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Acta Physica Polonica A

Josephson-Like Effect in Mesoscopic Loop Structures

Wioletta Paśko

Published Nov 1, 2005• 0 citations
Publisher

Abstract

The quantum interference is considered in time-dependent magnetic field that is quantum beats in mesoscopic loop structure.The similarities between this effect and Josephson, scalar Aharonov-Bohm and Aharonov-Casher effects, as well as their differences are treated and a possible application of the effect to the construction of the device, complementary to SQUIDs, is analysed.

DOI
10.12693/aphyspola.108.817

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The quantum interference is considered in time-dependent magnetic field that is quantum beats in mesoscopic loop structure.The similarities between this effect and Josephson, scalar Aharonov-Bohm and Aharonov-Casher effects, as well as their differences are treated and a possible application of the effect to the construction of the device, complementary to SQUIDs, is analysed.
We briefly review the theoretical formulations and applications of the Aharonov--Bohm effect and the Aharonov--Casher effect with emphasis on mesoscopic physics. Topics relating to the Aharonov--Bohm effect include: locality, periodicity, non-integrable phase factors, Abelian gauge theory, interference, the spectrum and persistent current of electrons on a ring pierced by a magnetic field, Onsager reciprocity relations, and Aharonov--Bohm interferometer. Topics relating to the Aharonov--Casher effect include: a magnetic dipole in an electric field, locality, periodicity, non-Abelian gauge invariance, SU(2) non-integrable phase factors, spin-orbit coupling, Pauli equation, Rashba Hamiltonian, Aharonov--Casher interferometer, conductance and polarization in two-channel systems due to the Aharonov--Casher effect.
A one-dimensional quantum waveguide theory for mesoscopic structures is proposed, and the boundary conditions of the wave functions at an intersection are given. The Aharonov-Bohm effect is quantitatively discussed with use of this theory, and the reflection, transmission amplitudes, etc., are given as functions of the magnetic flux, the arm lengths, and the wave vector. It is found that the oscillating current consists of a significant component of the second harmonic. This theory is also applied to investigate quantum-interference devices. The results on the Aharonov-Bohm effect and the quantum-interference devices are found to be in agreement with previous theoretical results.
Motivated by the interest to testable, exactly solvable models of quantum behavior in the time-dependent potentials, which may be important in studying (and in proof) basic quantum mechanical laws, as well as in considering the possibility of using the electronic components suggested to hypothetical ``quantum computers,'' we develop a method of solving the Schr\"odinger equation in a certain class of time-periodic and space-dependent one-dimensional potentials. In particular, it is shown that the quasistationary electronic state in the one-dimensional cyclic mesoscopic metallic ring in a rotating-potential field displays periodic variation of quasienergy in the function of magnetic flux threading the ring (the Aharonov-Bohm effect) and oscillation, superposed on the monotonous dependence, in the function of angular velocity of rotating potential (the effect similar to Rabi and/or Bloch oscillation). At large speed of rotation, quasienergy decreases rather than increases with the increase of angular velocity. The dependence of quasienergy on flux in space periodic potential displays standard hc∕ehc∕ehc∕e periodicity as well as the periodicity with a larger period, Nhc∕eNhc∕eNhc∕e, where NNN is the number of sites in the loop, corresponding to one flux quantum per lattice site. This is an interference effect similar to one observed in the fractional quantum Hall effect but, unlike in the latter, not requiring the concept of ``fractional electron charge,'' e∕Ne∕Ne∕N. The physical significance of the quasienergy states is clarified by studying the quantum transitions between the states as well as by investigating the energy flow between the ring and the external source of the potential.
By exploiting the Aharonov-Casher effect we demonstrate a suppression of magnetic flux tunneling in a Hybrid Charge Quantum Interference Device. The main part of this device is two Josephson junctions with a small superconducting island between them. To minimize phase fluctuations across Josephson junctions, this structure is embedded in a compact super-inductive NbN loop. The Interference between the flux tunneling paths is determined by the island-induced charge, which is controlled by an external voltage. The charge sensitive operation of the device is subjected to poisoning by the quasiparticles generated in the NbN film.