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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…

Quantum dots attached to BCS superconducting leads exhibit a $0-\pi$ impurity quantum phase transition, which can be experimentally controlled either by the gate voltage or by the superconducting phase difference. For the pertinent…

Topological superconductivity in quasi-one-dimensional systems is a novel phase of matter with possible implications for quantum computation. Despite years of effort, a definitive signature of this phase in experiments is still debated. A…

We theoretically investigate Josephson junctions with a phase shift of $\pi$ in various proximity induced one-dimensional superconductor models. One of the salient experimental signatures of topological superconductors, namely the…

Coherent tunneling processes of multiple Cooper pairs across a Josephson junction give rise to higher harmonics in the current phase relation. In this work, we propose and study Josephson junctions based on…

We study supercurrent and proximity vortices in a Josephson junction made of disordered surface states of a three-dimensional topological insulator with a proximity induced in-plane helical magnetization. In a regime where the rotation…

The coupling of superconductivity to unconventional materials may lead to novel quantum states and potential applications. Controlling the quality of the superconductor-normal metal interface is of crucial importance to the understanding…

We perform supercurrent and tunneling spectroscopy measurements on gate-tunable InAs/Al Josephson junctions (JJs) in an in-plane magnetic field, and report on phase shifts in the current-phase relation measured with respect to an absolute…

The magnetic state of a quantum dot attached to superconducting leads is experimentally shown to be controlled by the superconducting phase difference across the dot. This is done by probing the relation between the Josephson current and…

For Josephson junctions based on s-wave superconductors, time-reversal symmetry is known to allow for powerful relations between the normal-state junction properties, the excitation spectrum, and the Josephson current. Here we provide…

Designing the spatial profile of the superconducting gap -- gap engineering -- has long been recognized as an effective way of controlling quasiparticles in superconducting devices. In aluminum films, their thickness modulates the gap;…

We study phase-controlled planar Josephson junctions comprising a two-dimensional electron gas with strong spin-orbit coupling and d-wave superconductors, which have an advantage of high critical temperature. We show that a region between…

Resistance of a Josephson junction array consisting of randomly distributed lead (Pb) islands on exfoliated single layer graphene shows a broad superconducting transition to zero with an onset temperature close to the transition temperature…

The co-integration of spin, superconducting, and topological systems is emerging as an exciting pathway for scalable and high-fidelity quantum information technology. High-mobility planar germanium is a front-runner semiconductor for…

Setting up strong Josephson coupling in van der Waals materials in close proximity to superconductors offers several opportunities both to inspect fundamental physics and to develop novel cryogenic quantum technologies. Here we show…

A time-periodic drive enables the engineering of non-equilibrium quantum systems by hybridizing Floquet sidebands. We investigated DC voltage-biased planar Josephson junctions built upon epitaxial Al/InAs heterostructures in which the…

Experiments on planar Josephson junction architectures have recently been shown to provide an alternative way of creating topological superconductors hosting accessible Majorana modes. These zero-energy modes can be found at the ends of a…

Intrinsic Rashba spin-orbital coupling (SOC) can exist in centrosymmetric materials with local inversion symmetry breaking. Here we show that such a SOC can induce topological superconductivity together with an in-plane Zeeman field in…

In many cases inhomogeneities are known to exist near the metal (or superconductor)- insulator transition, as follows from well-known domain-wall arguments. If the conducting regions are large enough, and if they have superconducting…

We consider theoretically a Josephson junction with a superconducting critical current density which has a random sign along the junction's surface. We show that the ground state of the junction corresponds to the phase difference equal to…