Unitarity in periodic potentials and correlated s­waveCooper pair insulators

Predrag NikolićGeorge Mason University

March 21, 2011

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)

2/10

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)

• 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?

3/10Unitarity in periodic potentials & correlated s-wave Cooper pair insulators

• 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

4/10Unitarity in periodic potentials & correlated s-wave Cooper pair insulators

Exact renormalization group:

, , … = 0

+ + …

5/10

RG: Only particles or holes

d=2 d=3

Unitarity in periodic potentials & correlated s-wave Cooper pair insulators

Intra-band Cooper

Inter-band Cooper

Exciton

Ext. s-wave resonating singlet (iron-based superconductors)

RG: Both particles & holes

6/10

RG: ε=d-2 expansion– 17 tractable fixed points

Unitarity in periodic potentials & correlated s-wave Cooper pair insulators

• 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

7/10Unitarity in periodic potentials & correlated s-wave Cooper pair insulators

– Non-analytic change in the excitation spectrum

– Non-equilibrium phase transition

– Driven condensate: Cooper-pair laser

Mott-band insulator distinction

8/10

P.N, Zlatko Tešanović, Phys.Rev. B 83, 064501 (2011)

Unitarity in periodic potentials & correlated s-wave Cooper pair insulators

• 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

9/10Unitarity in periodic potentials & correlated s-wave Cooper pair insulators

• 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