GI PERTURBATIONS, UNITARITY AND FRAME INDEPENDENCE IN HIGGS INFLATION
Unitarity in periodic potentials and correlated swave...
Transcript of Unitarity in periodic potentials and correlated swave...
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Unitarity in periodic potentials and correlated swaveCooper pair insulators
Predrag NikolićGeorge Mason University
March 21, 2011
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Y.Wang, et.al,Phys.Rev.B 73, 024510 (2006)
(Princeton)
T.Hanaguri, et.al,Nature 430, 1001 (2004)
(Cornell)
R. W. Crane, et.el,Phys.Rev.B 75, 184530 (2007)
(Johns Hopkins)
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Pseudogap: quantum vortex liquid?
Unitarity in periodic potentials & correlated s-wave Cooper pair insulators
Vortex dynamics theory in cuprates:
Z.Tesanovic, Phys.Rev.Lett. 93, 217004 (2004)L.Balents, et.al, Phys.Rev. B 71, 144508 (2005)PN., S.Sachdev, Phys.Rev.B 73, 134511 (2006)
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• 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)
Is there a universal picture?
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• SF-I pairing transitions – (p) ..... particle dominated – (h) ..... hole dominated – (ph) .. relativistic
• Tuning parameters – Chemical potential μ – Interaction strength U – Lattice potential & depth V
Interacting fermions in a lattice
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Exact renormalization group:
, , … = 0
+ + …
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RG: Only particles or holes
d=2 d=3
Unitarity in periodic potentials & correlated s-wave Cooper pair insulators
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Intra-band Cooper
Inter-band Cooper
Exciton
Ext. s-wave resonating singlet (iron-based superconductors)
RG: Both particles & holes
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RG: ε=d-2 expansion– 17 tractable fixed points
Unitarity in periodic potentials & correlated s-wave Cooper pair insulators
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• 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, Phys.Rev. B 83, 064523 (2011)
RG & Cooper pair insulators
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– Non-analytic change in the excitation spectrum
– Non-equilibrium phase transition
– Driven condensate: Cooper-pair laser
Mott-band insulator distinction
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P.N, Zlatko Tešanović, Phys.Rev. B 83, 064501 (2011)
Unitarity in periodic potentials & correlated s-wave Cooper pair insulators
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• Microscopic pairing mechanism (?) – Short-range AF correlations ⇒ gap (antinodal) – Weak effective attractive interaction from pair-hopping (antinodal)
– Superconductivity + low temperature + d=2 ⇒ “BEC regime”
• 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 (?)
Pseudogap in cuprates
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• Renormalization group in band insulators – Fixed points ⇒ scattering resonances – Run-away flow ⇒ correlated (bosonic Mott) insulators – Implications for non-equilibrium
• 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
Conclusions
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P.N, Zlatko Tešanović, Phys.Rev. B 83, 064501 (2011)
P.N, Phys.Rev. B 83, 064523 (2011)
Unitarity in periodic potentials & correlated s-wave Cooper pair insulators