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.

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.

Quantum phase tomography of a strongly driven qubit.

The interference between repeated Landau-Zener transitions in a qubit swept through an avoided level crossing results in Stückelberg oscillations in qubit magnetization, a hallmark of the coherent strongly driven regime in two-level systems. The two-dimensional Fourier transforms of the resulting oscillatory patterns are found to exhibit a family of one-dimensional curves in Fourier space, in agreement with recent observations in a superconducting qubit. We interpret these images in terms of time evolution of the quantum phase of the qubit state and show that they can be used to probe dephasing mechanisms.

Coherent particle transfer in an on-demand single-electron source.

Electron transfer from a localized state in a quantum dot into a ballistic conductor generally results in particle-hole excitations. We study this effect, considering a resonance level with time-dependent energy coupled to particle states in the Fermi sea. We find that, as the resonance level is driven through the Fermi-level, particle-hole excitations can be suppressed for certain driving protocols. In particular, such noiseless transfer occurs if the level moves with constant rapidity, its energy changing linearly with time. A scheme to study the coherence of particle transfer is proposed.

Vacuum polarization and screening of supercritical impurities in graphene.

Screening of charge impurities in graphene is analyzed using the exact solution for vacuum polarization obtained from the massless Dirac-Kepler problem. For the impurity charge below a certain critical value, no density perturbation is found away from the impurity, in agreement with perturbation theory. For the supercritical charge, however, the polarization distribution is shown to have a power law profile, leading to screening of the excess charge at large distances. The Dirac-Kepler scattering states give rise to standing wave oscillations in the local density of states which are prominent in the supercritical regime.

Atomic collapse and quasi-Rydberg states in graphene.

Charge impurities in graphene can host an infinite family of Rydberg-like resonance states of massless Dirac particles. These states, appearing for supercritical charge, are described by Bohr-Sommerfeld quantization of collapsing classical trajectories that descend on point charge, in analogy to the hydrogenic Rydberg states relation with planetary orbits. Strong tunnel coupling of these states to the Dirac continuum leads to resonance features in scattering on the impurities that manifest themselves in transport properties and in the local density of states.

Coherent quasiclassical dynamics of a persistent current qubit.

A new regime of coherent quantum dynamics of a qubit is realized at low driving frequencies in the strong driving limit. Coherent transitions between qubit states occur via the Landau-Zener process when the system is swept through an energy-level avoided crossing. The quantum interference mediated by repeated transitions gives rise to an oscillatory dependence of the qubit population on the driving-field amplitude and flux detuning. These interference fringes, which at high frequencies consist of individual multiphoton resonances, persist even for driving frequencies smaller than the decoherence rate, where individual resonances are no longer distinguishable. A theoretical model that incorporates dephasing agrees well with the observations.

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.

Zeeman splitting of zero-bias anomaly in Luttinger liquids.

Tunneling density of states (DOS) in Luttinger liquid has a dip at zero energy, commonly known as the zero-bias anomaly. In the presence of a magnetic field, in addition to the zero-bias anomaly, the DOS develops two peaks separated from the origin by the Zeeman energy. We show that these finite-bias anomalies are characterized by a power-law behavior of the DOS and the differential conductance, and find the corresponding exponents at arbitrary strength of the electron-electron interaction. The developed theory is applicable to various kinds of quantum wires, including carbon nanotubes.

Tail states in clean superconductors with magnetic impurities.

We analyze the behavior of the density of states in a singlet s-wave superconductor with weak magnetic impurities in the clean limit. By using the method of optimal fluctuation and treating the order parameter self-consistently we show that the density of states is finite everywhere in the superconducting gap, and that it varies as ln(N(E) proportional to -/E-Delta(0)/((7-d)/4) near the mean field gap edge Delta(0) in a d-dimensional superconductor. In contrast to most studied cases the optimal fluctuation is strongly anisotropic.

Electromechanical noise in a diffusive conductor.

Electrons moving in a conductor can transfer momentum to the lattice via collisions with impurities and boundaries, giving rise to a fluctuating mechanical stress tensor. The root-mean-squared momentum transfer per scattering event in a disordered metal (of dimension L greater than the mean-free path l and screening length xi) is found to be reduced below the Fermi momentum by a factor of order l/L for shear fluctuations and (xi/L)(2) for pressure fluctuations. The excitation of an elastic bending mode by the shear fluctuations is estimated to fall within current experimental sensitivity for a nanomechanical oscillator.