Topological phase diagram of a two-subband electron system

We present a phase diagram for a two-dimensional electron system with two p opulated subbands. Using a gated GaAs/AlGaAs single quantum well, we have m apped out the phases of various quantum Hall states in the density-magnetic field plane. The experimental phase diagram shows a very different topolog y from the conventional Landau fan diagram, We find regions of negative dif ferential Hall resistance which are interpreted as preliminary evidence of the long sought reentrant quantum Hall transitions. We discuss the origins of the anomalous topology and the negative differential Hall resistance in terms of the Landau level and subband mixing.