Nazarov Group

theoretical physics group at TU Delft

J. Reutlinger, L. Glazman, Yu. V. Nazarov, and W. Belzig
Phys. Rev. B 106, 214513 – Published 16 December 2022

Link to arxiv.org

ABSTRACT: The energy levels of a quasicontinuous 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 a secondary 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 E_Th ≫Δ, with E_Th 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 Δ_g with the value between the level spacing in the cavity
δ_s and the quasiclassical value of the gap E_g. 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 et al. [Phys. Rev. Lett. 86, 874 (2001)] for the distribution of the minigap edge in the opposite limit
E_Th≪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 in agreement with the known random matrix models featuring a square root singularity in the density of states.

Janis Erdmanis and Yuli V. Nazarov
Phys. Rev. B 106, 235406 – Published 7 December 2022

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 ac modulation of the gate voltage gives rise to the pronounced plateaus of quantized current of the width of the order of Coulomb blockade threshold. We theoretically investigate the setup distinguishing three regimes of 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 plateaus of the quantized current. We investigate the finite temperature effects, finding an empirical scaling for the smoothing of integer plateaus.

Janis Erdmanis, Árpád Lukács, and Yuli V. Nazarov
Phys. Rev. B 106, 125422 – Published 22 September 2022

Link to arxiv.org

ABSTRACT:
A generic semiclassical superconducting nanostructure connected to multiple superconducting terminals hosts a quasicontinuous spectrum of Andreev states. The spectrum is sensitive to the superconducting phases of the terminals. It can be either gapped or gapless depending on the point in the multidimensional parametric space of these phases. Special points in this space correspond to setting some terminals to the phase 0 and the rest to the phase of π. For a generic nanostructure, three distinct spectra come together in the vicinity of a special point: two gapped phases of different topology and a gapless phase separating the two by virtue of topological protection. In this paper, we show that a weak interaction manifesting as quantum fluctuations of superconducting phases drastically changes the spectrum in a narrow vicinity of a special point. We develop an interaction model and derive a universal generic quantum action that describes this situation. The action is complicated incorporating a nonlocal in time matrix order parameter, and its full analysis is beyond the scope of the present paper. Here, we identify and address two limits: the semiclassical one and the quantum one, concentrating on the first-order interaction correction in the last case. In both cases, we find that the interaction squeezes the domain of the gapless phase in the narrow vicinity of the point so the gapped phases tend to contact each other immediately defying the topological protection. We identify the domains of strong coupling where the perturbation theory does not work. In the gapless phase, we find the logarithmic divergence of the first-order corrections. This leads us to an interesting hypothesis: weak interaction might induce an exponentially small gap in the formerly gapless phase.

Victor Boogers, Janis Erdmanis, and Yuli Nazarov
Phys. Rev. B 105, 235437 – Published 27 June 2022
Link to arxiv.org

ABSTRACT:
It has been shown that a Weyl point in a superconducting nanostructure may give rise to a Weyl disk where two quantum states are almost degenerate in a two-dimensional manifold in the parametric space. This opens up the possibility of a holonomic quantum manipulation: A transformation of the wave function upon an adiabatic change of the parameters within the degenerate manifold. In this paper, we investigate in detail the opportunities for holonomic manipulation in Weyl disks. We compute the connection at the manifold in quasiclassical approximation to show it is Abelian and can be used for a phase gate. To provide a closed example of quantum manipulation that includes a state preparation and readout, we augment the holonomic gate with a change of parameters that brings the system out of the degenerate subspace. For numerical illustrations, we use a finite value of quasiclassical parameter and exact quantum dynamics. We investigate the fidelity of an example gate for different execution times. We evaluate the decoherence rate and show it can be made small to ensure a wide frequency range where an adiabatic manipulation remains coherent.

E. V. Repin and Y. V. Nazarov
Phys. Rev. B 105, L041405 – Published 12 January 2022 (Letter, Editor’s Suggestion)
Link to arxiv
ABSTRACT: The technology of superconductor-semiconductor nanowire devices has matured in recent years. This makes it feasible to make more complex and sophisticated devices. We investigate multiterminal superconductor-semiconductor wires to access the feasibility of another topological phenomenon: Weyl singularities in their spectrum. We have found an abundance of Weyl singularities for devices with an intermediate size of the electrodes. We describe their properties and the ways the singularities emerge and disappear upon variation of the setup parameters.

Y. Chen and Y. V. Nazarov
Phys. Rev. B 104, 104506 – Published 15 September 2021
Link to arxiv
ABSTRACT: A Weyl point in a superconducting nanostructure is a generic minimum model of a topological singularity at low energies. We connect the nanostructure to normal leads thereby immersing the topological singularity in the continuous spectrum of the electron states in the leads. This sets another simple and generic model useful to comprehend the modification of low-energy singularity in the presence of a continuous spectrum. The tunnel coupling to the leads gives rise to new low-energy scale at which all topological features are smoothed. We investigate superconducting and normal currents in the nanostructure at this scale. We show how the tunnel currents can be used for detection of the Weyl point. Importantly, we find that the topological charge is not concentrated in a point but rather is spread over the parameter space in the vicinity of the point. We introduce and compute the resulting topological charge density. We also reveal that the pumping to the normal leads helps to detect and investigate the topological effects in the vicinity of the point.

Y. Chen and Y. V. Nazarov
Phys. Rev. B 103, 165424 – Published 26 April 2021

Link to arxiv.org

ABSTRACT: We investigate transport in a superconducting nanostructure housing a Weyl point in the spectrum of Andreev bound states. A minimum magnet state is realized in the vicinity of the point. One or more normal-metal leads are tunnel-coupled to the nanostructure. We have shown that this minimum magnetic setup is suitable for realization of all common goals of spintronics: detection of a magnetic state, conversion of electric currents into spin currents, potentially reaching the absolute limit of one spin per charge transferred, and detection of spin accumulation in the leads. The peculiarity and possible advantage of the setup is the ability to switch between magnetic and nonmagnetic states by tiny changes of the control parameters: superconducting phase differences. We employ this property to demonstrate the feasibility of less common spintronic effects: spin on demand and alternative spin current.

Viktoriia Kornich, Xiaoli Huang, Evgeny Repin, and Yuli V. Nazarov
Phys. Rev. Lett. 126, 117701 – Published 19 March 2021

Link to arxiv

ABSTRACT: We propose a scheme to perform braiding and all other unitary operations with Majorana modes in one dimension that, in contrast to previous proposals, is solely based on resonant manipulation involving the first excited state extended over the modes. The detection of the population of the excited state also enables initialization and read-out. We provide an elaborated illustration of the scheme with a concrete device.

Y. Chen and Y. V. Nazarov
Phys. Rev. B 103, 045410 – Published 12 January 2021 (Editors’ Suggestion)

Link to arxiv.org

ABSTRACT: We propose a four-state quantum system, or quantum unit, that can be realized in superconducting heterostructures. The unit combines the states of a spin and an Andreev qubit providing the opportunity of quantum superpositions of their states. This functionality is achieved by tunnel coupling between a four-terminal superconducting heterostructure housing a Weyl point and a quantum dot. The quantum states in the vicinity of the Weyl point are extremely sensitive to small changes of superconducting phase; this gives rich opportunities for quantum manipulation. We establish an effective Hamiltonian for the setup and describe the peculiarities of the resulting spectrum. We concentrate on the four-state subspace and explain how to make a double qubit in this setup. We review various ways to achieve quantum manipulation in the unit: this includes resonant, adiabatic, diabatic manipulation and combinations of those. We provide detailed illustrations of designing arbitrary quantum gates in the unit.

Julia S. Meyer, Manuel Houzet, and Yuli V. Nazarov
Phys. Rev. Lett. 125, 097006 – Published 28 August 2020

Link to arxiv.org

ABSTRACT: We show that the annihilation dynamics of excess quasiparticles in superconductors may result in the spontaneous formation of large spin-polarized clusters. This presents a novel scenario for spontaneous spin polarization. We estimate the relevant scales for aluminum, finding the feasibility of clusters with a huge total spin that could be spread over microns. The fluctuation dynamics of such large spins may be detected by measuring the flux noise in a loop hosting a cluster.