Order parameter phase locking as a cause of a zero bias peak in the differential tunneling conductance of bilayers with electron-hole pairing

Abstract

In n-p bilayer systems an exotic phase-coherent state emerges due to Coulomb pairing of n-layer electrons with p-layer holes. Unlike Josephson junctions, the order parameter phase may be locked by matrix elements of interlayer tunneling in n-p bilayers. Here we show how the phase locking phenomenon specifies the response of the electron-hole condensate to interlayer voltages. In the absence of an applied magnetic field, the phase is steady-state (locked) at low interlayer voltages, V<V_c, however the phase increases monotonically with time (is unlocked) at V>V_c. The change in the system dynamics at V=V_c gives rise to a peak in the differential tunneling conductance. The peak width V_c is proportional to the absolute value of the tunneling matrix element |T_{12}|, but its height does not depend on |T_{12}|; thus the peak is sharp for small |T_{12}|. A sufficiently strong in-plane magnetic field reduces considerably the peak height. The present results are in qualitative agreement with the zero bias peak behavior that has recently been observed in bilayer quantum Hall ferromagnets with spontaneous interlayer phase coherence.