High temperature superconductivity
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Outline:. Basic facts concerning the cuprates. Stripes: What are they and why do they occur. Experimental signatures of stripes. Are stripes good or bad for superconductivity ? . Consequences of stripe formation :. Fractionalization. Confinement. High Temperature Superconductivity:.

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High temperature superconductivity

Outline:

  • Basic facts concerning the cuprates

  • Stripes: What are they and why do they occur

  • Experimental signatures of stripes

  • Are stripes good or bad for superconductivity ?

  • Consequences of stripe formation:

  • Fractionalization

  • Confinement

High Temperature Superconductivity:

S. Kivelson

V. Emery

E. Carlson

M. Granath

V. Oganesyan

X-J. Zhou

Z-X. Shen

D. Orgad

Racah Institute, Hebrew University, Jerusalem


The cuprates basic structure

The Cuprates: Basic Structure

  • Universal element – CuO planes

  • Parent (undoped) compounds – Heisenberg antiferromagnets

  • Hole doping by chemical substitution / Oxygen doping


The cuprates typical phase diagram

Renner et al.

Harris et al.

Warren et al.

Takagi et al.

T

tunneling

UD Bi2212

Puchkov et al.

NMR

ARPES

Pseudogap

AF

SC

DC resistivity

x

under

optimal

over

Neutron scattering, Specific heat …

doping

Optical conductivity

The Central Question: What happens to an AF upon doping with holes?

The Cuprates: Typical Phase Diagram


Holes in an af why do stripes occur

Holes in an AF : Why Do Stripes Occur?

Coulomb Interactions

PHASE SEPARATION

STRIPES

Kinetic Energy

Frustration


Stripes in other systems competing interactions

Stripes in Other Systems: Competing Interactions

Ferrofluid between glass plates

Ferromagnetic garnet film

l~1cm

l~10mm

l~10mm

l~400A

Ferromagnetic garnet film

Block copolymers film


Stripe signatures in s k w

ky

kx

ky

kx

Stripe Signatures in S(k,w)

Real Space

Momentum Space


Experimental evidence for stripes neutron scattering

Experimental Evidence for Stripes: Neutron Scattering

ky

Static stripe

order (LNSCO)

kx

0.25

E=24.5meV

Dynamic stripes

(YBCO)

0.12

Mook et al.

Tranquada et al.


Experimental evidence for stripes arpes

LNSCO

Experimental Evidence for Stripes: ARPES

Angle Resolved PhotoEmission Spectroscopy measures

the single hole spectral function


Experimental evidence for stripes tunneling microscopy

Experimental Evidence for Stripes: Tunneling Microscopy

B=5T

B=0

Howald et al.

Hoffman et al.


Consequences of stripe formation spin gap and enhanced sc correlations

  • The spin-gap creates an amplitude of the SC order parameter

  • Provides high pairing scale (avoid Coulomb repulsion)

Consequences of Stripe Formation: Spin-gap and Enhanced SC Correlations

Stripes

Doped Spin Ladders: known to be spin-gapped

T

PG

AF

SC

x


A problem

Bad News:

It also enhances CDW correlations:

more divergent !

Old problem from search for organic superconductors

A Problem …

Good News:

In 1D a spin-gap enhances pairing:

divergent for Kc>1/2

(Kc<1 for repulsive interactions)


And its resolution

T

Stripe fluctuations

(quantum, thermal or quenched)

are necessary for high Tc!

y2

y1

Nematic?

Phase

Stiffness

L1

L2

Phase

Stiffness

PG

AF

SC

Yamada et al.

x

static

fluctuating

dissolved

x

y

… And Its Resolution

Stripe fluctuations dephase CDW coupling:

Stripe fluctuations enhance phase coupling:


Consequences of stripe formation electron fractionalization above t c

In a Fermi liquid the elementary excitations have the quantum numbers

of an electron

Mo surface

state

multi-qp

background

Valla et al.

qp peak

In a Luttinger liquid the excitations come in

4 flavors

MDC

EDC

EDC

MDC

Consequences of Stripe Formation:Electron Fractionalization Above Tc


Evidence for fractionalization

ARPES in La1.25Nd0.6Sr0.15CuO4

Breakdown of W-F Law

1DEG

in Pr1.85Ce0.15CuO4

Orgad et al.

Hill et al.

Sharp in Momentum

Broad in Energy

Evidence for Fractionalization


Below t c a coherent peak

Not a Conventional QP

  • Not present above Tc

  • Intensity grows below Tc

  • Energy and lifetime not

  • temperature dependent

Below Tc: A Coherent Peak

Optimally Doped BSCCO (Tc=91K)

Fedorov et al.


Josephson coupling confines 1d solitons

and

Charge and spin solitons create

phase shift in pair field

s

c

Frustrated Josephson Coupling

between solitons

Bound spin-charge soliton pair

Josephson Coupling Confines 1D Solitons

The electronic operator

creates kinks in


A k w in the superconducting phase

Feng et al.

A<(k,w) in the Superconducting Phase

incoherent

  • Quasiparticle weight depends on superfluid density:


Conclusions

Conclusions

  • Stripes are ubiquitous in the cuprate high temperature

  • superconductors

  • They are important for high temperature

  • superconductivity

  • There is evidence that the normal state of the cuprates

  • is fractionalized

  • In a quasi-one-dimensional superconductor Tc also

  • marks a confinement transition


Landau theory of stripe phases

Stripes are “charge driven” :

Spin order is secondary and may be absent

Landau Theory of Stripe Phases

Coupled charge (CDW) order and spin (SDW) order

Zachar et al.


Spin gap proximity effect

“system”

“environment”

tunneling

is relevant.

Spin-gap Proximity Effect

Single particle tunneling irrelevant

possible

Pair tunneling

When

The spin modes and the relative charge phase mode are gapped.

The only gapless mode involves the total SC phase

  • Kinetic energy driven pairing

  • Repulsive interactions within system and environment increase a

  • Repulsive interactions between system and environment decrease a

  • Pre-existing spin-gap in environment decreases a


Arpes and stripes

LNSCO

LSCO

Zhou et al.

ARPES and Stripes

Angle Resolved PhotoEmission Spectroscopy measures

the single hole spectral function

LNSCO


Disordered stripe array spectral weight

Disordered Stripe Array: Spectral Weight

Low Energy Spectral Weight

Granath et al.


Disordered stripe array interacting spectral function

Disordered Stripe Array: Interacting Spectral Function

Granath et al.


A model quasi one dimensional superconductor

Weak Pair Tunneling

(Couples charge and spin)

A Model:Quasi-one-dimensional Superconductor

Charge: Gapless

Spin: Gapped


Prediction new magnetic resonance

  • Spin 1 mode that exists below 0.4 Tc

  • 2kF mode: should appear around

  • Threshold at 2Ds

Prediction: New Magnetic Resonance

Neutron scattering measures the spin-spin correlation function:

creates 2 spin solitons and 2 charge solitons

Treat more massive spin solitons as static and solve for the charges:

s

s

Get effective Schrodinger equation for spins:


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