Z_{4} parafermions in Weakly Interacting Superconducting Constrictions at the Helical Edge of Quantum Spin Hall Insulators.

Parafermions are generalizations of Majorana fermions that may appear in interacting topological systems. They are known to be powerful building blocks of topological quantum computers. Existing proposals for realizations of parafermions typically rely on strong electronic correlations which are hard to achieve in the laboratory. We identify a novel physical system in which parafermions generically develop. It is based on a quantum constriction formed by the helical edge states of a quantum spin Hall insulator in the vicinity of an ordinary s-wave superconductor. Interestingly, our analysis suggests that Z_{4} parafermions are emerging bound states in this setup in the weakly interacting regime. Furthermore, we identify a situation in which Majorana fermions and parafermions can coexist.

Lévy Flights due to Anisotropic Disorder in Graphene.

We study transport properties of graphene with anisotropically distributed on-site impurities (adatoms) that are randomly placed on every third line drawn along carbon bonds. We show that stripe states characterized by strongly suppressed backscattering are formed in this model in the direction of the lines. The system reveals Lévy-flight transport in the stripe direction such that the corresponding conductivity increases as the square root of the system length. Thus, adding this type of disorder to clean graphene near the Dirac point strongly enhances the conductivity, which is in stark contrast with a fully random distribution of on-site impurities, which leads to Anderson localization. The effect is demonstrated both by numerical simulations using the Kwant code and by an analytical theory based on the self-consistent T-matrix approximation.

Fractional Wigner Crystal in the Helical Luttinger Liquid.

The properties of the strongly interacting edge states of two dimensional topological insulators in the presence of two-particle backscattering are investigated. We find an anomalous behavior of the density-density correlation functions, which show oscillations that are neither of Friedel nor of Wigner type: they, instead, represent a Wigner crystal of fermions of fractional charge e/2, with e the electron charge. By studying the Fermi operator, we demonstrate that the state characterized by such fractional oscillations still bears the signatures of spin-momentum locking. Finally, we compare the spin-spin correlation functions and the density-density correlation functions to argue that the fractional Wigner crystal is characterized by a nontrivial spin texture.

First-order character and observable signatures of topological quantum phase transitions.

Topological quantum phase transitions are characterized by changes in global topological invariants. These invariants classify many-body systems beyond the conventional paradigm of local order parameters describing spontaneous symmetry breaking. For noninteracting electrons, it is well understood that such transitions are continuous and always accompanied by a gap closing in the energy spectrum, given that the symmetries protecting the topological phase are maintained. Here, we demonstrate that a sufficiently strong electron-electron interaction can fundamentally change the situation: we discover a topological quantum phase transition of first-order character in the genuine thermodynamic sense that occurs without a gap closing. Our theoretical study reveals the existence of a quantum critical endpoint associated with an orbital instability on the transition line between a 2D topological insulator and a trivial band insulator. Remarkably, this phenomenon entails unambiguous signatures related to the orbital occupations that can be detected experimentally.

Color-dependent conductance of graphene with adatoms.

We study ballistic transport properties of graphene with a low concentration of vacancies or adatoms. The conductance of graphene doped to the Dirac point is found to depend on the relative distribution of impurities among different sites of the honeycomb lattice labeled in general by six colors. The conductivity is shown to be sensitive to the crystal orientation if adatom sites have a preferred color. Our theory is confirmed by numerical simulations using recursive Green's functions with no adjustable parameters.

Andreev-like reflections with cold atoms.

We propose a setup in which Andreev-like reflections predicted for 1D transport systems could be observed time dependently using cold atoms in a 1D optical lattice. Using time-dependent density matrix renormalization group methods we analyze the wave packet dynamics as a density excitation propagates across a boundary in the interaction strength. These phenomena exhibit good correspondence with predictions from Luttinger liquid models and could be observed in current experiments in the context of the Bose-Hubbard model.

Measuring the momentum of a nanomechanical oscillator through the use of two tunnel junctions.

We propose a way to measure the momentum p of a nanomechanical oscillator. The p detector is based on two tunnel junctions in an Aharonov-Bohm-type setup. One of the tunneling amplitudes depends on the motion of the oscillator, the other one not. Although the coupling between the detector and the oscillator is assumed to be linear in the position x of the oscillator, it turns out that the finite-frequency noise output of the detector will in general contain a term proportional to the momentum spectrum of the oscillator. This is a true quantum phenomenon, which can be realized in practice if the phase of the tunneling amplitude of the detector is tuned by the Aharonov-Bohm flux Phi to a p-sensitive value.

Temperature dependence of coulomb drag between finite-length quantum wires.

We evaluate the Coulomb drag current in two finite-length Tomonaga-Luttinger-liquid wires coupled by an electrostatic backscattering interaction. The drag current in one wire shows oscillations as a function of the bias voltage applied to the other wire, reflecting interferences of the plasmon standing waves in the interacting wires. In agreement with this picture, the amplitude of the current oscillations is reduced with increasing temperature. This is a clear signature of non-Fermi-liquid physics because for coupled Fermi liquids the drag resistance is always expected to increase as the temperature is raised.

Sub-Poissonian shot noise in graphene.

We calculate the mode-dependent transmission probability of massless Dirac fermions through an ideal strip of graphene (length L, width W, no impurities or defects) to obtain the conductance and shot noise as a function of Fermi energy. We find that the minimum conductivity of order e2/h at the Dirac point (when the electron and hole excitations are degenerate) is associated with a maximum of the Fano factor (the ratio of noise power and mean current). For short and wide graphene strips the Fano factor at the Dirac point equals 1/3, 3 times smaller than for a Poisson process. This is the same value as for a disordered metal, which is remarkable since the classical dynamics of the Dirac fermions is ballistic.

Shot-noise detection in a carbon nanotube quantum dot.

An on-chip detection scheme for high frequency signals is used to detect noise generated by a quantum dot formed in a single wall carbon nanotube. The noise detection is based on photon assisted tunneling in a superconductor-insulator-superconductor junction. Measurements of shot noise over a full Coulomb diamond are reported with excited states and inelastic cotunneling clearly resolved. Super-Poissonian noise is detected in the case of inelastic cotunneling.

Emission of polarization-entangled microwave photons from a pair of quantum dots.

We describe a mechanism for the production of polarization-entangled microwaves using intraband transitions in a pair of quantum dots. This proposal relies neither on spin-orbit coupling nor on control over electron-electron interactions. The quantum correlation of microwave polarizations is obtained from orbital degrees of freedom in an external magnetic field. We calculate the concurrence of emitted microwave photon pairs and show that a maximally entangled Bell pair is obtained in the limit of weak interdot coupling.

Optimal spin-entangled electron-hole pair pump.

A nonperturbative theory is presented for the creation by an oscillating potential of spin-entangled electron-hole pairs in the Fermi sea. In the weak potential limit, considered earlier by Samuelsson and Büttiker, the entanglement production is much less than 1 bit per cycle. We demonstrate that a strong potential oscillation can produce an average of one Bell pair per two cycles, making it an efficient source of entangled flying qubits.

How irrelevant operators affect the determination of fractional charge.

We show that the inclusion of irrelevant terms in the Hamiltonian describing tunneling between edge states in the fractional quantum Hall effect can lead to a variety of nonperturbative behaviors in intermediate energy regimes and, in particular, affect crucially the determination of charge through shot noise measurements. We show, for instance, that certain combinations of relevant and irrelevant terms can lead to an effective measured charge nue in the strong backscattering limit and an effective measured charge e in the weak backscattering limit, in sharp contrast with standard perturbative expectations. This provides a possible scenario to explain the experimental observations by Comforti et al. [Nature (London) 416, 515 (2002)]], which are so far not understood.

Landauer-type transport theory for interacting quantum wires: application to carbon nanotube y junctions.

We propose a Landauerlike theory for nonlinear transport in networks of one-dimensional interacting quantum wires (Luttinger liquids). A concrete example of current experimental focus is given by carbon nanotube Y junctions. Our theory has three basic ingredients that allow one to explicitly solve this transport problem: (i) radiative boundary conditions to describe the coupling to external leads, (ii) the Kirchhoff node rule describing charge conservation, and (iii) density matching conditions at every node.

Coulomb drag shot noise in coupled Luttinger liquids.

Coulomb drag shot noise has been studied theoretically for 1D interacting electron systems, which are realized, e.g., in single-wall nanotubes. We show that under adiabatic coupling to external leads, the Coulomb drag shot noise of two coupled or crossed nanotubes contains surprising effects, in particular, a complete locking of the shot noise in the tubes. In contrast to Coulomb drag of the average current, the noise locking is based on a symmetry of the underlying Hamiltonian and is not limited to asymptotically small energy scales.