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For the first time the persistent current in a 2D free-electron system hasbeen calculated analytically. The tight binding model is considered on a squarelattice with filling factor 1/2. The array has a shape of rectangle withboundary 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 ofthe magnetic flux in torus geometry. An analytical expression is obtained forthe energy and for the components of the persistent current (PC) at a givenflux and temperature. It is shown that at zero temperature the PC density isproportional to the vector potential with the coefficient which does not dependon the size of the system. This happens because the Fermi surface for a squarelattice at filling factor 1/2 is flat. Both the energy and the PC are periodicfunctions 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 aspectratio of the rectangle. The magnitude of PC is the same as in superconductors.Therefore, a 3D system constructed from a macroscopic number of isolatedcoaxial cylinders at zero temperature reminds the London's superconductor. Itexhibits 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 magnitudeof PC decays with $T$ as $\exp(-\pi TR_{ef}/2at)$, where $t$ is the hoppingamplitude and $a$ is the lattice constant.

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