Manuel Houzet

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.

Current-current correlations in hybrid superconducting and normal-metal multiterminal structures

We consider a hybrid system consisting of two normal metal leads weakly connected to a superconductor. Current-current correlations of the normal leads are studied in the tunneling limit at subgap voltages and temperatures. We find that only two processes contribute to the cross-correlation: the crossed Andreev reflection (emission of electrons in different leads) and the elastic cotunneling. Both processes are possible due to the finite size of the Cooper pair. Noise measurements can thus be used to probe directly the superconducting wave function without the drawbacks appearing in average current measurements where the current is dominated by direct Andreev reflection processes. By tuning the voltages it is possible to change the sign of the cross-correlation. Quantitative predictions are presented both in the diffusive and ballistic regimes.

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.

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.

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.

In-plane magnetic field anisotropy of the Fulde-Ferrell-Larkin-Ovchinnikov state in layered superconductors.

There is strong experimental evidence of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state formation in layered organic superconductors in a parallel magnetic field. We study theoretically the interplay between the orbital effect and the FFLO modulation in this case and demonstrate that the in-plane critical field anisotropy drastically changes at the transition to the FFLO state. The very peculiar angular dependence of the superconducting onset temperature which is predicted may serve for unambiguous identification of the FFLO modulation. The obtained results permit us to suggest the modulated phase stabilization as the origin of the magnetic-field angle dependence of the onset of superconductivity experimentally observed in (TMTSF)2ClO4 organic conductors.

Theory of domain-wall superconductivity in superconductor/ferromagnet bilayers

We analyze the enhancement of the superconducting critical temperature of superconducting/ferromagnetic bilayers due to the appearance of localized superconducting states in the vicinity of magnetic domain walls in the ferromagnet. We consider the case when the main mechanism of the superconductivity destruction via the proximity effect is the exchange field. We demonstrate that the influence of the domain walls on the superconducting properties of the bilayer may be quite strong if the domain-wall thickness is of the order of the superconducting coherence length.

Topological Josephson phi0-junctions

We study the effect of amagnetic field on the current-phase relation of a topological Josephson junction formed by connecting two superconductors through the helical edge states of a quantum spin-Hall insulator. We predict that the Zeeman effect along the spin quantization axis of the helical edges results in an anomalous Josephson relation that allows for a supercurrent to flow in the absence of superconducting phase bias. We relate the associated field-tunable phase shift phi(0) in the Josephson relation of such a phi(0) junction to the existence of a so-called helical superconductivity, which may result from the interplay of the Zeeman effect and spin-orbit coupling. We analyze the dependence of the magneto-supercurrent on the junction length and discuss its observability in suitably designed hybrid structures subject to an in-plane magnetic field.

Ac Josephson effect in topological Josephson junctions

Abstract Topological superconductors admit zero-energy Majorana bound states at their boundaries. In this review article, we discuss how to probe these Majorana bound states in Josephson junctions between two topological superconductors. In the absence of an applied bias, the presence of these states gives rise to an Andreev bound state whose energy varies 4π-periodically in the superconducting phase difference. An applied voltage bias leads to a dynamically varying phase according to the Josephson relation. Furthermore, it leads to dynamics of the occupation of the bound state via its non-adiabatic coupling to the continuum. While the Josephson relation suggests a fractional Josephson effect due to the 4π-periodicity of the bound state, its observability relies on the conservation of the occupation of the bound state on the experimentally probed time scale. We study the lifetime of the bound state and identify the time scales it has to be compared to. In particular, we are interested in signatures of the fractional Josephson effect in the Shapiro steps and in current noise measurements. We also discuss manifestations of the zero-energy Majorana states on the dissipative subgap current.

Interplay of paramagnetic, orbital, and impurity effects on the phase transition of a normal metal to the superconducting state

We derive the generalized Ginzburg-Landau free energy functional for conventional and unconventional singlet superconductors in the presence of paramagnetic, orbital and impurity effects. Within the mean field theory, we determine the criterion for appearence of the non uniform (Fulde-Ferrell-Larkin-Ovchinnikov) superconducting state, with vortex lattice structure and additional modulation along the magnetic field. We also discuss the possible change of the order of transition from normal to superconducting state. We find that the superconducting phase diagram is very sensitive to geometrical effects such as the nature of the order parameter and the shape of the Fermi surface. In particular, we obtain the qualitative phase diagrams for three-dimensional isotropic s-wave superconductors and in quasi two-dimensional d-wave superconductors under magnetic field perpendicular to the conducting layers. In addition, we determine the criterion for instability toward non uniform superconducting state in s-wave superconductors in the dirty limit.