1996/12/31 by E. V. Tsiper, Tsiper, E. V., A. L. Efros +1
Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #Magnetic properties of thin films #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/9612253
18 revtex preprint pages + 4 ps figures
openalex publication_date 1996/12/31 · arxiv created 1997/03/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 2πϕx and 2πϕy. 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 ϕ0/q and ϕ0/s where ϕ0=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 Hc decays with an effective size of the system, Hc∼ 1/Ref. The magnitude of PC decays with T as exp(-πTRef/2at), where t is the hopping amplitude and a is the lattice constant.