Drastic effect of weak interaction near special points in semiclassical multiterminal superconducting nanostructures


Publications

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.

Holonomic quantum manipulation in the Weyl disk


Publications

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.

Weyl points in multiterminal hybrid superconductor-semiconductor nanowire devices


Publications

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.

Weyl point immersed in a continuous spectrum: An example from superconducting nanostructures


Publications

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.

Spintronics with a Weyl point in superconducting nanostructures


Publications

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.

Braiding and All Quantum Operations with Majorana Modes in 1D


Publications

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.

Spin Weyl quantum unit: A theoretical proposal


Publications

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.

Dynamical Spin Polarization of Excess Quasiparticles in Superconductors


Publications

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.

Overlapping Andreev states in semiconducting nanowires: Competition of one-dimensional and three-dimensional propagation


Publications

Viktoriia Kornich, Hristo S. Barakov, and Yuli V. Nazarov
Phys. Rev. B 101, 195430 – Published 20 May 2020

Link to arxiv.org

ABSTRACT: The recent proposals of devices with overlapping Andreev bound states (ABS) open up opportunities to control and fine tune their spectrum that can be used in various applications in quantum sensing and manipulation. In this paper, we study the ABS in a device consisting of a semiconducting nanowire covered with three superconducting leads. The ABS are formed at two junctions where the wire is not covered. They overlap in the wire where the electron propagation is 1D and in one of the leads where the propagation is 3D. We identify a number of regimes where these two overlaps either dominate or compete, depending on the junction separation L as compared to the correlation lengths xi(w), xi(s) in the wire and in the lead, respectively. We utilize a simple model of 1D electron spectrum in the nanowire and take into account the quality of the contact between the nanowire and the superconducting lead. We present the spectra for different L, detailing the transition from a single ABS in the regime of strong 1D hybridization to two almost independent ABS hybridized at the degeneracy points, in the regime of weak 1D hybridization. We present the details of merging the upper ABS with the continuous spectrum upon decreasing L. We study in detail the effect of quantum interference due to the phase accumulated during the electron passage between the junctions. We develop a perturbation theory for analytical treatment of hybridization. We address an interesting separate case of fully transparent junctions. We derive and exemplify a perturbation theory suitable for the competition regime demonstrating the interference of 1D and two 3D transmission amplitudes.

Probability distributions of continuous measurement results for two noncommuting variables and postselected quantum evolution


Publications

A. Franquet and Yuli V. Nazarov
Phys. Rev. A 100, 062109 – Published 6 December 2019

Link to arxiv.org

ABSTRACT: We address the statistics of a simultaneous continuous weak linear measurement of two noncommuting variables on a few-state quantum system subject to a postselected evolution. The results of both postselected quantum measurement and simultaneous monitoring of two noncommuting variables differ drastically from the results of either classical or quantum projective measurement. We explore the peculiarities arising from the combination of the two. We concentrate on the distribution function of two measurement outcomes integrated over a time interval. We formulate a proper formalism for the evaluation of such distribution, and further compute and discuss the resulting statistics for 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 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 the anomalously large values of the time-integrated output cumulants in the limit of short measurement times and zero overlap between initial and final states, and give the detailed distributions for this case. We term this situation sudden jump. We present the numerical evaluation of the probability distributions for experimentally relevant parameters in several regimes and demonstrate that interference effects in the postselected measurement can be accurately predicted even if they are small.