Fluctuational internal Josephson effect in topological insulator film

Abstract: Tunneling between opposite surfaces of topological insulator thin film populated by electrons and holes is considered. We predict considerable enhancement of tunneling conductivity by Cooper electron-hole pair fluctuations that are precursor of their Cooper pairing. Cooper pair fluctuations lead to the critical behavior of tunneling conductivity in vicinity of critical temperature with critical index \nu=2. If the pairing is suppressed by disorder the behavior of tunneling conductivity in vicinity of quantum phase transition is also critical with the index \mu=2. The effect can be interpreted as fluctuational internal Josephson effect and it is general phenomenon for electron-hole bilayers. The peculiarities of the effect in other realizations of electron-hole bilayer are discussed.