Dimensional crossover in quantum networks: from macroscopic to mesoscopic Physics

TL;DR

This study investigates how quantum interference effects in metallic networks transition from macroscopic to mesoscopic behavior as the network size varies, revealing a new regime of size-dependent quantum oscillations.

Contribution

It demonstrates the dimensional crossover in quantum networks, showing the transition from incoherent superposition to phase coherent regimes as size scales change.

Findings

Observation of both AAS and AB oscillations across all network sizes.

Identification of a new size dependence of quantum oscillations in the crossover regime.

Evidence of a phase coherent regime along one direction and macroscopic along the other.

Abstract

We report on magnetoconductance measurements of metallic networks of various sizes ranging from 10 to $10^{6}$ plaquettes, with anisotropic aspect ratio. Both Altshuler-Aronov-Spivak (AAS) $h/2e$ periodic oscillations and Aharonov-Bohm (AB) $h/e$ periodic oscillations are observed for all networks. For large samples, the amplitude of both oscillations results from the incoherent superposition of contributions of phase coherent regions. When the transverse size becomes smaller than the phase coherent length $L_\phi$, one enters a new regime which is phase coherent (mesoscopic) along one direction and macroscopic along the other, leading to a new size dependence of the quantum oscillations.