Solid-State Analog of an Optical Interferometer

Abstract

To some extend one may treat a metal ring with two probes as a solid-state analog of an optical interferometer. One node can be considered as a beam splitter (bi-prism, for example), and the electric current at the other node as an equivalent to a light intensity of an interference pattern formed at a screen. In optics, to obtain a stationary pattern one should use a monochromatic source of radiation, as afterwards in a conventional passive media (i.e. air) the phase of the radiation is preserved. On the contrary, in solids the phase of a conducting electron wavefunction is randomly altered due to inelastic collisions (mainly phonons at high temperatures). Hence, to satisfy the condition of phase coherence, one should use loops with the circumference smaller than the characteristic phase breaking length. At temperatures T < 1 K micron-size metal loops may fall into this limit. Experimentally the quantum interference manifests itself as periodic oscillations of the magnetoresistance [1]. In typical nanostructures with the diameter d ~ 1 um, the magnitude of the effect is rather small ΔR/ R < 10^-3. The amplitude of the oscillations rapidly decreases with the increase of the loop circumference due to higher probability of the inelastic scattering events in a longer path. The unwanted phase breaking is eliminated in a superconducting state. As the resistance of a pure superconductor is zero, one should study magnetic field dependencies of the other superconducting parameters: critical temperature [2] or current [3], for example. The magnitude of the Little-Parks effect [2] in a loop with circumference L is proportional to ~ξ²/L2, where ξ is the superconducting coherence length, and may reach ΔT~ 10 mK for a micrometer-size “dirty limit” aluminum loop [3,4]. In both cases the period of oscillations in units of magnetic flux through the area of the loop ΔΦ is equal to the flux quantum New York:φ₀ = h/q, where q is the effective particle charge is the electron charge e for normal metals and 2e for superconductors.