Commensurate-incommensurate transitions of quantum Hall stripe states in double quantum well systems

Abstract

In higher Landau levels $(N>0)$ and around filling factors $\ensuremath{\nu}=4N+1,$ a two-dimensional electron gas in a double quantum well system supports a stripe ground state in which the electron density in each well is spatially modulated. When a parallel magnetic field is added in the plane of the wells, tunneling between the wells acts as a spatially rotating effective Zeeman field coupled to the ``pseudospins'' describing the well index of the electron states. For small parallel fields, these pseudospins follow this rotation, but at larger fields they do not, and a commensurate-incommensurate transition results. Working in the Hartree-Fock approximation, we show that the combination of stripes and commensuration in this system leads to a very rich phase diagram. The parallel magnetic field is responsible for oscillations in the tunneling matrix element that induce a complex sequence of transitions between commensurate and incommensurate liquid or stripe states. The homogeneous and stripe states we find can be distinguished by their collective excitations and tunneling $I\ensuremath{-}V,$ which we compute within the time-dependent Hartree-Fock approximation.