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Shape Resonance at a Lifshitz Transition for High Temperature Superconductivity in Multiband Superconductors

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Abstract

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. This superconducting phase provides a particular case of topological superconductivity with multiple condensates of different winding numbers.

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Authors and Affiliations

  1. Advanced Light Source, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA, 94720, USA

    Davide Innocenti

  2. Institute for Microelectronics and Microsystems, IMM CNR, Via del Fosso del Cavaliere 100, 00133, Roma, Italy

    Antonio Valletta

  3. Physics Department, Sapienza University of Rome, P. le Aldo Moro 2, 00185, Roma, Italy

    Antonio Bianconi

  4. Dipartimento di Ingegneria Meccanica, Università di Roma Tor Vergata, 00133, Roma, Italy

    Davide Innocenti

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  1. Davide Innocenti
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Innocenti, D., Valletta, A. & Bianconi, A. Shape Resonance at a Lifshitz Transition for High Temperature Superconductivity in Multiband Superconductors. J Supercond Nov Magn 24, 1137–1143 (2011). https://doi.org/10.1007/s10948-010-1096-y

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