Two electrons interacting at a mesoscopic beam splitter.

The nonlinear response of a beam splitter to the coincident arrival of interacting particles enables numerous applications in quantum engineering and metrology. Yet, it poses considerable challenges to control interactions on the individual particle level. Here, we probe the coincidence correlations at a mesoscopic constriction between individual ballistic electrons in a system with unscreened Coulomb interactions and introduce concepts to quantify the associated parametric nonlinearity.

Tunable effective length of fractional Josephson junctions.

Topological Josephson junctions (TJJs) have been a subject of widespread interest due to their hosting of Majorana zero modes. In long junctions, i.e.

Electron-Tunneling-Assisted Non-Abelian Braiding of Rotating Majorana Bound States.

It has been argued that fluctuations of fermion parity are harmful for the demonstration of non-Abelian anyonic statistics. Here, we demonstrate a striking exception in which such fluctuations are actively used. We present a theory of coherent electron transport from a tunneling tip into a Corbino geometry Josephson junction where four Majorana bound states (MBSs) rotate.

Superconducting Quantum Interference in Edge State Josephson Junctions.

We study superconducting quantum interference in a Josephson junction linked via edge states in two-dimensional (2D) insulators. We consider two scenarios in which the 2D insulator is either a topological or a trivial insulator supporting one-dimensional (1D) helical or nonhelical edge states, respectively. In equilibrium, we find that the qualitative dependence of critical supercurrent on the flux through the junction is insensitive to the helical nature of the mediating states and can, therefore, not be used to verify the topological features of the underlying insulator.

Detecting the Exchange Phase of Majorana Bound States in a Corbino Geometry Topological Josephson Junction.

A phase from an adiabatic exchange of Majorana bound states (MBS) reveals their exotic anyonic nature. For detecting this exchange phase, we propose an experimental setup consisting of a Corbino geometry Josephson junction on the surface of a topological insulator, in which two MBS at zero energy can be created and rotated. We find that if a metallic tip is weakly coupled to a point on the junction, the time-averaged differential conductance of the tip-Majorana coupling shows peaks at the tip voltages eV=±(α-2πl)ℏ/T_{J}, where α=π/2 is the exchange phase of the two circulating MBS, T_{J} is the half rotation time of MBS, and l an integer.

Detection of spin entanglement via spin-charge separation in crossed Tomonaga-Luttinger liquids.

We investigate tunneling between two spinful Tomonaga-Luttinger liquids (TLLs) realized, e.g., as two crossed nanowires or quantum Hall edge states.

Proposal for an all-electrical detection of crossed Andreev reflection in topological insulators.

Using a generalized wave matching method we solve the full scattering problem for quantum spin Hall insulator-superconductor (SC)-quantum spin Hall insulator junctions. We find that for systems narrow enough so that the bulk states in the SC part couple both edges, the crossed Andreev reflection (CAR) is significant and the electron cotunneling (T) and CAR become spatially separated. We study the effectiveness of this separation as a function of the system geometry and the level of doping in the SC.

Phonon-induced backscattering in helical edge states.

A single pair of helical edge states as realized at the boundary of a quantum spin Hall insulator is known to be robust against elastic single particle backscattering as long as time reversal symmetry is preserved. However, there is no symmetry preventing inelastic backscattering as brought about by phonons in the presence of Rashba spin orbit coupling. In this Letter, we show that the quantized conductivity of a single channel of helical Dirac electrons is protected even against this inelastic mechanism to leading order.

How to distinguish between specular and retroconfigurations for Andreev reflection in graphene rings.

We numerically investigate Andreev reflection in a graphene ring with one normal conducting and one superconducting lead by solving the Bogoliubov-de Gennes equation within the Landauer-Büttiker formalism. By tuning chemical potential and bias voltage, it is possible to switch between regimes where electron and hole originate from the same band (retroconfiguration) or from different bands (specular configuration) of the graphene dispersion, respectively. We find that the dominant contributions to the Aharonov-Bohm conductance oscillations in the subgap transport are of period h/2e in retroconfiguration and of period h/e in specular configuration, confirming the predictions obtained from a qualitative analysis of interfering scattering paths.

Electric field control of spin rotation in bilayer graphene.

The manipulation of the electron spin degree of freedom is at the core of the spintronics paradigm, which offers the perspective of reduced power consumption, enabled by the decoupling of information processing from net charge transfer. Spintronics also offers the possibility of devising hybrid devices able to perform logic, communication, and storage operations. Graphene, with its potentially long spin-coherence length, is a promising material for spin-encoded information transport.

Quantum dots and spin qubits in graphene.

This is a review on graphene quantum dots and their use as a host for spin qubits. We discuss the advantages but also the challenges to use graphene quantum dots for spin qubits as compared to the more standard materials like GaAs. We start with an overview of this young and fascinating field and then discuss gate-tunable quantum dots in detail.

Josephson light-emitting diode.

We consider an optical quantum dot where an electron level and a hole level are coupled to respective superconducting leads. We find that electrons and holes recombine producing photons at discrete energies as well as a continuous tail. Further, the spectral lines directly probe the induced superconducting correlations on the dot.

Tomonaga-Luttinger liquid features in ballistic single-walled carbon nanotubes: conductance and shot noise.

We study the electrical transport properties of well-contacted ballistic single-walled carbon nanotubes in a three-terminal configuration at low temperatures. We observe signatures of strong electron-electron interactions: the conductance exhibits bias-voltage-dependent amplitudes of quantum interference oscillation, and both the current noise and Fano factor manifest bias-voltage-dependent power-law scalings. We analyze our data within the Tomonaga-Luttinger liquid model using the nonequilibrium Keldysh formalism and find qualitative and quantitative agreement between experiment and theory.

Quantum simulator for the hubbard model with long-range coulomb interactions using surface acoustic waves.

An experimental scheme for a quantum simulator of strongly correlated electrons is proposed. Our scheme employs electrons confined in a two-dimensional electron gas in a GaAs/AlGaAs heterojunction. Two surface acoustic waves are then induced in the substrate, creating a two-dimensional "egg-carton" potential.

Mesoscopic resonating valence bond system on a triple dot.

We theoretically introduce a mesoscopic pendulum from a triple dot. The pendulum is fastened through a singly occupied dot (spin qubit). Two other strongly capacitively coupled islands form a double-dot charge qubit with one electron in excess oscillating between the two low-energy charge states (1,0) and (0,1).

Dynamical Coulomb blockade and spin-entangled electrons.

We consider the creation of mobile and nonlocal spin-entangled electrons from tunneling of a BCS-superconductor (SC) to two normal leads of finite resistivity. The resulting dynamical Coulomb blockade effect, which we describe phenomenologically in terms of an electromagnetic environment, is shown to be enhanced for tunneling of two electrons from a Cooper pair into the same lead compared to the desired pair-split process where each electron enters a different lead. Conversely, this latter process is suppressed by a finite separation between the tunneling points on the SC.