Localized states due to expulsion of resonant impurity levels from the continuum in bilayer graphene.

The Anderson impurity problem is considered for a graphene bilayer subject to a gap-opening bias. In-gap localized states are produced even when the impurity level overlaps with the continuum of band electrons. The effect depends strongly on the polarity of the applied bias as long as hybridization with the impurity occurs within a single layer. For an impurity level inside the conduction band a positive bias creates the new localized in-gap state. A negative bias does not produce the same result and leads to a simple broadening of the impurity level. The implications for transport are discussed including a possibility of the gate-controlled Kondo effect.

Intersubband edge singularity in metallic nanotubes.

The tunneling density of states of both the massless and massive (gapped) particles in metallic carbon nanotubes is known to have an anomalous energy dependence. This is the result of coupling to multiple low-energy bosonic excitation (plasmons). For both kinds of particles the ensuing effect is the suppression of the density of states by electron-electron interactions. We demonstrate that the optical absorption between gapless and gapped states is affected by the many-body effects in the opposite way. The absorption probability is enhanced compared with the noninteracting value and develops a power-law frequency dependence, A(ω) ∝ (ω - Δ)(-γ), where γ≈0.2 for typical nanotubes.

Guided plasmons in graphene p-n junctions.

Spatial separation of electrons and holes in graphene gives rise to the existence of plasmon waves confined to the boundary region. A theory of such guided plasmon modes within hydrodynamics of electron-hole liquid is developed. For plasmon wavelengths smaller than the size of charged domains, plasmon dispersion is found to be omega proportional to q(1/4). The frequency, velocity, and direction of propagation of guided plasmon modes can be easily controlled by the external electric field. In the presence of a magnetic field, a spectrum of additional gapless magnetoplasmon excitations is obtained. Our findings indicate that graphene is a promising material for nanoplasmonics.

Mesoscopic spin-hall effect in 2D electron systems with smooth boundaries.

The spin-Hall effect in a ballistic 2D electron gas with Rashba-type spin-orbit coupling and smooth edge confinement is studied. We predict that the interplay of semiclassical electron motion and quantum dynamics of spins leads to several distinct features in spin density along the edge that originate from the accumulation of turning points from many classical trajectories. A strong peak is found near a point of the vanishing of electron Fermi velocity in the lower spin-split subband. It is followed by a strip of negative spin density that extends until the crossing of the local Fermi energy with the degeneracy point where the two spin subbands intersect. Beyond this crossing there is a wide region of a smooth positive spin density. The total amount of spin accumulated in each of these features exceeds greatly the net spin across the entire edge. The features become more pronounced for shallower boundary potentials.

Dynamic conductivity in graphene beyond linear response.

The independence of the dynamic conductivity of intrinsic graphene of frequency takes its origin in the compensation of the vanishing density of states by the diverging matrix element of the corresponding interband transition. The applicability of the linear response approach, however, breaks down when this matrix element becomes comparable with the inverse electron lifetime. We show that the physics of the ac conductivity in this regime is determined by Rabi oscillations and obtain it beyond the first-order perturbation theory. Under strong applied electric fields, the induced current eventually saturates at a value determined by the frequency and the lifetime. We also calculate the electromagnetic response of a graphene sheet and find that the optical transparency is increased by the nonlinear effects and make experimental predictions.

Scattering of plasmons at the intersection of two metallic nanotubes: implications for tunneling.

We study theoretically the plasmon scattering at the intersection of two metallic carbon nanotubes. We demonstrate that, for a small angle of crossing theta<<1, the transmission coefficient is an oscillatory function of lambda/theta, where lambda is the interaction parameter of the Luttinger liquid in an individual nanotube. We calculate the tunnel density of states nu(omega,x) as a function of energy omega and distance x from the intersection. In contrast with a single nanotube, we find that, in the geometry of crossed nanotubes, conventional "rapid" oscillations in nu(omega,x) due to the plasmon scattering acquire an aperiodic "slow-breathing" envelope which has lambda/theta nodes.

Charge response function and a novel plasmon mode in graphene.

Polarizability of noninteracting 2D Dirac electrons has a 1/square root(qv-omega) singularity at the boundary of electron-hole excitations. The screening of this singularity by long-range electron-electron interactions is usually treated within the random phase approximation. The latter is exact only in the limit of N-->infinity, where N is the "color" degeneracy. We find that the ladder-type vertex corrections become crucial close to the threshold as the ratio of the nth order ladder term to the same order random phase approximation contribution is ln(n)|qv-omega|/N(n). We perform an analytical summation of the infinite series of ladder diagrams which describe the excitonic effect. Beyond the threshold, qv>omega, the real part of the polarization operator is found to be positive leading to the appearance of a strong and narrow plasmon resonance.

Spin hall edge spin polarization in a ballistic 2D electron system.

Universal properties of the spin Hall effect in ballistic 2D electron systems are addressed. The net spin polarization across the edge of the conductor is second order, approximately lambda2, in spin-orbit coupling constant independent of the form of the boundary potential, with the contributions of normal and evanescent modes each being approximately radical lambda but of opposite signs. This general result is confirmed by the analytical solution for a hard-wall boundary, which also yields the detailed distribution of the local spin polarization. The latter shows fast (Friedel) oscillations with the spin-orbit coupling entering via the period of slow beatings only. Long-wavelength contributions of evanescent and normal modes exactly cancel each other in the spectral distribution of the local spin density.

Effect of electron-electron interactions on the conductivity of clean graphene.

Minimal conductivity of a single undoped graphene layer is known to be of the order of the conductance quantum, independent of the electron velocity. We show that this universality does not survive electron-electron interaction, which results in nontrivial frequency dependence. We begin with analyzing the perturbation theory in the interaction parameter g for the electron self-energy and observe the failure of the random-phase approximation. The optical conductivity is then derived from the quantum kinetic equation, and the exact result is obtained in the limit when g<<1<< g|lnomega|.

Smearing of the two-dimensional Kohn anomaly in a nonquantizing magnetic field: implications for interaction effects.

Thermodynamic and transport characteristics of a clean two-dimensional interacting electron gas are shown to be sensitive to the weak perpendicular magnetic field even at temperatures much higher than the cyclotron energy, when the quantum oscillations are completely washed out. We demonstrate this sensitivity for two interaction-related characteristics: electron lifetime and the tunnel density of states. The origin of the sensitivity is traced to the field-induced smearing of the Kohn anomaly; this smearing is the result of curving of the semiclassical electron trajectories in magnetic field.

Zero-bias tunneling anomaly in a clean 2D electron gas caused by smooth density variations.

We show that smooth variations, delta n(r), of the local electron concentration in a clean 2D electron gas give rise to a zero-bias anomaly in the tunnel density of states, nu(omega), even in the absence of scatterers, and thus, without the Friedel oscillations. The energy width, omega 0, of the anomaly scales with the magnitude, delta n, and characteristic spatial extent, D, of the fluctuations as (delta n/D)2/3, while the relative magnitude delta nu/nu scales as (delta n/D). With increasing omega, the averaged delta nu oscillates with omega. We demonstrate that the origin of the anomaly is a weak curving of the classical electron trajectories due to the smooth inhomogeneity of the gas. This curving suppresses the corrections to the electron self-energy which come from the virtual processes involving two electron-hole pairs.

Generation of spin current by Coulomb drag.

Coulomb drag between two quantum wires is exponentially sensitive to the mismatch of their electronic densities. The application of a magnetic field can compensate this mismatch for electrons of opposite spin directions in different wires. The resulting enhanced momentum transfer leads to the conversion of the charge current in the active wire to the spin current in the passive wire.

Pseudospin ferromagnetism in double-quantum-wire systems.

We propose that a pseudospin ferromagnetic (i.e., interwire coherent) state can exist in a system of two parallel wires of finite width in the presence of a perpendicular magnetic field. This novel quantum many-body state appears when the interwire distance decreases below a certain critical value which depends on the magnetic field. We determine the phase boundary of the ferromagnetic phase by analyzing the softening of the spin-mode velocity using the bosonization approach. We also discuss the signatures of this state in tunneling and Coulomb drag experiments.

Breached superfluidity via p-wave coupling.

Anisotropic pairing between fermion species with different Fermi momenta opens two-dimensional areas of gapless excitations, thus producing a spatially homogeneous state with coexisting superfluid and normal fluids. This breached pairing state is stable and robust for arbitrarily small mismatch and weak p-wave coupling.

Spin current and polarization in impure two-dimensional electron systems with spin-orbit coupling.

We derive the transport equations for two-dimensional electron systems with Rashba spin-orbit interaction and short-range spin-independent disorder. In the limit of slow spatial variations, we obtain coupled diffusion equations for the electron density and spin. Using these equations we calculate electric-field induced spin accumulation and spin current in a finite-size sample for an arbitrary ratio between spin-orbit energy splitting Delta and elastic scattering rate tau(-1). We demonstrate that the spin-Hall conductivity vanishes in an infinite system independent of this ratio.

Coulomb drag by small momentum transfer between quantum wires.

We demonstrate that in a wide range of temperatures Coulomb drag between two weakly coupled quantum wires is dominated by processes with a small interwire momentum transfer. Such processes, not accounted for in the conventional Luttinger liquid theory, cause drag only because the electron dispersion relation is not linear. The corresponding contribution to the drag resistance scales with temperature as T2 if the wires are identical, and as T5 if the wires are different.

Zero-bias anomaly in disordered wires.

We calculate the low-energy tunneling density of states nu(epsilon,T) of an N-channel disordered wire, taking into account the electron-electron interaction nonperturbatively. The finite scattering rate 1/tau results in a crossover from the Luttinger liquid behavior at higher energies, nu proportional to epsilon(alpha), to the exponential dependence nu(epsilon,T = 0) proportional to exp(-epsilon*/epsilon) at low energies, where epsilon* proportional to 1/(Ntau). At finite temperature T, the tunneling density of states depends on the energy through the dimensionless variable epsilon/root square[epsilon*T]. At the Fermi level nu(epsilon = 0,T)proportional to exp(-root square[epsilon*/T]).

Nonlinear voltage dependence of the shot noise in mesoscopic degenerate conductors with strong electron-electron scattering.

It is shown that measurements of zero-frequency shot noise can provide information on electron-electron interaction, because the strong interaction results in the nonlinear voltage dependence of the shot noise in metallic wires. This is due to the fact that the Wiedemann-Franz law is no longer valid in the case of considerable electron-electron interaction. The deviations from this law increase the noise power and make it strongly dependent on the ratio of electron-electron and electron-impurity scattering rates.