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. The full counting statistics of joint detection allows us to explore the interaction-mediated energy exchange. We observe an increase from 50% up to 70% in coincidence counts between statistically indistinguishable on-demand sources and a correlation signature consistent with the independent tomography of the electron emission. Analytical modelling and numerical simulations underpin the consistency of the experimental results with Coulomb interactions between two electrons counterpropagating in a quadratic saddle potential. Coulomb repulsion energy and beam splitter dispersion define a figure of merit, which in this experiment is demonstrated to be sufficiently large to enable future applications, such as single-shot in-flight detection and quantum logic gates.

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. junctions where the junction length exceeds the superconducting coherence length, TJJs manifest themselves in specific features of the critical current (Beenakker 2013Phys. Rev. Lett.110017003). Here we propose to couple the helical edge states mediating the TJJ to additional channels or quantum dots, by which the effective junction length can be increased by tunable parameters associated with these couplings, so that such measurements become possible even in short junctions. Besides effective low-energy models that we treat analytically, we investigate realizations by a Kane-Mele model with edge passivation and treat them numerically via tight binding models. In each case, we explicitly calculate the critical current using the Andreev bound state spectrum and show that it differs in effectively long junctions in the cases of strong and weak parity changing perturbations (quasiparticle poisoning).

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. While the MBSs rotate, electron tunneling happens from the tip to one of the MBSs thereby changing the fermion parity of the MBSs. The tunneling events in combination with the rotation allow us to identify a novel braiding operator that does not commute with the braiding cycles in the absence of tunneling, revealing the non-Abelian nature of MBSs. The time-averaged tunneling current exhibits resonances as a function of the tip voltage with a period that is a direct consequence of the interference between the noncommuting braiding operations. Our work opens up a possibility for utilizing parity nonconserving processes to control non-Abelian states.

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. However, upon applying a finite voltage bias smaller than the superconducting gap to a relatively long junction, the finite-frequency interference pattern in the nonequilibrium transport current is qualitatively different for helical edge states as compared to nonhelical ones.

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. This result constitutes a clear experimental signature of Majorana fermion exchange.

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. When injecting into each TLL one electron of opposite spin, the dc current measured after the crossing differs for singlet, triplet, or product states. This is a striking new non-Fermi liquid feature because the (mean) current in a noninteracting beam splitter is insensitive to spin entanglement. It can be understood in terms of collective excitations subject to spin-charge separation. This behavior may offer an easier alternative to traditional entanglement detection schemes based on current noise, which we show to be suppressed by the interactions.

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. Moreover, we show that the spatial separation of both effects allows for an all-electrical measurement of CAR and T separately in a five-terminal setup or by using the spin selection of the quantum spin Hall effect in an H-bar structure.

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. Because of the robustness against disorder and moderate changes to the system, this provides a clear signature to distinguish both types of Andreev reflection processes in graphene.

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. We further demonstrate that this result remains valid when Coulomb interaction is included in the framework of a helical Tomonaga Luttinger liquid.

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. However, the small spin-orbit interaction is also a limitation for the design of conventional devices based on the canonical Datta-Das spin field-effect transistors. An alternative solution can be found in magnetic doping of graphene or, as discussed in the present work, in exploiting the proximity effect between graphene and ferromagnetic oxides (FOs). Graphene in proximity to FO experiences an exchange proximity interaction, that acts as an effective Zeeman field for electrons in graphene, inducing a spin precession around the magnetization axis of the FO. Here we show that in an appropriately designed double-gate field-effect transistor, with a bilayer graphene channel and FO used as a gate dielectric, spin-precession of carriers can be turned ON and OFF with the application of a differential voltage to the gates. This feature is directly probed in the spin-resolved conductance of the bilayer.

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. We calculate the bound states for three different quantum dot architectures where a bulk gap allows for confinement via electrostatic fields: (i) graphene nanoribbons with armchair boundaries, (ii) a disc in single-layer graphene, and (iii) a disc in bilayer graphene. In order for graphene quantum dots to be useful in the context of spin qubits, one needs to find reliable ways to break the valley degeneracy. This is achieved here, either by a specific termination of graphene in (i) or in (ii) and (iii) by a magnetic field, without the need of a specific boundary. We further discuss how to manipulate spin in these quantum dots and explain the mechanism of spin decoherence and relaxation caused by spin-orbit interaction in combination with electron-phonon coupling, and by hyperfine interaction with the nuclear-spin system.

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. At energies close to the applied bias voltage eV(sd), a parameter range exists, where radiation proceeds in pairwise emission of polarization correlated photons. At energies close to 2eV(sd), emitted photons are associated with Cooper pair transfer and are reminiscent of Josephson radiation. We discuss how to probe the coherence of these photons in a SQUID geometry via single-photon interference.

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. The dynamics of the electrons in this potential are described by a Hubbard model with long-range Coulomb interactions. Estimates of the Hubbard parameters suggest that observations of quantum phase transition phenomena are within experimental reach.

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.

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). The triple dot is placed between two superconducting leads. Under realistic conditions, the main proximity effect stems from the injection of resonating singlet (valence) bonds on the triple dot. This gives rise to a Josephson current that is charge- and spin-dependent and, as a consequence, exhibits a distinct resonance as a function of the superconducting phase difference.

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.