Enhancement of tunnel conductivity by Cooper pair fluctuations in electron-hole bilayer

Influence of Cooper pair fluctuations that are precursor of pairing of electrons and holes located on opposite surfaces of topological insulator film on tunnel conductivity between the surfaces is investigated. Due to restrictions caused by momentum and energy conservation dependence of tunnel conductivity on external bias voltage has peak that becomes more prominent with decreasing of disorder and temperature. We have shown that Cooper pair fluctuations considerably enhance tunneling and height of the peak diverges in vicinity of critical temperature with critical index nu = 2. Width of the peak tends to zero in proximity of critical temperature. Pairing of electrons and holes can be suppressed by disorder and in vicinity of quantum critical point height of the peak also diverges as function of Cooper pair damping with critical index mu = 2.