Theory of Correlated Superconductors: s vs. dwave
Predrag Nikolić George Mason University
December 10, 2010
Acknowledgments
Zlatko Tešanović Peter Armitage Subir Sachdev Anton Burkov Arun Paramekanti IQM @ Johns Hopkins IQM @ Johns Hopkins Harvard Waterloo Toronto
• Affiliations and sponsors
The Center for Quantum Science
Pseudogap: quantum vortex liquid
T.Hanaguri, et.al, Nature 430, 1001 (2004) (Cornell)
Y.Wang, et.al, R. W. Crane, et.el, Phys.Rev.B 73, 024510 (2006) Phys.Rev.B 75, 184530 (2007) (Princeton) (Johns Hopkins) Is there a universal picture?
• Correlated superconductors & pseudogap – QED3 (Tesanovic, Franz, Vafek, Herbut...) – Nodal liquid (Balents, Fisher, Nayak) – Competing orders (Tesanovic, Balents, Sachdev...)
• What about electrons? – Why pairing correlations in the normal state? What does it mean?
• A universal theory of pairing correlations? – Insight from unitarity? (BEC-BCS crossover)
Unitarity (scattering resonance)
• Universality @ unitarity – Quantum critical point – Zero density
M.Y.Veillette, D.E.Sheehy, L.Radzihovsky; Phys.Rev. A 75, 043614 (2007) Y.Nishida, D.T.Son; PRL 97, 050403 (2006) P.N., S.Sachdev; Phys.Rev. A 75, 033608 (2007)
Unitarity in lattice potentials
• SF-I pairing transitions – (p)..... particle dominated – (h)..... hole dominated – (ph) .. relativistic
• Tuning parameters – Chemical potential μ – Interaction strength U – Lattice potential & depth V
BEC-BCS crossover channels
Bound singlet of two conduction band or two valence band fermions
Bound singlet of a conduction and a valence band fermion
Exciton: bound singlet of a particle and a hole
Assisted resonance? Extended s-wave resonating singlet (iron-based superconductors)
Renormalization group
• Universality class of the SF-I transition – bosonic mean-field or XY: d=2, or strong coupling in d>2 – pair-breaking: weak coupling in d>2: P.N, arXiv:1006.2378
Bosonic Mott insulators
• Insulator adjacent to the SF • Bosonic Mott insulator – Mott (BEC) or band (BCS) – No symmetry breaking required – Bosonic low energy excitations D.M.Eagles; Phys.Rev. 186, 456 (1969) – Large fermion gap P.N., Zlatko Tešanović, arXiv:1008.4369
Mott-band insulator distinction
• Quantum phase transition – Non-analytic change of the ground-state manifold as a function of tuning parameters
• A generalization to the whole spectrum – Non-analytic change of the Hamiltonian (density matrix) as a function of tuning parameters
Non-equilibrium pairing transitions
• Cooper pair laser – Sharp non-equilibrium distinction between band and Mott insulators • Numerics? – Quantum Monte Carlo – Negative-U Hubbard model
• Experiments – Heterostructures: SC + narrow bandgap material – Superlattices – Cold atoms
Non-trivial Mott insulators
• Broken symmetries – Pair density waves (particle-particle BEC) – Magnetic, nematic... (p-wave pairs) – Charge, spin, valley density waves (particle-hole BEC) – Valence-bond crystals (inter-valley particle-hole BEC)
• Topological orders – Spin liquids (particle-hole) – Fractional quantum Hall states (even-denominator ν) – Fractional quantum spin Hall states? (strongly correlated “topological insulators”)
Implications
• Generic ingredients for Cooper pair mottness – “Independent” gap for fermionic excitations – Effective attractive interactions between fermions – Proximity to a superconducting phase – Low temperatures + d=2, or strong interactions in d>2
• Amorphous superconducting films – Disorder: a source of fermion gap – Superconductivity + low temperature + d=2 – Consequence: bosonic response out of equilibrium
Pseudogap in cuprates
• Microscopic pairing mechanism – Short-range AF correlations ⇒ gap (antinodal) – Hole pair hopping does not frustrate spins ⇒ effective weak attractive interaction (antinodal) – Superconductivity + low temperature + d=2 – Consequence: “BEC regime” for antinodal quasiparticles
• Complications due to d-wave pairing – Low energy fermions have small DOS – Low energy bosons have large DOS, dominate response – Nodal pairbreaking occurs, but anomalously slow
Conclusions
• Effective scattering resonances – Weak-coupling universality in generic band insulators – BEC-BCS crossovers in various channels – Path to strongly correlated states of fermions
• Bosonic Mott insulators from electrons – Adjacent to superfluid phases in effective BEC regimes – Susceptible to symmetry breaking or topological order
• Systems of interest – Cuprates, amorphous superconducting films... – Re-entrant superconductors, topological insulators, cold atoms...