Electron and composite-fermion edge states in nonuniform magnetic fields

Abstract

We investigate the electron transport in two-dimensional electron systems, where spatially nonuniform magnetic fields are applied, using the noninteracting-electron approach and composite-fermion edge state theory. The nonuniform magnetic fields divide the conductor into three different regions, such that the upper and the lower regions are incompressible with different filling factors, which are controlled by different uniform magnetic fields, while the magnetic field varies monotonously in the middle region. In both cases of the integer and the fractional quantum Hall regimes, it is found that current-carrying magnetic edge states are formed in the middle region. We show that the current in the middle region is proportional to the filling-factor difference between the upper and the lower incompressible regions when the magnetic field in the middle region is not reversed. However, when the magnetic fields in the upper and the lower regions are antiparallel to each other, the current is not simply proportional to the filling-factor difference and depends on the nonuniform distribution of magnetic fields and electron-electron interactions that can give rise to incompressible strips in the middle region. We also study the composite-fermion edge states for fractional quantum-Hall systems with v = p/(mp + 1) under uniform magnetic fields, where p is a negative integer. For both cases of a constant and a diverging composite-fermion mass, we show that the net current carried by composite fermions in each compressible region is the same as that by electrons although the effective composite-fermion chemical potential decreases as the electron chemical potential increases.