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.

Microwave Spectroscopy of a Weakly Pinned Charge Density Wave in a Superinductor.

A chain of small Josephson junctions (a.k.a. superinductor) emerged recently as a high-inductance, low-loss element of superconducting quantum devices. We notice that the intrinsic parameters of a typical superinductor in fact place it into the Bose glass universality class for which the propagation of waves in a sufficiently long chain is hindered by pinning. Its weakness provides for a broad crossover from the spectrum of well-resolved plasmon standing waves at high frequencies to the low-frequency excitation spectrum of a pinned charge density wave. We relate the scattering amplitude of microwave photons reflected off a superinductor to the dynamics of a Bose glass. The dynamics at long and short scales compared to the Larkin pinning length determines the low- and high-frequency asymptotes of the reflection amplitude.

Coulomb Blockade of a Nearly Open Majorana Island.

We consider the ground-state energy and the spectrum of the low-energy excitations of a Majorana island formed of topological superconductors connected by a single-mode junction of arbitrary transmission. Coulomb blockade results in e-periodic modulation of the energies with the gate-induced charge. We find the amplitude of modulation as a function of reflection coefficient R. The amplitude scales as sqrt[R] in the limit R→0. At larger R, the dependence of the amplitude on the Josephson and charging energies is similar to that of a conventional-superconductor Cooper-pair box. The crossover value of R is small and depends on the ratio of the charging energy to superconducting gap.

Enhancement of the Upper Critical Field in Disordered Transition Metal Dichalcogenide Monolayers.

We calculate the effect of impurities on the superconducting phase diagram of transition metal dichalcogenide monolayers in the presence of an in-plane magnetic field. Because of strong intrinsic spin-orbit coupling, the upper critical field greatly surpasses the Pauli limit at low temperatures. We find that it is insensitive to intravalley scattering and, ultimately, limited by intervalley scattering.

Nontrivial Chern Numbers in Three-Terminal Josephson Junctions.

Recently, it has been predicted that the Andreev bound state spectrum of four-terminal Josephson junctions may possess zero-energy Weyl singularities. Using one superconducting phase as a control parameter, these singularities are associated with topological transitions between time-reversal symmetry broken phases with different Chern numbers. Here we show that such topological transitions may also be tuned with a magnetic flux through the junction area in a three-terminal geometry.

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.

Spin-resolved Andreev levels and parity crossings in hybrid superconductor-semiconductor nanostructures.

The physics and operating principles of hybrid superconductor-semiconductor devices rest ultimately on the magnetic properties of their elementary subgap excitations, usually called Andreev levels. Here we report a direct measurement of the Zeeman effect on the Andreev levels of a semiconductor quantum dot with large electron g-factor, strongly coupled to a conventional superconductor with a large critical magnetic field. This material combination allows spin degeneracy to be lifted without destroying superconductivity. We show that a spin-split Andreev level crossing the Fermi energy results in a quantum phase transition to a spin-polarized state, which implies a change in the fermionic parity of the system. This crossing manifests itself as a zero-bias conductance anomaly at finite magnetic field with properties that resemble those expected for Majorana modes in a topological superconductor. Although this resemblance is understood without evoking topological superconductivity, the observed parity transitions could be regarded as precursors of Majorana modes in the long-wire limit.

Dynamics of Majorana states in a topological Josephson junction.

Topological Josephson junctions carry 4π-periodic bound states. A finite bias applied to the junction limits the lifetime of the bound state by dynamically coupling it to the continuum. Another characteristic time scale, the phase adjustment time, is determined by the resistance of the circuit "seen" by the junction. We show that the 4π periodicity manifests itself by an even-odd effect in Shapiro steps only if the phase adjustment time is shorter than the lifetime of the bound state. The presence of a peak in the current noise spectrum at half the Josephson frequency is a more robust manifestation of the 4π periodicity, as it persists for an arbitrarily long phase adjustment time. We specify, in terms of the circuit parameters, the conditions necessary for observing the manifestations of 4π periodicity in the noise spectrum and Shapiro step measurements.

Superharmonic long-range triplet current in a diffusive Josephson junction.

We study the Josephson current through a long ferromagnetic bilayer in the diffusive regime. For noncollinear magnetizations, we find that the current-phase relation is dominated by its second harmonic, which corresponds to the long-range coherent propagation of two triplet pairs of electrons.

Inelastic microwave photon scattering off a quantum impurity in a Josephson-junction array.

Quantum fluctuations in an anharmonic superconducting circuit enable frequency conversion of individual incoming photons. This effect, linear in the photon beam intensity, leads to ramifications for the standard input-output circuit theory. We consider an extreme case of anharmonicity in which photons scatter off a small set of weak links within a Josephson junction array. We show that this quantum impurity displays Kondo physics and evaluate the elastic and inelastic photon scattering cross sections. These cross sections reveal many-body properties of the Kondo problem that are hard to access in its traditional fermionic version.

Andreev current induced by ferromagnetic resonance.

We study charge transport through a metallic dot coupled to a superconducting and a ferromagnetic lead with a precessing magnetization due to ferromagnetic resonance. Using the quasiclassical theory, we find that the magnetization precession induces a dc current in the subgap regime even in the absence of a bias voltage. This effect is due to the rectification of the ac spin currents at the interface with the ferromagnet; it exists in the absence of spin current in the superconductor. When the dot is strongly coupled to the superconductor, we find a strong enhancement in a wide range of parameters as compared to the induced current in the normal state.

Nonequilibrium Josephson effect through helical edge states.

We study Josephson junctions between superconductors connected through the helical edge states of a two-dimensional topological insulator in the presence of a magnetic barrier. As the equilibrium Andreev bound states of the junction are 4π periodic in the superconducting phase difference, it was speculated that, at finite dc bias voltage, the junction exhibits a fractional Josephson effect with half the Josephson frequency. Using the scattering matrix formalism, we show that his effect is absent in the average current. However, clear signatures can be seen in the finite-frequency current noise. Furthermore, we discuss other manifestations of the Majorana bound states forming at the edges of the superconductors.

Cross correlation of incoherent multiple Andreev reflections.

We use a semiclassical theory to calculate the current correlations in a multiterminal structure composed of a normal metallic dot connected to all superconducting leads at arbitrary voltage and temperature. This theory holds when the proximity effect is suppressed in the dot. At low voltage, eV<

Persistent currents in one dimension: the counterpart of Leggett's theorem.

We discuss the sign of the persistent current of N electrons in one dimensional rings. Using a topology argument, we establish lower bounds for the free energy in the presence of arbitrary electron-electron interactions and external potentials. Those bounds are the counterparts of upper bounds derived by Leggett. Rings with odd (even) numbers of polarized electrons are always diamagnetic (paramagnetic). We show that unpolarized electrons with N being a multiple of four exhibit either paramagnetic behavior or a superconductorlike current-phase relation.

Ferromagnetic Josephson junction with precessing magnetization.

The Josephson current in a diffusive superconductor-ferromagnet-superconductor junction with precessing magnetization is calculated within the quasiclassical theory of superconductivity. When the junction is phase biased, a stationary current (without ac component) can flow through it despite the nonequilibrium condition. A large critical current is predicted due to a dynamically induced long range triplet proximity effect. Such an effect could be observed in a conventional hybrid device close to the ferromagnetic resonance.