High THigh Tcc Superconductors & Superconductors &

QEDQED33 theory theory ofof the cuprates the cuprates

Tami Pereg-BarneaTami Pereg-Barnea

UBCUBC

tami@physics.ubc.catami@physics.ubc.ca

outlineoutline

High THigh Tcc – Known and unknown – Known and unknown Some experimental facts and phenomenologySome experimental facts and phenomenology

ModelsModels Attempts to solve the problemAttempts to solve the problem The inverted approachThe inverted approach

QEDQED33 – formulations and consequences – formulations and consequences

FactsFacts

The parent compounds are AF insulators.The parent compounds are AF insulators.

2D layers of CuO2D layers of CuO22

Superconductivity is the condensation of Superconductivity is the condensation of Cupper pairs with a D-wave pairing Cupper pairs with a D-wave pairing potential.potential. The cuprates are superconductors of The cuprates are superconductors of type IItype IIThe “normal state” is a non-Fermi liquid, The “normal state” is a non-Fermi liquid, strange metal.strange metal.

YBCO microwave conductivity

BSCCOARPES

Underdoped Bi2212

Neutron scattering – () resonance in YBCO

PhenomenologyPhenomenology

The superconducting state is a D-wave BCS The superconducting state is a D-wave BCS superconductors with a Fermi liquid of nodal superconductors with a Fermi liquid of nodal quasiparticles.quasiparticles.

The AF state is well described by a Mott-The AF state is well described by a Mott-Hubbard model with large U repulsion.Hubbard model with large U repulsion.

The pseudogap is strange!The pseudogap is strange! Gap in the excitation of D-wave symmetry but no Gap in the excitation of D-wave symmetry but no

superconductivitysuperconductivity Non Fermi liquid behaviour – anomalous power laws in Non Fermi liquid behaviour – anomalous power laws in

verious observables.verious observables.

Phase diagramPhase diagramAF

AF

AF

Theoretical approachesTheoretical approaches

Starting from the Hubbard model at ½ Starting from the Hubbard model at ½ filling.filling.

Slave bosons SU(2) gauge theoriesSlave bosons SU(2) gauge theoriesSpin and charge separationSpin and charge separationStripesStripes

PhenomenologicalPhenomenologicalSO(5) theorySO(5) theoryDDW competing orderDDW competing order

The inverted approachThe inverted approach

Use the phenomenology of d-SC as a Use the phenomenology of d-SC as a starting point.starting point.

““Destroy” superconductivity without closing Destroy” superconductivity without closing the gap and march backwards along the the gap and march backwards along the doping axis.doping axis.

The superconductivity is lost due to The superconductivity is lost due to quantum/thermal fluctuations in the phase quantum/thermal fluctuations in the phase of the order parameter.of the order parameter.

Vortex Antivortex unbindingVortex Antivortex unbinding

Emery & Kivelson Nature 374, 434 (1995)Franz & Millis PRB 58, 14572 (1998)

Phase fluctuationsPhase fluctuations

Assume Assume 00 = | = ||= const.|= const.

Treat exp{iTreat exp{i(r)} as a quantum number – sum (r)} as a quantum number – sum over all paths.over all paths.

Fluctuations in Fluctuations in are smooth (spin waves) or are smooth (spin waves) or singular (vortices).singular (vortices).

Perform the Franz Tešanović transformation - a Perform the Franz Tešanović transformation - a singular gauge transformation.singular gauge transformation.

The phase information is encoded in the dressed The phase information is encoded in the dressed fermions and two new gauge fields.fermions and two new gauge fields.

FormalismFormalism

Start with the BdG Start with the BdG HamiltonianHamiltonian

FT transformation – in FT transformation – in order to avoid branch order to avoid branch cuts.cuts.

The transformed HamiltonianThe transformed Hamiltonian

The gauge field aThe gauge field a couples couples

minimallyminimally a a

The resulting partition The resulting partition function is averaged over all function is averaged over all A, B configurations and the A, B configurations and the two gauge fields are coarse two gauge fields are coarse grained.grained.

The physical pictureThe physical picture

RG arguments show that RG arguments show that vv is massive is massive

and therefore it’s interaction with the and therefore it’s interaction with the Toplogical fermions is irrelevant.Toplogical fermions is irrelevant.

The The aa field is massive in the dSC phase field is massive in the dSC phase

(irrelevant at low E) and massless at the (irrelevant at low E) and massless at the pseudogap.pseudogap.

The kinetic energy of The kinetic energy of aa is Maxwell - like. is Maxwell - like.

Quantum “Electro” DynamicsQuantum “Electro” Dynamics

Linearization of the theory Linearization of the theory around the nodes.around the nodes.

Construction of 2 Construction of 2 4-component Dirac 4-component Dirac spinors.spinors.

Dressed QP’sDressed QP’s

QED3 Spectral functionOptimally doped BSCCO

Above Tc

T.Valla et al. PRL (’00)

Chiral Symmetry Breaking Chiral Symmetry Breaking AF order AF order

The theory of Quantum electro dynamics has an The theory of Quantum electro dynamics has an

additional symmetry, that does not exist in the additional symmetry, that does not exist in the

original theory.original theory.

The Lagrangian The Lagrangian

is invariant under the global transformation is invariant under the global transformation

where where is a linear is a linear

combination ofcombination of

The symmetry is broken spontaneously through The symmetry is broken spontaneously through

the interaction of the fermions and the gauge the interaction of the fermions and the gauge

field.field.

The symmetry breaking (mass) terms that are The symmetry breaking (mass) terms that are

added to the action, written in the original nodal added to the action, written in the original nodal

QP operators represent:QP operators represent: Subdominant d+is SC order parameterSubdominant d+is SC order parameter Subdominant d+ip SC order parameterSubdominant d+ip SC order parameter Charge density wavesCharge density waves Spin density wavesSpin density waves

AntiferromagnetismAntiferromagnetism

The spin density wave is described by:The spin density wave is described by:

where where , , labels denote nodes. labels denote nodes.

The momentum transfer is Q, which spans two The momentum transfer is Q, which spans two antipodal nodes.antipodal nodes.At ½ filling, Q → (At ½ filling, Q → (,,) – commensurate ) – commensurate Antiferromagnetism.Antiferromagnetism.

_

SummarySummary

Inverted approach: dSC → PSG → AFInverted approach: dSC → PSG → AF

View the pseudogap as a phase disordered View the pseudogap as a phase disordered superconductor.superconductor.

Use a singular gauge transformation to Use a singular gauge transformation to encode the phase fluctuation in a gauge field encode the phase fluctuation in a gauge field and get QEDand get QED33 effective theory. effective theory.

Chirally symmetric QEDChirally symmetric QED33 Pseudogap Pseudogap

Broken symmetry Broken symmetry Antiferromagnetism Antiferromagnetism