Novel A-B type oscillations in a 2-D electron gas in inhomogenous magnetic fields

We present results from a quantum and semiclassical theoretical study of the \(\rho_{xy}\) and \(\rho_{xx}\) resistivities of a high mobility 2-D electron gas in the presence of a dilute random distribution of tubes with magnetic flux \(\Phi\) and radius \(R\), for arbitrary values of \(k_f R\) and \(F=e\Phi/h\). We report on novel Aharonov-Bohm type oscillations in \(\rho_{xy}\) and \(\rho_{xx}\), related to degenerate quantum flux tube resonances, that satisfy the selection rule \({(k_fR)}^2=4F(n+{1\over 2})\), with \(n\) an integer. We discuss possible experimental conditions where these oscillations may be observed.