Weak Chaos in a Quantum Kepler Problem

Transition from regular to chaotic dynamics in a crystal made of singular scatterers $U(r)=\lambda |r|^{-\sigma}$ can be reached by varying either sigma or lambda. We map the problem to a localization problem, and find that in all space dimensions the transition occurs at sigma=1, i.e., Coulomb potential has marginal singularity. We study the critical line sigma=1 by means of a renormalization group technique, and describe universality classes of this new transition. An RG equation is written in the basis of states localized in momentum space. The RG flow evolves the distribution of coupling parameters to a universal stationary distribution. Analytic properties of the RG equation are similar to that of Boltzmann kinetic equation: the RG dynamics has integrals of motion and obeys an H-theorem. The RG results for sigma=1 are used to derive scaling laws for transport and to calculate critical exponents.Comment: 28 pages, ReVTeX, 4 EPS figures, to appear in the I. M. Lifshitz memorial volume of Physics Report

Optical activity of noncentrosymmetric metals

We describe the phenomenon of optical activity of noncentrosymmetric metals in their normal and superconducting states. The found conductivity tensor contains the linear in wave vector off diagonal part responsible for the natural optical activity. Its value is expressed through the ratio of light frequency to the band splitting due to the spin-orbit interaction. The Kerr rotation of polarization of light reflected from the metal surface is calculated. In the additional file "Erratum" I've pointed out the sign error in arXiv:1001.2113 ( PRB v.81, 094525 (2010)) that leads to the wrong statement about the Kerr effect in light reflection from the surface of media without space parity.Comment: 9 pages + 2 pages of Erratum. arXiv admin note: text overlap with arXiv:0903.330

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

Quantum and Classical Binomial Distributions for the Charge Transmitted through Coherent Conductor

We discuss controversial results for the statistics of charge transport through coherent conductors. Two distribution functions for the charge transmitted was obtained previously, first by L.Levitov and G.Lesovik, [JETP Letters Vol.55 p.555 (1992)] and the other initially by the same authors [ibid. Vol.58 p.230 (1993)], and later the result was reproduced by several authors. The latter distribution functions actually coincides with classical binomial distribution (though obtained purely quantum mechanically) former (result of 1992) is different and we call it here quantum binomial distribution. The two distribution function represent two opposite universal limits - one is purely quantum, where interference is important, and the other is semiclassical, where interference is smeared out. We show, that high order charge correlators, determined by the either distribution functions, can all be measured in different setups. The high order current correlators, starting the third order, reveal (missed in previous studies) special oscillating frequency dependence on the scale of the inverted time flight from the obstacle to the measuring point. Depending on setup, the oscillating terms give substantially different contributions.Comment: 4 pages; english versio

Tunable Fermi-Edge Resonance in an Open Quantum Dot

Resonant tunneling in an open mesoscopic quantum dot is proposed as a vehicle to realize a tunable Fermi-edge resonance with variable coupling strength. We solve the x-ray edge problem for a generic nonseparable scatterer and apply it to describe tunneling in a quantum dot. The tunneling current power law exponent is linked to the S-matrix of the dot. The control of scattering by varying the dot shape and coupling to the leads allows to explore a wide range of exponents. Transport properties, such as weak localization, mesoscopic conductance fluctuations, and sensitivity to Wigner-Dyson ensemble type, have their replicas in the Fermi-edge singularity.Comment: 4 pages, 3 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