Colloquium: Alexander Finkelstein, Weizmann Institute & Texas A&M University

Abstract: An insulating phase was experimentally found to show 2e-Little-Parks oscillations suggesting the existence of a phase coherence in some insulating systems. I will try to give a theoretical explanation of this phenomenon.                                                                                                
We studied a mechanism of spin-triplet odd-frequency superconducting pairing between electrons in strongly disordered conductors. We show that mixing the conventional superconducting fluctuations above the transition temperature or critical magnetic field together with the spin part of repulsive Coulomb interaction results in an effective interaction which mediates the s-wave spin-triplet odd-frequency pairing in the particle-particle (Cooper) channel. Diffusion of electrons lead to the pronounced frequency dependence of the effective interaction required for this type of pairing. Thus, regular spin-singlet superconducting state in strongly disordered films may be accompanied by an intermediate phase characterized by spin-triplet odd- frequency pairing between fermions. We show that the transition into this phase may occur through the first order phase transition. Therefore, domains with different spin projection of the spin-triplet order parameter are expected to occur.        

                                                                      
We argue that the spin-triplet odd-frequency paired phase corresponds to the insulating state experimentally found in highly disordered films of InO and TiN. These materials show a superconducting-insulator transition as a function of magnetic field when the superconductivity is suppressed. At even higher magnetic field a reentrance into highly resistive conducting state occurs. The insulating phase is experimentally found to show 2e-Little-Parks oscillations suggesting the existence of a phase coherence in this state.

An ultimate picture for the description of the exotic insulating behavior is as follows: Domains with different spin polarization of the spin-triplet odd-frequency pairing block the supercurrent, while phase coherence still results in the 2e-Little-Parks oscillations. Absence of a bulk supercurrent makes the system to be an insulator (a sort of super-insulator) at low temperatures.
The work was performed in collaboration with Dr. Vladimir Zyuzin, now at the Landau Institute.