Supercurrent in the presence of direct transmission and a resonant localized state


Preprints unpublished

Hristo Barakov, Yuli V. Nazarov

Link to arxiv.org

ABSTRACT: Inspired by recent experimental findings that will be presented elsewhere, we formulate and investigate a model of a superconducting junction that combines the electron propagation in a quantum channel with an arbitrary transmission, and that through a localized state. Interesting situation occurs if the energy of the localized state is close to Fermi level, that is, the state is in resonant tunnelling regime. Since this energy is affected by the gate voltage, we expect a drastic modification of transport properties of the junction in a narrow interval of the gate voltages where the energy distance to Fermi level is of the order of Γ,Δ, Γ being the energy broadening of the localized state, Δ being the superconducting energy gap.
We consider the model neglecting the interaction in the localized state, as well as accounting for the interaction in a simplistic mean-field approach where it manifests itself as a spin-splitting. This spin splitting is also contributed by external magnetic field. We also take into account the spin-orbit interaction that can be significant in realistic experimental circumstances.
In normal state, we find that the model may describe both peak and dip in the transmission at resonant gate voltage. Spin splitting splits the positions of these peculiarities. Fano interference of the transmission amplitudes results in an asymmetric shape of the peaks/dips. In superconducting state, the spin splitting results in a complex dependence of the superconducting current on the superconducting phase. In several cases, this is manifested as a pair of 0−π transitions in the narrow interval of gate voltages.
The article in the present form is not intended for a journal submission.

Abundance of Weyl points in semiclassical multi-terminal superconducting nanostructures


Preprints unpublished

Hristo Barakov, Yuli V. Nazarov

Link to arxiv.org

ABSTRACT: We show that the quasi-continuous gapless spectrum of Andreev bound states in multi-terminal semi-classical superconducting nanostructures exhibits a big number of topological singularities. We concentrate on Weyl points in a 4-terminal nanostructure, compute their density and correlations in 3D parameter space for a universal RMT model as well as for the concrete nanostructures described by the quantum circuit theory. We mention the opportunities for experimental observation of the effect in a quasi-continuous spectrum.

Universal Properties of Mesoscopic Fluctuations of the Secondary “Smile” Gap


Preprints unpublished

Johannes Reutlinger, Leonid I. Glazman, Yuli V. Nazarov, Wolfgang Belzig

Link to arxiv.org

ABSTRACT: The energy levels of a quasi-continuous spectrum in mesoscopic systems fluctuate in positions, and the distribution of the fluctuations reveals information about the microscopic nature of the structure under consideration. Here, we investigate mesoscopic fluctuations of the secondary “smile” gap, that appears in the quasiclassical spectrum of a chaotic cavity coupled to one or more superconductors. Utilizing a random matrix model, we compute numerically the energies of Andreev levels and access the distribution of the gap widths. We mostly concentrate on the universal regime ETh≫Δ with ETh being the Thouless energy of the cavity and Δ being the superconducting gap. We find that the distribution is determined by an intermediate energy scale Δg with the value between the level spacing in the cavity δs and the quasiclassical value of the gap Eg. From our numerics we extrapolate the first two cumulants of the gap distribution in the limit of large level and channel number. We find that the scaled distribution in this regime is the Tracy-Widom distribution: the same as found by Vavilov at al. [Phys. Rev. Lett. \textbf{86}, 874 (2001)] for the distribution of the minigap edge in the opposite limit ETh≪Δ. This leads us to the conclusion that the distribution found is a universal property of chaotic proximity systems at the edge of a continuous spectrum.

Synchronization of Bloch oscillations by gate voltage modulation


Preprints unpublished

Janis Erdmanis, Yuli Nazarov

Link to arxiv.org

ABSTRACT: We propose to synchronize Bloch oscillations in a double phase-slip junction by modulating the gate voltage rather than the bias voltage. We show this is advantageous and the relatively small a.c. modulation of the gate voltage gives rise to the pronounced plateaux of quantized current of the width of the order of Coulomb blockade threshold.
We theoretically investigate the setup distinguishing three regimes of the strong, weak, and intermediate coupling defined by the ratio of the gate capacitance C and the effective capacitance of the phase-slip junctions. An important feature of the intermediate coupling regime is the occurrence of the fractional plateaux of the quantized current. We investigate the finite temperature effects finding an empirical scaling for the smoothing of integer plateaux.

Topological numbers of quantum superpositions of topologically non-trivial bands


Preprints unpublished

E. V. Repin, Y. V. Nazarov

Link to arxiv.org

ABSTRACT: In this Article we address the definition and values of topological numbers of the manifolds of wavefunctions – bands obtained by quantum superposition of the wavefunctions that belong to topologically distinct manifolds. The problem, although simple in essence, can be formulated as a paradox: it may seem that quantum superposition implies non-integer topological numbers.
We show that the results are different for superpositions that are created dynamically and for those obtained by stationary mixing of the manifolds. For dynamical superpositions we have found that the observable related to the topological number is non-integer indeed. For static superpositions the resulting bands bear integer topological numbers. We illustrate how the number quantization is restored upon avoided crossing of topologically distinct subbands. The crossings lead to the exchange of topological numbers between the bands. We consider complicated phase diagrams arising from this and show the absence of triple critical points and abundance of quadruple critical points that are rare in thermodynamic phase diagrams. We illustrate these features considering the bilayer Haldane model.

Statistics of continuous weak quantum measurement of an arbitrary quantum system with multiple detectors


Preprints unpublished

Albert Franquet, Yuli V. Nazarov, Hongduo Wei

Link to arxiv:

Abstract: In this paper, we establish a general theoretical framework for the description of continuous quantum measurements and the statistics of the results of such measurements. The framework concerns the measurement of an arbitrary quantum system with arbitrary number of detectors under realistic assumption of instant detector reactions and white noise sources. We attend various approaches to the problem showing their equivalence. The approaches include the full counting statistics (FCS) evolution equation a for pseudo-density matrix, the drift-diffusion equation for a density matrix in the space of integrated outputs, and discrete stochastic updates. We provide the derivation of the underlying equations from a microscopic approach based on full counting statistics method, a phenomenological approach based on Lindblad construction, and interaction with auxiliary quantum systems representing the detectors. We establish the necessary conditions on the phenomenological susceptibilities and noises that guarantee the unambiguous interpretation of the measurement results and the positivity of the density matrix. Our results can be easily extended to describe various quantum feedback schemes where the manipulation decision is based on the values of detector outputs.

Probability distributions of continuous measurement results for two non-commuting variables and conditioned quantum evolution


Preprints unpublished

A. Franquet, Yuli V. Nazarov

Link to arxiv

Abstract: We address the statistics of a simultaneous CWLM of two non-commuting variables on a few-state quantum system subject to a conditioned evolution. Both conditioned quantum measurement and that of two non-commuting variables differ drastically for either classical or quantum projective measurement, and we explore the peculiarities brought by the combination of the two. We put forward a proper formalism for the evaluation of the distributions of measurement outcomes. We compute and discuss the statistics in idealized and experimentally relevant setups. We demonstrate the visibility and manifestations of the interference between initial and final states in the statistics of measurement outcomes for both variables in various regimes. We analytically predict the peculiarities at the circle O21+O22=1 in the distribution of measurement outcomes in the limit of short measurement times and confirm this by numerical calculation at longer measurement times. We demonstrate analytically anomalously large values of the time-integrated output cumulants in the limit of short measurement times(sudden jump) and zero overlap between initial and final states, and give the detailed distributions. We present the numerical evaluation of the probability distributions for experimentally relevant parameters in several regimes and demonstrate that interference effects in the conditioned measurement can be accurately predicted even if they are small.