Interaction-driven topological insulator states in strained graphene

The electronic properties of graphene can be manipulated via mechanical deformations, which opens prospects for studying the Dirac fermions in new regimes and for new device applications. Certain natural configurations of strain generate large nearly uniform pseudo-magnetic fields, which have opposite signs in the two valleys, and give rise to flat spin- and valley-degenerate pseudo Landau levels (PLLs). Here we consider the effect of the Coulomb interactions in strained graphene with uniform pseudo-magnetic field. We show that the spin/valley degeneracies of the PLLs get lifted by the interactions, giving rise to topological insulator-like states. In particular, when a nonzero PLL is quarter- or three-quarter filled, an anomalous quantum Hall state spontaneously breaking time-reversal symmetry emerges. At half-filled PLL, weak spin-orbital interaction stabilizes time-reversal-symmetric quantum spin-Hall state. These many-body states are characterized by the quantized conductance and persist to a high temperature scale set by the Coulomb interactions, which we estimate to be a few hundreds Kelvin at moderate strain values. At fractional fillings, fractional quantum Hall states breaking valley symmetry emerge. These results suggest a new route to realizing robust topological insulator states in mesoscopic graphene.Comment: 5 page

Peierls-type Instability and Tunable Band Gap in Functionalized Graphene

Functionalizing graphene was recently shown to have a dramatic effect on the electronic properties of this material. Here we investigate spatial ordering of adatoms driven by the RKKY-type interactions. In the ordered state, which arises via a Peierls-instability-type mechanism, the adatoms reside mainly on one of the two graphene sublattices. Bragg scattering of electron waves induced by sublattice symmetry breaking results in a band gap opening, whereby Dirac fermions acquire a finite mass. The band gap is found to be immune to the adatoms' positional disorder, with only an exponentially small number of localized states residing in the gap. The gapped state is stabilized in a wide range of electron doping. Our findings show that controlled adsorption of adatoms or molecules provides a route to engineering a tunable band gap in graphene.Comment: 6 pgs, 3 fg

Fermi-Edge Resonance and Tunneling in Nonequilibrium Electron Gas

Fermi-edge singularity changes in a dramatic way in a nonequilibrium system, acquiring features which reflect the structure of energy distribution. In particular, it splits into several components if the energy distribution exhibits multiple steps. While conventional approaches, such as bosonization, fail to describe the nonequilibrium problem, an exact solution for a generic energy distribution can be obtained with the help of the method of functional determinants. In the case of a split Fermi distribution, while the `open loop' contribution to Green's function has power law singularities, the tunneling density of states profile exhibits broadened peaks centered at Fermi sub-levels.Comment: 5 pages, 1 figur

Ordering of magnetic impurities and tunable electronic properties of topological insulators

We study collective behavior of magnetic adatoms randomly distributed on the surface of a topological insulator. As a consequence of the spin-momentum locking on the surface, the RKKY-type interactions of two adatom spins depend on the direction of the vector connecting them, thus interactions of an ensemble of adatoms are frustrated. We show that at low temperatures the frustrated RKKY interactions give rise to two phases: an ordered ferromagnetic phase with spins pointing perpendicular to the surface, and a disordered spin-glass-like phase. The two phases are separated by a quantum phase transition driven by the magnetic exchange anisotropy. Ferromagnetic ordering occurs via a finite-temperature phase transition. The ordered phase breaks time-reversal symmetry spontaneously, driving the surface states into a gapped state, which exhibits an anomalous quantum Hall effect and provides a realization of the parity anomaly. We find that the magnetic ordering is suppressed by potential scattering. Our work indicates that controlled deposition of magnetic impurities provides a way to modify the electronic properties of topological insulators.Comment: 4+ pages, 2 figure

Nature of the spin liquid state of the Hubbard model on honeycomb lattice

Recent numerical work (Nature 464, 847 (2010)) indicates the existence of a spin liquid phase (SL) that intervenes between the antiferromagnetic and semimetallic phases of the half filled Hubbard model on a honeycomb lattice. To better understand the nature of this exotic phase, we study the quantum $J_1-J_2$ spin model on the honeycomb lattice, which provides an effective description of the Mott insulating region of the Hubbard model. Employing the variational Monte Carlo approach, we analyze the phase diagram of the model, finding a phase transition between antiferromagnet and an unusual $Z_2$ SL state at $J_2/J_1\approx 0.08$, which we identify as the SL phase of the Hubbard model. At higher $J_2/J_1\gtrsim 0.3$ we find a transition to a dimerized state with spontaneously broken rotational symmetry.Comment: 5 pages, 6 figure

Tunable Electron Interactions and Fractional Quantum Hall States in Graphene

The recent discovery of fractional quantum Hall states in graphene raises the question of whether the physics of graphene and its bilayer offers any advantages over GaAs-based materials in exploring strongly-correlated states of two-dimensional electrons. Here we propose a method to continuously tune the effective electron interactions in graphene and its bilayer by the dielectric environment of the sample. Using this method, the charge gaps of prominent FQH states, including \nu=1/3 or \nu=5/2 states, can be increased several times, or reduced all the way to zero. The tunability of the interactions can be used to realize and stabilize various strongly correlated phases in the FQH regime, and to explore the transitions between them.Comment: 4.2 pages, 5 figure