Tunneling in two-layer systems with electron-hole coupling (Review article)

Abstract

A phase-coherent state of electron–hole pairs may emerge in two-layer n–p systems, which is generated by the Coulomb attraction of electrons of the n-layer to holes of the p-layer. Unlike a Josephson junctions, the order parameter phase in n–p bilayers is locked by interlayer tunneling matrix elements T12. The phase locking determines the response of the electron–hole condensate to the electric voltage between the layers: the phase is constant at low voltages V Vc. The change in the system dynamics at V = Vc results in a peak along the differential tunneling conductance. The width of the Vc peak is proportional to the absolute value of the tunneling matrix element |T12|, while its height does not depend on |T12|. Thus, for small |T12| the peak is tall and narrow. In the case of long two-layer systems, a magnetic field parallel to the layers significantly reduces the peak height. In small two-layer systems, the height of the tunneling conductance peak as a function of a parallel magnetic field is similar to the Fraunhofer diffraction pattern. The interlayer differential tunneling conductance peak is also strongly suppressed by temperature, due to thermal interlayer voltage fluctuations.