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We develop a theory of charge transport along the quantum Hall edge proximitized by a superconductor. We note that generically Andreev reflection of an edge state is suppressed if translation invariance along the edge is preserved. Disorder in a “dirty” superconductor enables the Andreev reflection but makes it random. As a result, the conductance of a proximitized segment is a stochastic quantity with giant sign-alternating fluctuations and zero average. We find the statistical distribution of the conductance and its dependence on electron density, magnetic field, and temperature. Our theory provides an explanation of a recent experiment with a proximitized edge state. The properties of edge states at the boundary between a quantum Hall insulator and a superconductor have recently been under scrutiny. Here, the authors find theoretically that Andreev reflection of an edge state is possible only if the superconductor is in the disordered limit, leading to stochastic edge state conductance and providing an explanation of a recent experiment.

One-dimensional quantum fluids are conventionally described by using an effective hydrodynamic approach known as Luttinger liquid theory. As the principal simplification, a generic spectrum of the constituent particles is replaced by a linear one, which leads to a linear hydrodynamic theory. We show that to describe the measurable dynamic response functions one needs to take into account the nonlinearity of the generic spectrum and thus of the resulting quantum hydrodynamic theory. This nonlinearity leads, for example, to a qualitative change in the behavior of the spectral function. The universal theory developed in this article is applicable to a wide class of one-dimensional fermionic, bosonic, and spin systems.

The tuneability and control of quantum nanostructures in two-dimensional materials offer promising perspectives for their use in future electronics. It is hence necessary to analyze quantum transport in such nanostructures. Material properties such as a complex dispersion, topology, and charge carriers with multiple degrees of freedom, are appealing for novel device functionalities but complicate their theoretical description. Here, we study quantum tunnelling transport across a few-electron bilayer graphene quantum dot. We demonstrate how to uniquely identify single- and two-electron dot states’ orbital, spin, and valley composition from differential conductance in a finite magnetic field. Furthermore, we show that the transport features manifest splittings in the dot’s spin and valley multiplets induced by interactions and magnetic field (the latter splittings being a consequence of bilayer graphene’s Berry curvature). Our results elucidate spin- and valley-dependent tunnelling mechanisms and will help to utilize bilayer graphene quantum dots, e.g., as spin and valley qubits.

The promise of single Cooper-pair quantum circuits based on tunnel junctions for metrology and quantum information applications is severely limited by the influence of offset charges: random, slowly drifting microscopic charges inherent in many solid-state systems. By shunting a small junction with the Josephson kinetic inductance of a series array of large-capacitance tunnel junctions, thereby ensuring that all superconducting islands are connected to the circuit by at least one large junction, we have realized a new superconducting artificial atom that is totally insensitive to offset charges. Yet its energy levels manifest the anharmonic structure associated with single Cooper-pair effects, a useful component for solid-state quantum computation.

A transmon qubit embedded in a high-impedance environment acts in a way dual to a conventional Josephson junction. In analogy to the AC Josephson effect, biasing of the transmon by a direct current leads to the oscillations of voltage across it. These oscillations are known as the Bloch oscillations. We find the Bloch oscillations spectrum, and show that the zero-point fluctuations of charge make it broadband. Despite having a broad-band spectrum, Bloch oscillations can be brought in resonance with an external microwave radiation. The resonances lead to steps in the voltage-current relation, which are dual to the conventional Shapiro steps. We find how the shape of the steps depends on the environment impedance R , parameters of the transmon, and the microwave amplitude. The Bloch oscillations rely on the insulating state of the transmon which is realized at impedances exceeding the Schmid transition point, R  >  R Q  =  h /(2 e ) 2 . When a Josephson junction is embedded into a highly-resistive environment, it loses its superconducting properties and starts to behave as an insulator. This results in voltage oscillations across the current-biased junction - the Bloch oscillations. Here the authors develop a fully quantum theory of this effect.

The lifetime of plasmonic excitations in semiconducting carbon nanotubes is found to strongly depend on the carrier density, offering a platform to study non-conventional one-dimensional electron dynamics and realize integrated nanophotonic devices.

Even though bulk metallic systems contain a very large number of strongly interacting electrons, their properties are well described within Landau's Fermi liquid theory of non-interacting quasiparticles. Although many higher-dimensional systems can be successfully understood on the basis of such non-interacting theories, this is not possible for one-dimensional systems. When confined to narrow channels, electron interaction gives rise to such exotic phenomena as spin–charge separation and the emergence of correlated-electron insulators. Such strongly correlated electronic behaviour has recently been seen in experiments on one-dimensional carbon nanotubes and nanowires, and this behaviour challenges the theoretical description of such systems.

The superconducting proximity effect in semiconductor nanowires has recently enabled the study of new superconducting architectures, such as gate-tunable superconducting qubits and multiterminal Josephson junctions. As opposed to their metallic counterparts, the electron density in semiconductor nanosystems is tunable by external electrostatic gates, providing a highly scalable and in situ variation of the device properties. In addition, semiconductors with large g -factor and spin–orbit coupling have been shown to give rise to exotic phenomena in superconductivity, such as φ 0 Josephson junctions and the emergence of Majorana bound states. Here, we report microwave spectroscopy measurements that directly reveal the presence of Andreev bound states (ABS) in ballistic semiconductor channels. We show that the measured ABS spectra are the result of transport channels with gate-tunable, high transmission probabilities up to 0.9, which is required for gate-tunable Andreev qubits and beneficial for braiding schemes of Majorana states. For the first time, we detect excitations of a spin-split pair of ABS and observe symmetry-broken ABS, a direct consequence of the spin–orbit coupling in the semiconductor. Andreev bound states in semiconductor–superconductor hybrid structures are studied using microwave spectroscopy — a tool that could be also used for investigating Majorana modes.

The long-predicted suppression of quasiparticle dissipation in a Josephson junction when the phase difference across the junction is π is inferred from a sharp maximum in the energy relaxation time of a superconducting artificial atom. Quasiparticle dissipation in a Josephson junction Josephson junctions, which consist of two superconductors connected by a weak link, have a central role in quantum electronic applications, such as in sensitive magnetic field detectors, high-speed processing and quantum information networks. However, a fundamental prediction concerning the Josephson effect has not yet been confirmed. It is known that the current flowing through a Josephson junction is made up from superconducting Cooper pairs as well as excitations called quasiparticles, which contribute in a few different ways. One contribution causes dissipation but can in theory be suppressed by tuning the phase difference between the superconductors. This has been achieved experimentally. Ioan Pop et al . have made a qubit comprising a Josephson junction. The energy relaxation time of this qubit increases by almost two orders of magnitude owing to the suppression of quasiparticle dissipation. This finding confirms the existence of a fundamental quantum phenomenon predicted over 50 years ago. Owing to the low-loss propagation of electromagnetic signals in superconductors, Josephson junctions constitute ideal building blocks for quantum memories, amplifiers, detectors and high-speed processing units, operating over a wide band of microwave frequencies. Nevertheless, although transport in superconducting wires is perfectly lossless for direct current, transport of radio-frequency signals can be dissipative in the presence of quasiparticle excitations above the superconducting gap 1 . Moreover, the exact mechanism of this dissipation in Josephson junctions has never been fully resolved experimentally. In particular, Josephson’s key theoretical prediction that quasiparticle dissipation should vanish in transport through a junction when the phase difference across the junction is π (ref. 2 ) has never been observed 3 . This subtle effect can be understood as resulting from the destructive interference of two separate dissipative channels involving electron-like and hole-like quasiparticles. Here we report the experimental observation of this quantum coherent suppression of quasiparticle dissipation across a Josephson junction. As the average phase bias across the junction is swept through π, we measure an increase of more than one order of magnitude in the energy relaxation time of a superconducting artificial atom. This striking suppression of dissipation, despite the presence of lossy quasiparticle excitations above the superconducting gap, provides a powerful tool for minimizing decoherence in quantum electronic systems and could be directly exploited in quantum information experiments with superconducting quantum bits.

The long-predicted suppression of quasiparticle dissipation in a Josephson junction when the phase difference across the junction is [pi] is inferred from a sharp maximum in the energy relaxation time of a superconducting artificial atom.