Diamagnetism of a gas of 2D-fermions in strong non-homogeneous magnetic fields and anyons

Abstract

We study diamagnetism of a gas of spinless fermions moving in a non-homogeneous magnetic field$\vec B = B\left( {0, 0, 1/\cosh ^2 \left( {\left( {x - x_0 } \right)/\delta } \right)} \right)$ in the limit of weak non-homogeneity δ≫L, hereL is the linear dimension of the sample, and in the limit of strong fields. Total gas energy for the lowest levels, gas magnetization, static magnetic susceptibility, chemical potential and the gas compressibility are discussed and compared with the uniform field case using our recent results of the exact description of the spinless fermion motion in this field. The non-homogeneous field state of our gas of spinless fermions is preferred with respect to the uniform field state of the same gas within appropriate range of values of the parameters (B, L, δ) of the system. We discuss results of this paper in relation to the physics of anyons. It is pointed out that a transition from the uniform statistical field state to the non-homogeneous statistical field state may occur. Recent experimental results of optical measurements of circular dichroism and circular birefringence in hightemperature superconductors are controversial as concerns clear evidence of broken T- and P-symmetry. As one of possible sources of observed discrepancies may serve the phase transition considered in this paper.