Alex Zazunov

Helical Luttinger Liquid in Topological Insulator Nanowires

We derive and analyze the effective low-energy theory for interacting electrons in a cylindrical nanowire made of a strong topological insulator. Three different approaches provide a consistent picture for the band structure, where surface states forming inside the bulk gap correspond to one-dimensional bands indexed by total angular momentum. When a half-integer magnetic flux pierces the nanowire, we find a strongly correlated helical Luttinger liquid topologically protected against weak disorder. We describe how transport experiments can detect this state.

Anomalous Josephson Current through a Spin-Orbit Coupled Quantum Dot

For a general model of a mesoscopic multilevel quantum dot, we determine the necessary conditions for the existence of an anomalous Josephson current with spontaneously broken time-reversal symmetry. They correspond to a finite spin-orbit coupling, a suitably oriented Zeeman field, and the dot being a chiral conductor. We provide analytical expressions for the anomalous supercurrent covering a wide parameter regime.

Majorana single-charge transistor

We study transport through a Coulomb blockaded topologically nontrivial superconducting wire (with Majorana end states) contacted by metallic leads. An exact formula for the current through this interacting Majorana single-charge transistor is derived in terms of wire spectral functions. A comprehensive picture follows from three different approaches. We find Coulomb oscillations with universal halving of the finite-temperature peak conductance under strong blockade conditions, where the valley conductance mainly comes from elastic cotunneling. The nonlinear conductance exhibits finite-voltage sidebands due to anomalous tunneling involving Cooper pair splitting.

Coulomb blockade of Majorana fermion induced transport

We study Coulomb charging effects for transport through a topologically nontrivial superconducting wire, where Majorana bound states are present at the interface to normal-conducting leads. We construct the general Keldysh functional integral representation, and provide detailed results for the nonlinear current-voltage relation under weak Coulomb blockade conditions.

Transport through a molecular quantum dot in the polaron crossover regime

Universit´e de la M´edit´erann´ee, 13288 Marseille cedex 9, France(Dated: February 4, 2008)We consider resonant transport through a molecular quantum dot coupled to a local vibrationmode. Applying the non-equilibrium Green function technique in the polaron representation, wedevelop a non-perturbative scheme to calculate the electron spectral function of the molecule in theregime of intermediate electron-phonon coupling. With increasing tunneling coupling to the leads,correlations between polaron clouds become more important at relatively high temperature leadingto a strong sharpening of the peak structure in the spectral function. The detection of such featuresin the current-voltage characteristics is briefly discussed.

Transport properties of the Coulomb–Majorana junction

We provide a comprehensive theoretical description of low-energy quantum transport for a Coulomb-Majorana junction, where several helical Luttinger liquid nanowires are coupled to a joint mesoscopic superconductor with finite charging energy. Including the Majorana bound states formed near the ends of superconducting wire parts, we derive and analyze the Keldysh phase action describing nonequilibrium charge transport properties of the junction. The low-energy physics corresponds to a two-channel Kondo model with symmetry group SO(M), where M is the number of leads connected to the superconductor. Transport observables, such as the conductance tensor or current noise correlations, display non-trivial temperature or voltage dependences reflecting non-Fermi liquid behavior.

Anomalous Josephson current, incipient time-reversal symmetry breaking, and Majorana bound states in interacting multilevel dots

We study the combined effects of spin-orbit interaction, magnetic field, and Coulomb charging on the Josephson current-phase relation, I(\varphi), for a multi-level quantum dot tunnel-contacted by two conventional s-wave superconductors with phase difference \varphi. A general model is formulated and analyzed in the cotunneling regime (weak tunnel coupling) and in the deep subgap limit, fully taking into account interaction effects. We determine the conditions for observing a finite anomalous supercurrent I_a=I(\varphi=0). For a two-level dot with spin-orbit coupling and arbitrarily weak Zeeman field B, we find the onset behavior I_a\propto {\rm sgn}(B) in the presence of interactions, suggesting the incipient spontaneous breakdown of time-reversal symmetry. We also provide conditions for realizing spatially separated (but topologically unprotected) Majorana bound states in this system, which have a clear signature in the 2\pi-periodic current-phase relation.

Even–odd parity effects in Majorana junctions

We study a general Majorana junction, where N helical nanowires are connected to a common s-wave superconductor proximity-inducing Majorana bound states in the wires. The normal part of each wire (j = 1,...,N) acts as connected lead, where electrons can tunnel into the respective Majorana state γA,j. The Majorana states at the other end, γB,j, are coupled to each other by an arbitrary tunnel matrix. We examine the conditions for even–odd parity effects in the tunnel conductance for various junction topologies.

Supercurrent blockade in Josephson junctions with a Majorana wire

We study the Josephson effect for a topologically nontrivial superconducting (TS) wire with Majorana fermion end states and tunnel-coupled to s-wave BCS superconducting (S) electrodes. In an S-TS junction, no supercurrent flow is possible under fairly general conditions. For the S-TS-S junction, bulk TS quasiparticles must be accessible to have a Josephson effect. In the noninteracting case, we derive the exact current-phase relation (CPR) and find \pi-periodic behavior with negative critical current for weak tunnel couplings. Charging effects then cause the anomalous CPR

Magnetic scattering of Dirac fermions in topological insulators and graphene

I(\varphi)=I_c \cos\varphi