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We examine key aspects of the theory of the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) crossover, focusing on the temperature dependence of the chemical potential,μ. We identify an accurate method of determining the change ofμin the cuprate high temperature superconductors from angle-resolved-photoemission data (along the ‘nodal’ direction), and show thatμvaries by less than a few percent of the Fermi energy over a range of temperatures from far below to several times above the superconducting transition temperature,Tc. This shows, unambiguously, that not only are these materials always on the BCS side of the crossover (which is a phase transition in thed-wave case), but are nowhere near the point of the crossover (where the chemical potential approaches the band bottom).
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Josephson effects in twisted nodal superconductors
Motivated by the recent proposals for unconventional emergent physics in twisted bilayers of nodal superconductors, we study the peculiarities of the Josephson effect at the twisted interface between d-wave superconductors. We demonstrate that for clean interfaces with a twist angle θ0 in the range 0◦ < θ0 < 45◦, the critical current can exhibit nonmonotonic temperature dependence with a maximum at a nonzero temperature as well as a complex dependence on the twist angle at low temperatures. These effects are shown to reflect the destructive interference between the d-wave order parameters near the nodes at nonzero twist angle. Close to 45◦ we find that the critical current does not vanish due to Cooper pair cotunneling, which can lead to the transition to a time-reversal breaking superconducting d + id phase, which can be suppressed by the interface roughness. We provide a comprehensive theoretical analysis of experiments that can reveal this cotunneling for twisted superconductors close to θ0 = 45◦. In particular, we demonstrate that both the emergence of the Fraunhofer interference pattern near θ0 = 45◦ and fractional Shapiro steps yield unambiguous evidence of Cooper pair cotunneling, necessary for topological superconductivity.
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- Award ID(s):
- 2105048
- PAR ID:
- 10576007
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review B
- Volume:
- 111
- Issue:
- 1
- ISSN:
- 2469-9950
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1103/PhysRevB.111.014514
