Ordering effect of Coulomb interaction in ballistic double-ring systems

TL;DR

This paper investigates how Coulomb interactions induce an ordering effect in the magnetic field dependence of energy states in a chaotic double-ring system, transforming random fluctuations into periodic behavior.

Contribution

It demonstrates that electron-electron interactions can order the magnetic response in a chaotic double-ring system, leading to periodicity in energy levels.

Findings

Electron-electron interactions induce periodicity in energy states.

Charge fluctuations are the only disorder source in the ordered phase.

The period of the magnetic response is proportional to 1/(A_1 + A_2).

Abstract

We study a model of two concentric onedimensional rings with incommensurate areas $A_1$ and $A_2$, in a constant magnetic field. The two rings are coupled by a nonhomogeneous inter-ring tunneling amplitude, which makes the one-particle spectrum chaotic. For noninteracting particles the energy of the many-body ground state and the first excited state exhibit random fluctuations characterized by the Wigner-Dyson statistics. In contrast, we show that the electron-electron interaction orders the magnetic field dependence of these quantities, forcing them to become periodic functions, with period $ \propto 1/(A_1 + A_2)$. In such a strongly correlated system the only possible source of disorder comes from charge fluctuations, which can be controlled by a tunable inter-ring gate voltage.