Helical liquids and Majorana bound states in quantum wires

We show that the combination of spin-orbit coupling with a Zeeman field or strong interactions may lead to the formation of a helical liquid in single-channel quantum wires. In a helical liquid, electrons with opposite velocities have opposite spin precession. We argue that zero-energy Majorana bound states are formed in various situations when the wire is situated in proximity to a conventional s-wave superconductor. This occurs when the external magnetic field, the superconducting gap, or, in particular, the chemical potential vary along the wire. We discuss experimental consequences of the formation of the helical liquid and the Majorana bound states.Comment: 4+epsilon page

Quantum Transport through Nanostructures with Orbital Degeneracies

Geometric symmetries cause orbital degeneracies in a molecule's spectrum. In a single-molecule junction, these degeneracies are lifted by various symmetry-breaking effects. We study quantum transport through such nanostructures with an almost degenerate spectrum. We show that the master equation for the reduced density matrix must be derived within the singular-coupling limit as opposed to the conventional weak-coupling limit. This results in signatures of the density matrix's off-diagonal elements in the transport characteristics

Striped quantum Hall phases

Recent experiments seem to confirm predictions that interactions lead to charge density wave ground states in higher Landau levels. These new ``correlated'' ground states of the quantum Hall system manifest themselves for example in a strongly anisotropic resistivity tensor. We give a brief introduction and overview of this new and emerging field.Comment: 10 pages, 1 figure, updated reference to experimental wor

Fractional Shot Noise in the Kondo Regime

Low temperature transport through a quantum dot in the Kondo regime proceeds by a universal combination of elastic and inelastic processes, as dictated by the low-energy Fermi-liquid fixed point. We show that as a result of inelastic processes, the charge detected by a shot-noise experiment is enhanced relative to the noninteracting situation to a universal fractional value, $e^*=5/3 e$. Thus, shot noise reveals that the Kondo effect involves many-body features even at low energies, despite its Fermi-liquid nature. We discuss the influence of symmetry breaking perturbations.Comment: 4 pages, 2 figure

Topological superconducting phases in disordered quantum wires with strong spin-orbit coupling

Zeeman fields can drive semiconductor quantum wires with strong spin-orbit coupling and in proximity to s-wave superconductors into a topological phase which supports end Majorana fermions and offers an attractive platform for realizing topological quantum information processing. Here, we investigate how potential disorder affects the topological phase by a combination of analytical and numerical approaches. Most prominently, we find that the robustness of the topological phase against disorder depends sensitively and non-monotonously on the Zeeman field applied to the wire.Comment: 6 pages, 3 figures; published versio

Level Statistics and Localization for Two Interacting Particles in a Random Potential

We consider two particles with a local interaction $U$ in a random potential at a scale $L_1$ (the one particle localization length). A simplified description is provided by a Gaussian matrix ensemble with a preferential basis. We define the symmetry breaking parameter $\mu \propto U^{-2}$ associated to the statistical invariance under change of basis. We show that the Wigner-Dyson rigidity of the energy levels is maintained up to an energy $E_{\mu}$. We find that $E_{\mu} \propto 1/\sqrt{\mu}$ when $\Gamma$ (the inverse lifetime of the states of the preferential basis) is smaller than $\Delta_2$ (the level spacing), and $E_{\mu} \propto 1/\mu$ when $\Gamma > \Delta_2$. This implies that the two-particle localization length $L_2$ first increases as $|U|$ before eventually behaving as $U^2$.Comment: 4 pages REVTEX, 4 Figures EPS, UUENCODE

Theory of the Franck-Condon blockade regime

Strong coupling of electronic and vibrational degrees of freedom entails a low-bias suppression of the current through single-molecule devices, termed Franck-Condon blockade. In the limit of slow vibrational relaxation, transport in the Franck-Condon-blockade regime proceeds via avalanches of large numbers of electrons, which are interrupted by long waiting times without electron transfer. The avalanches consist of smaller avalanches, leading to a self-similar hierarchy which terminates once the number of transferred electrons per avalanche becomes of the order of unity. Experimental signatures of self-similar avalanche transport are strongly enhanced current (shot) noise, as expressed by giant Fano factors, and a power-law noise spectrum. We develop a theory of the Franck-Condon-blockade regime with particular emphasis on effects of electron cotunneling through highly excited vibrational states. As opposed to the exponential suppression of sequential tunneling rates for low-lying vibrational states, cotunneling rates suffer only a power-law suppression. This leads to a regime where cotunneling dominates the current for any gate voltage. Including cotunneling within a rate-equation approach to transport, we find that both the Franck-Condon blockade and self-similar avalanche transport remain intact in this regime. We predict that cotunneling leads to absorption-induced vibrational sidebands in the Coulomb-blockaded regime as well as intrinsic telegraph noise near the charge degeneracy point.Comment: 20 pages, 10 figures; minor changes, version published in Phys. Rev.