Giant persistent current in free-electron model with flat Fermi surface

TL;DR

This paper analytically calculates the persistent current in a 2D free-electron system with a flat Fermi surface, revealing giant currents and superconducting-like phenomena in mesoscopic systems.

Contribution

It provides the first analytical expression for persistent current in a 2D free-electron model with a flat Fermi surface, highlighting superconducting-like effects in mesoscopic systems.

Findings

Persistent current density is proportional to vector potential at zero temperature.

The system exhibits flux quantization and Meissner effect-like phenomena.

The persistent current magnitude decays exponentially with temperature.

Abstract

For the first time the persistent current in a 2D free-electron system has been calculated analytically. The tight binding model is considered on a square lattice with filling factor 1/2. The array has a shape of rectangle with boundary conditions in both directions twisted by $2\pi\phi_x$ and $2\pi\phi_y$. The components of the twist are associated with two components of the magnetic flux in torus geometry. An analytical expression is obtained for the energy and for the components of the persistent current (PC) at a given flux and temperature. It is shown that at zero temperature the PC density is proportional to the vector potential with the coefficient which does not depend on the size of the system. This happens because the Fermi surface for a square lattice at filling factor 1/2 is flat. Both the energy and the PC are periodic functions of the two flux components with the periods $\phi_0/q$ and $\phi_0/s$ where $\phi_0=hc/e$, and $q$ and $s$ are integers which depend on the aspect ratio of the rectangle. The magnitude of PC is the same as in superconductors. Therefore, a 3D system constructed from a macroscopic number of isolated coaxial cylinders at zero temperature reminds the London's superconductor. It exhibits the quantization of trapped flux as well as the Meissner effect. However, all the phenomena are of a mesoscopic nature. The critical field $H_c$ decays with an effective size of the system, $H_c\sim 1/R_{ef}$. The magnitude of PC decays with $T$ as $\exp(-\pi TR_{ef}/2at)$, where $t$ is the hopping amplitude and $a$ is the lattice constant.