Three Discoveries in Underdoped Cuprates

Giant Nernst effect Z. A. Xu et al., Nature 406, 486 (2000) “Electron Crystal” in STM M. Vershinin et al., Science 303, 1995 (2004); T. Hanaguri, C. Lupien et al., Nature 430, 1001 (2004) “Thermal metal” in non-SC YBCO Sutherland et al., cond-mat/050124

Pairing d-wave Pseudogap in Underdoped Cuprates

?

dSC

  “Normal” state appears strange and non-Fermi liquid in nature. Strong correlations among its fermionic excitations are apparent.

In contrast, the superconducting state appears BCS-like. Its low energy fermionic excitations are protected by a large d-wave (pseudo)gap.

Construct a theory in which a correlated d-wave superconductor serves as a reference state and the basis for exploration of the pseudogap. As x is reduced, quantum vortex-antivortex pairs are progressively admixed into the ground state. Key questions: i) How does such superconductor become “normal”? ii) What are the quantum ground states in natural proximity to such superconductor?

What is the “pseudogap” state?

iii) What is the low energy effective theory within the pseudogap whose role parallels that of a Fermi liquid in conventional metals?

QED

3

Phase Diagram

As doping decreases, the number of quantum vortex-antivortex pairs admixed into dSC ground state increases (n s << n 0 ).

Nernst Effect in HTS Courtesy of N.P. Ong Vortex fluctuations in the pseudogap state !!

BiSrCaCuO Z. A. Xu et al., Nature 406, 486 (2000)

HTS are

Nodal

d-wave Superconductors (Phase sensitive exps., ARPES, FT-STS, etc.)

Tsuei & Kirtley, 1997

FT-STS measured

D a 1.0 0.8 0.6 0.4 0.2

FT-STS from Davis’ group,

0.0 0.0 Nature 422, 520 (2003).

0.2 Fig. 4 0.4 0.6

k x

( / ) 0.8 1.0

ARPES

D(q), Mesot PRL 83,840 (1999)

Courtesy of J.C. Davis

“Thermal Metal” in YBCO

H = 0 p < p SC

Sutherland

et al

., cond-mat/050124 (2005)

YBCO : non-superconducting state is a thermal metal LSCO : non-superconducting state is an insulator

Courtesy of M. Sutherland

QED

3

Phase Diagram

As doping decreases, the number of quantum vortex-antivortex pairs admixed into dSC ground state increases (n s << n 0 ).

Quantum vortex-antivortex pairs unbind and ODLRO is destroyed (n s = 0). Still, BdG chiral symmetry of d-wave nodal qparticles remains, protecting gapless fermionic excitations !!

Chiral symmetry  d-wave amplitude stiffness

QED

3

Phase Diagram

As doping decreases, the number of quantum vortex-antivortex pairs admixed into dSC ground state increases (n s << n 0 ).

BdG chiral symmetry is finally broken, nodal fermions are gapped   AF/SDW Quantum vortex-antivortex pairs unbind and ODLRO is destroyed (n s = 0). Still, BdG chiral symmetry of d-wave nodal qparticles remains protecting gapless fermionic excitations !!

Chiral symmetry  d-wave amplitude stiffness

“Electron Crystal” in Underdoped Cuprates

M. Vershinin et al., Science

303

, 1995 (2004); T. Hanaguri, C. Lupien et al., Nature

430

, 1001 (2004) Underdoped

Ca 2-x Na

x

CuO 2 Cl 2

x=0.08 (I), 0.10 (SC), 0.12 (SC) Courtesy of J.C. Davis

Pseudogap State

150 pS

100K

Courtesy of A. Yazdani

K-Space Modulation along the Cu-O bond direction 500Å x 200 Å Cu-O

35 pS Vershinin et al. Science 303 , 1995 (2004)

Hofstadter Butterfly and Cooper Pair Density-Wave in HTS “Electron Crystal” in HTS (Vershinin, et al., Hanaguri, Lupien, et al.) Hofstadter “Butterfly” Spectrum Dual theory supplies the connection between two phenomena. It leads to Hofstadter “magic fractions” f = p/q for Cooper pair DW at special x: f = p/q = (1 – x)/2 !!

Pseudogap: Charge Insulator, Spin Conductor charge current

e e

Charge current cancels: J dual vortex solid.

c = 0 .

Charge center-of-mass is pinned to the lattice: Abrikosov-Hofstadter spin current Spin current J s is finite. Pseudogap is a spin (semi) metal: Spinful BdG nodal fermions with long range gauge field correlations -- chiral QED 3 .

The system consists of electrons paired in spin singlets (Cooper pairs) + unpaired electrons (BdG nodal fermions). Both carry charge (2e vs. e) but only BdG nodal fermions carry spin. As Cooper pairs and nodal fermions screen each other charges, the spin remains “free”   Wiedemann-Franz law is violated !!

Phase Diagram from Dual Theory of a d-wave Superconductor Antiferromagnet/SDW (Mott ins.) Pairing pseudogap (chiral QED 3 ) dSC Nodal pair DW (chiral QED 3 ) Supersolid Nodal Pair CDW is a charge insulator dual solid) but a spin conductor (Abrikosov-Hofstadter (chiral QED 3 )  thermal metal

QED

3

Phase Diagram