Supercurrent in the Presence of Direct Transmission and a Resonant Localized State.

We study the current-phase relation (CPR) of an InSb-Al nanowire Josephson junction in parallel magnetic fields up to 700 mT. At high magnetic fields and in narrow voltage intervals of a gate under the junction, the CPR exhibits π shifts. The supercurrent declines within these gate intervals and shows asymmetric gate voltage dependence above and below them. We detect these features sometimes also at zero magnetic field. The observed CPR properties are reproduced by a theoretical model of supercurrent transport via interference between direct transmission and a resonant localized state.

Braiding and All Quantum Operations with Majorana Modes in 1D.

We propose a scheme to perform braiding and all other unitary operations with Majorana modes in one dimension that, in contrast to previous proposals, is solely based on resonant manipulation involving the first excited state extended over the modes. The detection of the population of the excited state also enables initialization and read-out. We provide an elaborated illustration of the scheme with a concrete device.

Dynamical Spin Polarization of Excess Quasiparticles in Superconductors.

We show that the annihilation dynamics of excess quasiparticles in superconductors may result in the spontaneous formation of large spin-polarized clusters. This presents a novel scenario for spontaneous spin polarization. We estimate the relevant scales for aluminum, finding the feasibility of clusters with total spin S≃10^{4}ℏ that could be spread over microns. The fluctuation dynamics of such large spins may be detected by measuring the flux noise in a loop hosting a cluster.

Supercurrents in Unidirectional Channels Originate from Information Transfer in the Opposite Direction: A Theoretical Prediction.

It has been thought that the long chiral edge channels cannot support any supercurrent between the superconducting electrodes. We show theoretically that the supercurrent can be mediated by a nonlocal interaction that facilitates a long-distance information transfer in the direction opposite of electron flow. We compute the supercurrent for several interaction models, including that of an external circuit.

Theoretical Model to Explain Excess of Quasiparticles in Superconductors.

Experimentally, the concentration of quasiparticles in gapped superconductors always largely exceeds the equilibrium one at low temperatures. Since these quasiparticles are detrimental for many applications, it is important to understand theoretically the origin of the excess. We demonstrate in detail that the dynamics of quasiparticles localized at spatial fluctuations of the gap edge becomes exponentially slow. This gives rise to the observed excess in the presence of a vanishingly weak nonequilibrium agent.

Multi-terminal Josephson junctions as topological matter.

Topological materials and their unusual transport properties are now at the focus of modern experimental and theoretical research. Their topological properties arise from the bandstructure determined by the atomic composition of a material and as such are difficult to tune and naturally restricted to ≤3 dimensions. Here we demonstrate that n-terminal Josephson junctions with conventional superconductors may provide novel realizations of topology in n-1 dimensions, which have similarities, but also marked differences with existing 2D or 3D topological materials. For n≥4, the Andreev subgap spectrum of the junction can accommodate Weyl singularities in the space of the n-1 independent superconducting phases, which play the role of bandstructure quasimomenta. The presence of these Weyl singularities enables topological transitions that are manifested experimentally as changes of the quantized transconductance between two voltage-biased leads, the quantization unit being 4e(2)/h, where e is the electric charge and h is the Planck constant.

Control of Andreev bound state population and related charge-imbalance effect.

Motivated by recent experimental research, we study a superconducting constriction subject to a dc and ac phase bias. We consider the processes whereby the ac drive promotes one quasiparticle from an Andreev bound state to a delocalized state outside the superconducting gap. We demonstrate that with these processes one can control the population of the Andreev bound states in the constriction. We stress an interesting charge asymmetry of these processes that may produce a charge imbalance of accumulated quasiparticles, which depends on the phase.

Quantum phase slips in superconducting wires with weak inhomogeneities.

Quantum phase slips are traditionally considered in diffusive superconducting wires which are assumed homogeneous. We present a definite estimate for the amplitude of phase slips that occur at a weak inhomogeneity in the wire where local resistivity is slightly increased. We model such a weak link as a general coherent conductor and show that the amplitude is dominated by the topological part of the action. We argue that such weak links occur naturally in apparently homogeneous wires and adjust the estimate to that case. The fabrication of an artificial weak link would localize phase slips and facilitate a better control of the phase-slip amplitude.

Manifestly non-Gaussian fluctuations in superconductor-normal metal tunnel nanostructures.

We propose a mesoscopic setup which exhibits strong and manifestly non-Gaussian fluctuations of energy and temperature when suitably driven out of equilibrium. The setup consists of a normal metal island (N) coupled by tunnel junctions (I) to two superconducting leads (S), forming a SINIS structure, and is biased near the threshold voltage for quasiparticle tunneling, eV≈2Δ. The fluctuations can be measured by monitoring the time-dependent electric current through the system. This makes the setup suitable for the realization of feedback schemes which can be used to stabilize the temperature to the desired value.

Proposal for an optical laser producing light at half the Josephson frequency.

We describe a superconducting device capable of producing laser light in the visible range at half of the Josephson generation frequency with the optical phase of the light locked to the superconducting phase difference. It consists of two single-level quantum dots embedded in a p-n semiconducting heterostructure and surrounded by a cavity supporting a resonant optical mode. We study decoherence and spontaneous switching in the device.

Fully overheated single-electron transistor.

We consider the fully overheated single-electron transistor, where the heat balance is determined entirely by electron transfers. We find three distinct transport regimes corresponding to cotunneling, single-electron tunneling, and a competition between the two. We find an anomalous sensitivity to temperature fluctuations at the crossover between the two latter regimes that manifests in an exceptionally large Fano factor of current noise.

Quantum manipulation in a Josephson light-emitting diode.

We assess the suitability of the recently proposed Josephson LED for quantum manipulation purposes. We show that the device can both be used for on-demand production of entangled photon pairs and operated as a two-qubit gate. Also, one can entangle particle spin with photon polarization and/or measure the spin by measuring the polarization.

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.

Statistics of temperature fluctuations in an electron system out of equilibrium.

We study the statistics of the fluctuating electron temperature in a metallic island coupled to reservoirs via resistive contacts and driven out of equilibrium by either a temperature or voltage difference between the reservoirs. The fluctuations of temperature are well defined provided that the energy relaxation rate inside the island exceeds the rate of energy exchange with the reservoirs. We quantify these fluctuations in the regime beyond the Gaussian approximation and elucidate their dependence on the nature of the electronic contacts.

Nuclear tuning and detuning of the electron spin resonance in a quantum dot: theoretical consideration.

We study nuclear spin dynamics in a quantum dot close to the conditions of electron spin resonance. We show that at a small frequency mismatch, the nuclear field detunes the resonance. Remarkably, at larger frequency mismatch, its effect is opposite: The nuclear system is bistable, and in one of the stable states, the field accurately tunes the electron spin splitting to resonance. In this state, the nuclear field fluctuations are strongly suppressed, and nuclear spin relaxation is accelerated.

Elementary events of electron transfer in a voltage-driven quantum point contact.

We find that the statistics of electron transfer in a coherent quantum point contact driven by an arbitrary time-dependent voltage is composed of elementary events of two kinds: unidirectional one-electron transfers determining the average current and bidirectional two-electron processes contributing to the noise only. This result pertains at vanishing temperature while the extended Keldysh-Green's function formalism in use also enables the systematic calculation of the higher-order current correlators at finite temperatures.

Supercurrent reversal in quantum dots.

When two superconductors are electrically connected by a weak link--such as a tunnel barrier--a zero-resistance supercurrent can flow. This supercurrent is carried by Cooper pairs of electrons with a combined charge of twice the elementary charge, e. The 2e charge quantum is clearly visible in the height of voltage steps in Josephson junctions under microwave irradiation, and in the magnetic flux periodicity of h/2e (where h is Planck's constant) in superconducting quantum interference devices. Here we study supercurrents through a quantum dot created in a semiconductor nanowire by local electrostatic gating. Owing to strong Coulomb interaction, electrons only tunnel one-by-one through the discrete energy levels of the quantum dot. This nevertheless can yield a supercurrent when subsequent tunnel events are coherent. These quantum coherent tunnelling processes can result in either a positive or a negative supercurrent, that is, in a normal or a pi-junction, respectively. We demonstrate that the supercurrent reverses sign by adding a single electron spin to the quantum dot. When excited states of the quantum dot are involved in transport, the supercurrent sign also depends on the character of the orbital wavefunctions.

Electron transport in a double quantum dot governed by a nuclear magnetic field.

We investigate theoretically electron transfer in a double dot in a situation where spin blockade is lifted by nuclear magnetic field: this has been recently achieved in experiment [F. Koppens, Science 309, 1346 (2005)]. We show that for a given realization of nuclear magnetic field spin blockade can be restored by tuning external magnetic field; this may be useful for quantum manipulation of the device.

Full counting statistics with spin-sensitive detectors reveals spin singlets.

We study the full counting statistics of electric current to several drain terminals with spin-dependent entrance conductances. We show that the statistics of charge transfers can be interpreted in terms of single electrons and spin-singlet pairs coming from the source. If the source contains transport channels of high transparency, a significant fraction of electrons comes in spin-singlet pairs.