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We discuss the shape resonance in the superconducting gaps of a two-band superconductor by tuning the chemical potential at a Lifshitz transition for Fermi surface neck collapsing and for spot appearing. The high temperature superconducting scenario for complex matter shows the coexistence of a first BCS condensate made of Cooper pairs in the first band and a second boson-like condensate made of bosons like bipolarons, in the second band where the chemical potential is tuned near a Lifshitz transition. The interband coupling controls the shape resonance in the pair exchange between the two condensates. We discuss the particular BCS–Bose crossover that occurs at the shape resonance tuning the Lifshitz parameter (the energy difference between the chemical potential and the Lifshitz topological transition) like tuning the external magnetic field for the Feshbach resonances in ultracold gases …
Springer US
Publication date: 
1 Apr 2011

Davide Innocenti, Antonio Valletta, Antonio Bianconi

Biblio References: 
Volume: 24 Issue: 3 Pages: 1137-1143
Journal of Superconductivity and Novel Magnetism