Topological phase transition between the gap and the gapless superconductors

It is demonstrated that the known for a long time transition between the gap and gapless superconducting states in the Abrikosov-Gor'kov theory of superconducting alloy with paramagnetic impurities is of the Lifshitz type, i.e. of the $2\frac12$ order phase transition. We prove that this phase transition has a topological nature and is characterized by the corresponding change of the topological invariant, namely the Euler characteristic. We study the stability of such a transition with respect to the spatial fluctuations of the magnetic impurities critical concentration $n_s$ and show that the requirement for validity of its mean field description is unobtrusive: $\nabla \left( {\ln {n_s}} \right) \ll \xi^{-1}$ (here $\xi$ is the superconducting coherence length) Finally, we show that, similarly to the Lifshitz point, the $2\frac12$ order phase transition should be accompanied by the corresponding singularities, for instance, the superconducting thermoelectric effect has a giant peak exceeding the normal value of the Seebeck coefficient by the ratio of the Fermi energy and the superconducting gap. The concept of the experiment for the confirmation of $2\frac12$ order topological phase transition is proposed.Comment: 7 pages with the supplemental material and 3 figure

Mechanism of screening or enhancing the pseudogap throughout the two-band Bardeen-Cooper-Schrieffer to Bose-Einstein condensate crossover

We demonstrate the rise-and-fall of multiple pseudogaps in the Bardeen-Cooper-Schrieffer-Bose-Einstein-condensation (BCS-BEC) crossover in two-band fermionic systems having different pairing strengths in the deep band and in the shallow band. The striking features of this phenomenon are an unusual many-body screening of pseudogap state and the importance of pair-exchange couplings, which induces multiple pseudogap formation in the two bands. The multi-band configuration suppresses pairing fluctuations and the pseudogap opening in the strongly-interacting shallow band at small pair-exchange couplings by screening effects, with possible connection to the pseudogap phenomenology in iron based superconductors. On the other hand, the multiple pseudogap mechanism accompanies with the emergence of binary preformed Cooper pairs originating from interplay between intra-band and pair-exchange couplings.Comment: 7 pages, 5 figures and Supplemental Material (5 pages, 5 figures

Topological nature of the transition between the gap and the gapless superconducting states

Recently it was demonstrated that the long-known transition between the gap and gapless superconducting states in the Abrikosov-Gor'kov theory of superconducting alloy with paramagnetic impurities is of the Lifshitz's type, i.e. at zero temperature this is the $2\frac12$ order phase transition. Since transitions of this kind in a normal metal are always associated to certain topological changes, then below we clarify the topological nature of the transition under consideration. Namely, we demonstrate that the topological invariant which in process of the transition undergoes the change is nothing but the Euler characteristic. Alternatively, in terms of the theory of catastrophes one can relate this transition to appearance of the cuspidal edge at the corresponding surface of the density of states as the function of energy and superconducting order parameter. The concept of experiments for the confirmation of $2\frac12$ order topological phase transition is proposed. Obtained theoretical results can be applied for the explanation of recent experiments with lightwave-induced gapless superconductivity, for the interpretation of the disorder induced transition $s_{\pm}$-$s_{++}$ states via gapless phase in two-band superconductors, and the emergence of gapless color superconductivity in quantum chromodynamics.Comment: 6 pages, 2 figure

Coexistence of giant Cooper pairs with a bosonic condensate and anomalous behavior of energy gaps in the BCS-BEC crossover of a two-band superfluid Fermi gas

We investigate the Bardeen-Cooper-Schrieffer–Bose-Einstein condensation crossover in a two-band superfluid Fermi gas with an energy shift between the bands. When the intraband coupling in the cold (first) band is fixed as weak, we find that in the case of vanishing pair-exchange interband coupling and in the strong-coupling limit of the hot (second) band the system undergoes a transition to a single-component configuration with a full suppression of the first energy gap and a full redistribution of particles between bands. For nonvanishing pair-exchange interband coupling we reveal a nonmonotonic dependence of the energy gap in the first band vs intraband coupling in the second band, with the presence of a hump. In the case of weak interband coupling, the system shows a significant amplification of the intrapair correlation length of the condensate in the first band in the strong-coupling regime of the second band, which clearly indicates the coexistence of giant Cooper pairs and a bosonic condensate even for nonzero temperatures. This can lead to a nonmonotonic temperature dependence of the second energy gap with a peak. The here predicted coexistence of giant Cooper pairs and bosonic molecules can be verified by means of the visualization of vortex cores in two-component atomic condensates as well as in some iron-based superconductors

Mechanisms of screening or enhancing the pseudogap throughout the two-band Bardeen-Cooper-Schrieffer to Bose-Einstein condensate crossover

We demonstrate the rise and fall of multiple pseudogaps in the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover in two-band fermionic systems having different pairing strengths in the deep band and in the shallow band. The striking features of this phenomenon are an unusual many-body screening of the pseudogap state and the importance of pair-exchange couplings, which induces multiple pseudogap formation in the two bands. The multiband configuration suppresses pairing fluctuations and the pseudogap opening in the strongly interacting shallow band at small pair-exchange couplings by screening effects, with a possible connection to the pseudogap phenomenology in iron-based superconductors. On the other hand, the multiple pseudogap mechanism is accompanied by the emergence of binary preformed Cooper pairs originating from the interplay between intraband and pair-exchange couplings