induce phase transitions (or crossovers for finite systems) to regimes where fluctuations and collective effects dominate at low energies. Implications for experiments and numerical work on quantum dots are discussed.