Giant persistent current in a free-electron model with a flat Fermi surface
E.V. Tsiper and A.L. Efros
Department of Physics, University of Utah, Salt Lake City, UT 84112
The tight-binding model is considered for a square lattice with
filling factor 1/2. The array has the shape of a 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 fbr 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 a 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 the PC is the same
as for superconductors. Therefore, a 3D system constructed from a
macroscopic number of isolated coaxial cylinders at zero temperature
is reminiscent of London's superconductor. It exhibits the
quantization of trapped flux as well as the Meissner effect. However,
all of the phenomena are of a mesoscopic nature. The critical field
H-c decays with the effective size of the system, Hc similar to
1/Ref. The magnitude of the PC decays with T as exp(-pi TRef/2at),
where t is the hopping amplitude and a is the lattice constant.
J. Phys.: Cond. Matt. 10, 1053 (1998)
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