DFG-RSF: Quantum interferometry with interacting electronic systems
Final Report Abstract
Impressive recent progress in electronics is largely due to the use of low-dimensional nanostructures such as quantum wells, quantum wires and rings, as well as due to the continuous miniaturization of electronic devices down to nanoscales. The physics at these scales is governed by quantum coherence and quantum interference effects as well as by the effects of electron-electron interaction. Interference is a mechanism for manifestation of quantum-coherent phenomena and at the same time a tool to probe coherence. Interference of electron waves is at the heart of quantum mechanics. One of the most beautiful manifestations of the wave nature of electrons is the Aharonov-Bohm (AB) Effect. The key physical issue, phase sensitivity of the electron wavefunction to magnetic flux, enables designs of quantum AB interferometers that can be tuned by an external magnetic field. Interference is also of great technological importance. In particular, AB interferometers are used in practical applications for measurements of magnetic fields and are central elements in quantum interferometry based on low-dimensional electronic nanosystems. Another wellknown example of practical use of interference is a Superconducting Quantum Interference Device (SQUID), a circuit, which allows for high-precision measurements of magnetic fields and which is extensively studied today as a building block of prospective quantum computers. At the microscopic level, quantum interference determines conduction properties of disordered materials at low temperatures through the mechanism of Anderson localization. The goal of this DFG-RSF cooperation project was to investigate how strong electronelectron interactions transform the phenomenon of quantum interference. One one hand, interaction causes dephasing, thus reducing the visibility of interference patterns. At the same time, interaction gives rise to new, emerging degrees of freedom, which, in turn, can interfere. This is exactly what happens in a SQUID, where attraction between electrons gives rise to formation of Cooper pairs. These are described by a macroscopic wave function and are subject to interference. Another example is given by the edge states in topological matter. The work on the project was very successful. A key role in this success was played by an active cooperation between involved groups from Germany and Russia. Our main results are as follows: 1) We have investigated effects of interaction on Aharonov-Bohm interference in a single-channel quantum ring. A remarkable property of such system is spin-charge separation, i.e., fractionalization of an electron in spin and charge degrees of freedom. We have explored how it affects the quantum interference in a ring. 2) We have explored interferometers based on split Cooper pairs in superconducting systems. 3) We have investigated interferometers based on 1D chiral Majorana modes in hybrid structures formed by superconducting and magnetic layers on a surface of a topological insulator. We have determined characteristic features of these modes in thermal transport and noise. 4) We have generalized the well-known Jordan-Wigner mapping between spins and fermions from strictly 1D geometry to the case of spins placed on a tree. 5) We have explored ways to engineer Majorana bound states (that are of interest for topological quantum computations) in heterostructures of superconductors with magnetic materials hosting skyrmions. 6) We have explored quantum-interference phenomena around the superconductorinsulator transition in Josephson junction chains.
Publications
- Emulating Majorana fermions and their braiding by Ising spin chains, Physical Review B 96, 195402 (2017)
S.Backens, A.Shnirman, Yu.Makhlin, Y.Gefen, J.E.Mooij, and G.Schoen
(See online at https://doi.org/10.1103/PhysRevB.96.195402) - Spin-charge separation in an Aharonov-Bohm interferometer, Physical Review B 96, 115417 (2017)
A. P. Dmitriev, I. V. Gornyi, V. Yu. Kachorovskii, and D. G. Polyakov
(See online at https://doi.org/10.1103/PhysRevB.96.115417) - Superconductor-Insulator Transition in disordered Josephson junction chains, Phys. Rev. B 96, 064514 (2017)
M. Bard, I. V. Protopopov, I. V. Gornyi, A. Shnirman, A. D. Mirlin
(See online at https://doi.org/10.1103/PhysRevB.96.064514) - Thermoelectric transport in junctions of Majorana and Dirac channels, Physical Review B 95, 195425 (2017)
Dmitriy S. Shapiro, D. E. Feldman, Alexander D. Mirlin, and Alexander Shnirman
(See online at https://doi.org/10.1103/PhysRevB.95.195425) - Excess equilibrium noise in topological SNS junction between chiral Majorana liquids, Physical Review B 98, 245405 (2018)
Dmitriy S. Shapiro, Alexander D. Mirlin, and Alexander Shnirman
(See online at https://doi.org/10.1103/PhysRevB.98.245405) - Tunneling Aharonov-Bohm interferometer on helical edge states, Physical Review B 98, 045418 (2018)
A. Niyazov, D. N. Aristov, and V. Yu. Kachorovskii
(See online at https://doi.org/10.1103/PhysRevB.98.045418) - Jordan–Wigner transformations for tree structures, Scientific Reports 9, 2598 (2019)
Stefan Backens, Alexander Shnirman & Yuriy Makhlin
(See online at https://doi.org/10.1038/s41598-018-38128-8) - Majorana bound states in magnetic skyrmions imposed onto a superconductor, Physical Review B 100, 064504 (2019)
Stefan Rex, Igor V. Gornyi, and Alexander D. Mirlin
(See online at https://doi.org/10.1103/PhysRevB.100.064504) - Transport signatures of a Majorana qubit and read-out-induced dephasing, New Journal of Physics, Volume 21, April 2019
Lupei Qin, Xin-Qi Li, Alexander Shnirman and Gerd Schön
(See online at https://doi.org/10.1088/1367-2630/ab1431)
