2 5 Ju l 2 00 3 Distribution of equilibrium edge currents

We have studied the distribution of equilibrium edge current density in 2D system in a strong (quantizing) magnetic field. The case of half plane in normal magnetic field has been considered. The transition from classical strong magnetic field to ultraquantum limit has been investigated. We have shown that the edge current density oscillates and decays with distance from the edge. The oscillations have been attributed to the Fermi wavelength of electrons. The additional component of the current smoothly depending on the distance but sensitive to the occupation of Landau levels has been found. The temperature suppression of oscillations has been studied. The magnetic field acting on the low dimensional system is traditionally considered as homogeneous and coinciding with the external field. Nevertheless, the magnetization of such quantum system as atom substantially changes the magnetic field in the vicinity of nucleus. This is essential for some phenomena, e.g., NMR. The distribution of magnetic field in the systems with spatial quantization have been studied by authors in papers [1] using the linear approximation in an external field. This problem is close to the problem of orbital magnetism intensively investigated in different systems with separable and non-separable variables [2, 3, 4]. It was shown, that the susceptibility of a large system at low temperature strongly fluctuates and changes the sign when the Fermi level moves between the energy levels of the system. The goal of the present paper is to study the spatial distribution of equilibrium currents in 2D semi-infinite plane sample subjected to a strong magnetic field. Such mathematical setting is applicable for a sample of arbitrary shape if its characteristic dimensions exceed the inverse cyclotron diameter. Let us consider a semi-infinite plane x > 0, − ∞ < y < ∞, with hard border in a magnetic field B z = B. Assume the vector potential has gauge A y = Bx. The states in the presence of magnetic field can be described by the longitudinal momentum p and the transversal number n: ψ n, p (x)e ipy. Here and below ¯ h = 1. The wave functions can be expressed via the parabolic cylinder function D ν (x): ψ n,p (x) = CD νn √ 2 (x − x p) /a , C 2 ∞ −xp D νn √ 2x/a dx = 1. (1)