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We investigate plasma oscillations in long electromagnetically coupled superconducting nanowires. We demonstrate that in the presence of inter-wire coupling plasma modes in each of the wires get split into two “new” modes propagating with different velocities across the system. These plasma modes form an effective dissipative quantum environment interacting with electrons inside both wires and causing a number of significant implications for the low-temperature behavior of the systems under consideration.

We theoretically investigate non-local fluctuation effects in a system of two capacitively coupled superconducting nanowires. We demonstrate that quantum phase slips in one of these nanowires induce voltage fluctuations in another one. These fluctuations are characterized by zero average voltage and non-vanishing voltage noise which exhibits a non-trivial behavior as a function of frequency and bias current. It would be interesting to test our predictions in modern experiments with superconducting nanowires.

We develop a detailed theory describing a non-trivial interplay between non-equilibrium effects and long-range quantum coherence in superconducting hybrid nanostructures exposed to a temperature gradient. We establish a direct relation between thermoelectric and Josephson effects in such structures and demonstrate that at temperatures exceeding the Thouless energy of our device both phase-coherent thermoelectric signal and the supercurrent may be strongly enhanced due to non-equilibrium low energy quasiparticles propagating across the system without any significant phase relaxation. By applying a temperature gradient one can drive the system into a well pronounced $\pi$-junction state, thereby creating novel opportunities for applications of Andreev interferometers., Comment: 20 pages, 9 figures

It is widely believed that superconducting junctions involving topological insulators and hosting Majorana-like bound states may exhibit unusual "fractional" ($4\pi$-periodic) ac Josephson effect. Accordingly, "fractional" Shapiro steps on the current-voltage characteristics of such junctions are expected to occur under external microwave radiation. Here, we microscopically evaluate Shapiro steps in topologically trivial highly transparent superconducting weak links. The key features recovered within our analysis -- including, e.g., the so-called "missing" Shapiro steps -- turn out to be similar to those observed in topological Josephson junctions. Our results demonstrate that caution is needed while interpreting experimental results for superconducting weak links in terms of Majorana physics., Comment: 19 pages, 9 figures

We demonstrate that the supercurrent can be strongly enhanced in cross-like superconducting hybrid nanostructures (X-junctions) exposed to a temperature gradient. At temperatures T exceeding the Thouless energy of our X-junction the Josephson current decays algebraically with increasing T and can be further enhanced by a proper choice of the circuit topology. At large values of the temperature gradient the non-equilibrium contribution to the supercurrent may become as large as the equilibrium one at low T. We also predict a variety of transitions between 0- and $\pi$-junction states controlled by the temperature gradient as well as by the system geometry. Our predictions can be directly verified in modern experiments., Comment: 10 pages, 5 figures

We investigate superconductor-insulator quantum phase transitions in ultrathin capacitively coupled superconducting nanowires with proliferating quantum phase slips. We derive a set of coupled Berezinskii-Kosterlitz-Thouless-like renormalization group equations demonstrating that interaction between quantum phase slips in one of the wires gets modified due to the effect of plasma modes propagating in another wire. As a result, the superconductor-insulator phase transition in each of the wires is controlled not only by its own parameters but also by those of the neighboring wire as well as by mutual capacitance. We argue that superconducting nanowires with properly chosen parameters may turn insulating once they are brought sufficiently close to each other., 15 pages, 2 figures

We investigate the influence of quantum phase fluctuations on electron density of states (DOS) in ultrathin superconducting films and nanowires. Using an effective action approach we derive a non-perturbative correction to DOS in such systems. The main effect of phase fluctuations in quasi-two-dimensional films is the appearance of electron states at subgap energies while in quasi-one-dimensional nanowires fluctuations also lead to smearing of the gap edge singularity in DOS.

We work out a unified theory describing both non-local electron transport and cross-correlated shot noise in a three-terminal normal-superconducting-normal (NSN) hybrid nanostructure. We describe noise cross correlations both for subgap and overgap bias voltages and for arbitrary distribution of channel transmissions in NS contacts. We specifically address a physically important situation of diffusive contacts and demonstrate a non-trivial behavior of non-local shot noise exhibiting both positive and negative cross correlations depending on the bias voltages. For this case, we derive a relatively simple analytical expression for cross-correlated noise power which contains only experimentally accessible parameters., 10 pages

The current–voltage characteristics of superconductor–insulator–semiconductor (S1–I–S2) tunnel junctions, where superconducting electrode S2 is a thin nanowire, are studied experimentally. The observed blurring of the gap singularities is interpreted as a manifestation of the order parameter quantum fluctuations. We propose a model taking into account the broadening of the density of states due to the interaction of electrons with the Mooij–Schön plasmon mode emerging in a quasi-one-dimensional superconducting channel in the regime of quantum fluctuations of the order parameter. The model gives results that are in a reasonable qualitative agreement with the experimental data.

We analyze voltage fluctuations in superconducting nanowires with constrictions. We argue that quantum phase slips occurring in the constriction area are responsible for both equilibrium and non-equilibrium voltage noise in such systems. We evaluate the power spectrum of the voltage noise identifying its non-trivial dependence on both frequency and external bias.

We evaluate the frequency spectrum for an intrinsic quantum dissipative environment for the Josephson phase φ formed by subgap Andreev bound states in superconducting weak links. We also analyze the problem of macroscopic quantum tunneling (MQT) of φ in highly transparent weak links and identify several MQT regimes. Within the exponential accuracy, we derive the expression for the supercurrent quantum decay rate both at low temperatures and in the vicinity of the quantum-to-classical crossover.

At low temperatures non-equilibrium voltage fluctuations can be generated in current-biased superconducting nanowires due to proliferation of quantum phase slips (QPS) or, equivalently, due to quantum tunneling of magnetic flux quanta across the wire. In this paper we review and further extend recent theoretical results related to this phenomenon. Employing the phase-charge duality arguments combined with Keldysh path integral technique we analyze such fluctuations within the two-point and four-point measurement schemes demonstrating that voltage noise detected in such nanowires in general depends on the particular measurement setup. In the low frequency limit we evaluate all cumulants of the voltage operator which turn out to obey Poisson statistics and exhibit a power law dependence on the external bias. We also specifically address a non-trivial frequency dependence of quantum shot noise power spectrum S Ω for both longer and shorter superconducting nanowires. In particular, we demonstrate that S Ω decreases with increasing frequency Ω and vanishes beyond a threshold value of Ω at T → 0. Furthermore, we predict that S Ω may depend non-monotonously on temperature due to quantum coherent nature of QPS noise. The results of our theoretical analysis can be directly tested in future experiments with superconducting nanowires.

Superconducting properties of metallic nano-wires may strongly depend on specific experimental conditions. Here we consider a setup where superconducting phase fluctuations are restricted at one point inside the wire and equilibrium supercurrent flows along the wire segment of an arbitrary length $L$. Low temperature physics of this structure is essentially determined, on one hand, by smooth phase fluctuations and, on the other hand, by quantum phase slips. The zero temperature phase diagram is controlled by the wire cross section and consists of a truly superconducting phase and two different phases where superconductivity can be observed only at shorter length scales. One of the latter phases exhibits more robust short-scale superconductivity whereas another one demonstrates a power-law decay of the supercurrent with increasing $L$ already at relatively short scales., Comment: 7 pages, 1 figure

Quasi-one-dimensional superconducting channels host sound-like plasma modes propagating along the sample which are associated with fluctuations of the phase of the superconducting order parameter. Interaction between these electromagnetic excitations and charge carriers affects the electron density of states (DOS). I-V characteristics of tunnel S1-I-S2 junctions, where superconducting S2 electrode is a thin nanowire in the regime of quantum fluctuations have been studied. The observed broadening of the I-V dependencies at the gap edge is interpreted as the renormalization of DOS. The results are in reasonable agreement with the model, taking into consideration plasma modes in quasi-one-dimensional superconductors.

Quantum behavior of superconducting nanowires may essentially depend on the employed experimental setup. Here we investigate a setup that enables passing equilibrium supercurrent across an arbitrary segment of the wire without restricting fluctuations of its superconducting phase. The low temperature physics of the system is determined by a combined effect of collective sound-like plasma excitations and quantum phase slips. At $T=0$ the wire exhibits two quantum phase transitions, both being controlled by the dimensionless wire impedance $g$. While thicker wires with $g>16$ stay superconducting, in thinnest wires with $g, Comment: 8 pages, 2 figures

Continuing miniaturization of electronic devices, together with the quickly growing number of nanotechnological applications, demands a profound understanding of the underlying physics. Most of the fundamental problems of modern condensed matter physics involve various aspects of quantum transport and fluctuation phenomena at the nanoscale. In nanostructures, electrons are usually confined to a limited volume and interact with each other and lattice ions, simultaneously suffering multiple scattering events on impurities, barriers, surface imperfections, and other defects. Electron interaction with other degrees of freedom generally yields two major consequences, quantum dissipation and quantum decoherence. In other words, electrons can lose their energy and ability for quantum interference even at very low temperatures. These two different, but related, processes are at the heart of all quantum phenomena discussed in this book. This book presents copious details to facilitate the understanding of the basic physics behind a result and the learning to technically reproduce the result without delving into extra literature. The book subtly balances the description of theoretical methods and techniques and the display of the rich landscape of the physical phenomena that can be accessed by these methods. It is useful for a broad readership ranging from master’s and PhD students to postdocs and senior researchers.

We analyze a trade-off between thermal activation (TA) and quantum tunneling in the problem of supercurrent decay in superconducting junctions with highly transparent barriers. In such systems – unlike in conventional tunnel junctions – the supercurrent decay is essentially influenced by low energy Andreev levels forming an intrinsic quantum dissipative environment for the Josephson particle. We evaluate the temperature dependent supercurrent decay rate Γ(T) and elucidate a variety of different regimes for such a decay. We demonstrate that no classical-to-quantum crossover exists in the limit of fully transparent barriers, in which case quantum tunneling always prevails over TA.

We argue that at subgap energies quantum behavior of superconducting weak links can be exactly accounted for by an effective Hamiltonian for a Josephson particle in a quantum dissipative environment formed by Andreev levels. This environment can constitute an important source for intrinsic inelastic relaxation and dephasing in highly transparent weak links. We investigate the problem of macroscopic quantum tunneling in such weak links demonstrating that -- depending on the barrier transmission -- the supercurrent decay can be described by three different regimes: ($i$) weak intrinsic dissipation, ($ii$) strong intrinsic dissipation and ($iii$) strong capacitance renormalization. Crossover between quantum and thermally-assisted supercurrent decay regimes can also be strongly affected by the Andreev level environment., Comment: published version, 6 pages, 3 figures

Proximity induced quantum coherence of electrons in multi-terminal voltage-driven hybrid normal-superconducting nanostructures may result in a non-trivial interplay between topology-dependent Josephson and Aharonov-Bohm effects. We elucidate a trade-off between stimulation of the voltage-dependent Josephson current due to non-equilibrium effects and quantum dephasing of quasiparticles causing reduction of both Josephson and Aharonov-Bohm currents. We also predict phase-shifted quantum coherent oscillations of the induced electrostatic potential as a function of the externally applied magnetic flux. Our results may be employed for engineering superconducting nanocircuits with controlled quantum properties.