Disordered FFLO Phase
dLO-tunneling

Shown on the left is the tunneling density of states (DOS) spectrum of a 3 nm thick Al film in a 4 T parallel field at 80 mK. The tranisiton temperature of this film was 2.8 K. The two peaks on either side of V = 0 are the Zeeman-split BCS coherence peaks. Our interest in this spectrum is actually the excess states at zero bias (V = 0). The red curve is the prediction of a homogeneous BCS theory. Note that, although the theory captures the coherence peaks quite well, it predicts a much smaller density of states at the Fermi energy (i.e. at V = 0) than what is measured, see red arrow on left. The existence of these excess states has been known for more than 40 years, but an explanation has remained elusive. We now believe that the excess states may be attributable to a disordered FFLO phase.

We have shown that, contrary to popular belief, FFLO physics is not completely washed out by disorder, and, indeed our films are highly disordered. In fact, over a significant range of Zeeman fields we find evidence for a disordered Larkin-Ovchinnikov (d-LO) state characterized by bound states in domain walls and low energy spectral weight which accounts for the excess states at the Fermi energy. Calculations based on an attractive Hubbard model were carried out by Nandini Trivedi's group at Ohio St. Their model self-consistently accounts for the disorder and allows the pairing amplitude to adjust to the disorder profile. The novel d-LO phase is robust to variations in field and disorder and imprints a unique signature in the low-energy DOS within the superconducting gap.

DoS_evolution

The first two columns (from left to right) in the plot on the left show spatial maps of the local pairing amplitude delta and the magnetization m as a function of the reduced field h, as obtained from the Hubbard model calculations. The field is normalized by the parallel critical field, i.e. the Zeeman critical field. Note that near the critical field the order parameter can change sign. The third column show the DOS's of up and down electrons. The last column shows the total DOS. For intermediate fields the system exhibits disordered Larkin-Ovchinnikov states with domain walls. The brown regions in the second column are where the magnetization m is large, which occurs at domain walls where delta changes sign. White regions are hills or valleys of the disorder potential corresponding to empty sites or localized pairs that participate
in neither superconductivity nor magnetism.

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Disordered FFLO Phase