Robustness and Universality of Surface States in Dirac Materials

Ballistically propagating topologically protected states harbor exotic transport phenomena of wide interest. Here we describe a nontopological mechanism that produces such states at the surfaces of generic Dirac materials, giving rise to propagating surface modes with energies near the bulk band crossing. The robustness of surface states originates from the unique properties of Dirac-Bloch wavefunctions which exhibit strong coupling to generic boundaries. Surface states, described by Jackiw-Rebbi-type bound states, feature a number of interesting properties. Mode dispersion is gate tunable, exhibiting a wide variety of different regimes, including nondispersing flat bands and linear crossings within the bulk bandgap. The ballistic wavelike character of these states resembles the properties of topologically protected states; however, it requires neither topological restrictions nor additional crystal symmetries. The Dirac surface states are weakly sensitive to surface disorder and can dominate edge transport at the energies near the Dirac point.Comment: 16 pages, 4 figure

Dynamical Screening and Ferroelectric-type Excitonic Instability in Bilayer Graphene

Electron interactions in undoped bilayer graphene lead to instability of the gapless state, `which-layer' symmetry breaking, and energy gap opening at the Dirac point. In contrast to single layer graphene, the bilayer system exhibits instability even for arbitrarily weak interaction. A controlled theory of this instability for realistic dynamically screened Coulomb interactions is developed, with full acount of dynamically generated ultraviolet cutoff. This leads to an energy gap that scales as a power law of the interaction strength, making the excitonic instability readily observable.Comment: 4 pgs, 2 fg

Electron Viscosity, Current Vortices and Negative Nonlocal Resistance in Graphene

Quantum-critical states of diverse strongly correlated systems are predicted to feature universal collision-dominated transport resembling that of viscous fluids. However, investigation of these phenomena has been hampered by the lack of known macroscopic signatures of the hydrodynamic regime at criticality. Here we identify vorticity as such a signature and link it with an easily verifiable striking macroscopic transport behavior. Produced by the viscous flow, vorticity can drive electric current against an applied field, resulting in a negative nonlocal voltage. We argue that the latter may play the same role for the viscous regime as zero electrical resistance does for superconductivity. Besides offering a diagnostic of viscous transport which distinguishes it from ohmic currents, the sign-changing electrical response affords a robust tool for directly measuring the viscosity-to-resistivity ratio. The strongly interacting electron-hole plasma in high-mobility graphene provides a bridge between quantum-criticality and the wealth of fluid mechanics phenomena.Comment: submitted for publication, July 201

Quantum Anomalous Hall State in Bilayer Graphene

We present a symmetry-based analysis of competition between different gapped states that have been proposed in bilayer graphene (BLG), which are all degenerate on a mean field level. We classify the states in terms of a hidden SU(4) symmetry, and distinguish symmetry protected degeneracies from accidental degeneracies. One of the states, which spontaneously breaks discrete time reversal symmetry but no continuous symmetry, is identified as a Quantum Anomalous Hall (QAH) state, which exhibits quantum Hall effect at zero magnetic field. We investigate the lifting of the accidental degeneracies by thermal and zero point fluctuations, taking account of the modes softened under RG. Working in a 'saddle point plus quadratic fluctuations' approximation, we identify two types of RG- soft modes which have competing effects. Zero point fluctuations, dominated by 'transverse' modes which are unique to BLG, favor the QAH state. Thermal fluctuations, dominated by 'longitudinal' modes, favor a SU(4) symmetry breaking multiplet of states. We discuss the phenomenology and experimental signatures of the QAH state in BLG, and also propose a way to induce the QAH state using weak external magnetic fields.Comment: minor changes, made to match journal versio

Tunable Quantum Hall Edge Conduction in Bilayer Graphene through Spin-Orbit Interaction

Bilayer graphene, in the presence of a one-sided spin-orbit interaction (SOI) induced by a suitably chosen substrate, is predicted to exhibit unconventional Quantum Hall states. The new states arise due to strong SOI-induced splittings of the eight zeroth Landau levels, which are strongly layer-polarized, residing fully or partially on one of the two graphene layers. In particular, an Ising SOI in the meV scale is sufficient to invert the Landau level order between the $n=0$ and $n=1$ orbital levels under moderately weak magnetic fields $B \lesssim 10$\~T. Furthermore, when the Ising field opposes the $B$ field, the order of the spin-polarized levels can also be inverted. We show that, under these conditions, three different compensated electron-hole phases, with equal concentrations of electrons and holes, can occur at $\nu = 0$ filling. The three phases have distinct edge conductivity values. One of the phases is especially interesting, since its edge conduction can be turned on and off by switching the sign of the interlayer bias.Comment: 10 pages, 5 figure

Chirality-Assisted Electronic Cloaking in Bilayer Graphene Nanostructures

We show that the strong coupling of pseudospin orientation and charge carrier motion in bilayer graphene has a drastic effect on transport properties of ballistic p-n-p junctions. Electronic states with zero momentum parallel to the barrier are confined under it for one pseudospin orientation, whereas states with the opposite pseudospin tunnel through the junction totally uninfluenced by the presence of confined states. We demonstrate that the junction acts as a cloak for confined states, making them nearly invisible to electrons in the outer regions over a range of incidence angles. This behavior is manifested in the two-terminal conductance as transmission resonances with non-Lorentzian, singular peak shapes. The response of these phenomena to a weak magnetic field or electric-field-induced interlayer gap can serve as an experimental fingerprint of electronic cloaking.Comment: 5 pgs, 5 fg