Strongly Correlated Systems

Strongly Correlated Systems: High Temperature Superconductors Heavy Fermion Compounds Organic materials M.N.Kiselev. 2 OAK RIDGE NATIONAL LABORATORY ...

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M.N.Kiselev

Strongly Correlated Systems: High Temperature Superconductors Heavy Fermion Compounds Organic materials 1

Strongly Correlated Systems: High Temperature Superconductors

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 2

Superconductivity: what and what for • Zero resistance at finite (but low) temperatures − Discovered in 1911 by Kamerlingh-Onnes (Nobel Prize in 1913): Hg superconducting at 4.2 K − Later observed in other metals like Nb, Al, … but the critical temperature, Tc<23K

• Applications (examples):

MRI (without need for liquid He cooling?)

Loss free power transmission (without cooling?)

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Superconducting magnetically levitated train

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Superconducting magnet used to detonate mines

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Superconducting Cables

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Short history of superconductivity

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1908 Heinke Kemerlingh Onnes achieves very low temperature producing liquid He (< 4.2 K)

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1911 Onnes and Holst observe sudden drop in resistivity to essentially zero SC era starts

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1914 Persistent current experiments (Onnes)

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1933 Meissner-Ochsenfeld effect observed

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1935 Fritz and London theory

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1950 Ginsburg - Landau theory

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1957 BCS Theory (Bardeen, Coper, Schrieffer)

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1962 Josephson effect is observed

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1967 Observation of Flux Tubes in Type II superconductors (Abrikosov, Ginzburg, Leggett)

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1980 Tevatron: The first accelerator using superconducting magnets

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1986 First observation of Ceramic Superconductor at 35 K (Bednorz, Muller)

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1987 first ceramic superconductor at 92 K (above liquid Nitrogen at 77 K !) HTS era starts

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2003 discovery of a metallic compound the B2Mg superconducting at 39 K (x2 Tc of Nb3Sn) „

It took ~70 years to get first accelerator from conventional superconductors.

„

How long will it take for HTS or B2Mg to get to accelerator magnets? Have patience!

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What is a superconductor Below the critical temperature Tc the resistivity drops Cooper pair appearance

ρ(T ) = ρ 0 + cT 5

Below Tc the B-field lines are expelled out of a superconductor (perfect diamagnetic behaviour) Meissner 1933

phonon-einteraction

B=0 T < Tc B < Bc

Type I superconductors the superconductivity disappears as T > Tc | B > Bc | J > Jc

Type II superconductors For Bc1 < B < Bc2 there is a partial flux penetration through fluxoid vortexes and a mixed phase

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BCS Pairing mechanism • When electrons form pairs, they behave like bosons and can condensed into a macroscopic quantum state • Bardeen, Cooper, and Shriffer (BCS) develop rigorous description of pairing mechanism − Theory developed in the 1950s, Nobel Prize in 1973

• At T>20K, lattice vibration are strong and destroy pairs, superconductor becomes a normal metal OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 10

BCS theory Normal conducting state

‹ ‹

Superconducting state

Tc ~ 1/ √ M isotopic -> phonons should play a role in superconductivity Creation of Cooper pairs (over-screening effect) „ „ „

An e- attracts the surrounding ion creating a region of increased positive charge The lattice oscillations enhance the attraction of another passing by e- (Cooper pair) The interaction is strengthened by the surrounding sphere of conduction e- (Pauli principle)

In a superconductor the net effect of e-e- attraction through phonon interaction and the e-e- coulombian repulsion is attractive and the Cooper pair becomes a singlet state with zero momentum and zero spin ‹ To break a pair the excitation energy is ∆E = 2∆ ‹

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High Temperature Superconductivity • Doped YBa2Cu3O7

− Normal states is insulating / poor metal − Discovered to be a SC with Tc=30K in 1986 (75 years after KamerlinghOnnes) − 1987 Nobel Prize for Bednorz and Muller − Within years, other transition metal oxides were discovered with Tc>100K (liquid Nitrogen cooled SC)

• There is general agreement that the pairing mechanism is not phonon mediated OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 12

Some examples of HTSC Compounds • Mostly compounds • Record holder: Tc =138 K • High Hc2: Hc2 > 1000 000 G (YBCO)

Element

Tc (K)

Tc

7.80

Nb

9.25

La1.85Ba.15CuO4

30

YBa2Cu3O7+

93

Ca1-xSrxCuO2

110

Tl2Ba2Ca2Cu3O10

128

Hg0.8Tl0.2Ba2Ca2Cu3O8.33

138

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Crystal Structure and Fermi Surface

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Crystal Structure and Fermi Surface

H c

Hab

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Crystal Structure and Fermi Surface

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High Tc Superconductivity (conventional wisdom) • Model Copper oxide planes with single band 2D Hubbard models (Zhang & Rice, PRB 1989)

U t

• Still not solvable, but thousands of papers published every year • David Pines: “arguably the major problem in physics today”

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Microscopic Model: Why are Cuprates Unique? (1987)

o o cu

Cannot be reduced to a Hubbard Model because the ionization energy of Cu is nearly the same as the ionization energy of oxygen. OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 19

What interactions/orders exist in High-Tc Superconductor?

• Electron-phonon interaction

• Spin exchange interaction-antiferromagnetic order • Charge density waves, spin density waves and other competing orders. OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 20

Of the many proposed pairing mechanisms, few remain likely: • Quasi particles in AF background (Hirsch 02)

• Resonating valence bond (Anderson 87)

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Valence bonds in benzene

Resonance in benzene leads to a symmetric configuration of valence bonds (F. Kekulé, L. Pauling) OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 22

Valence bonds in benzene

Resonance in benzene leads to a symmetric configuration of valence bonds (F. Kekulé, L. Pauling) OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 23

Valence bonds in benzene

Resonance in benzene leads to a symmetric configuration of valence bonds (F. Kekulé, L. Pauling) OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 24

Phase Diagram and Competing Orders

PG: Pseudogap, SC: Superconductivity, CO: Competing order, AFM: Antiferromagnetic OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 25

Strongly Correlated Systems: Heavy Fermions

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Heavy Fermions

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Specific heat C T

tan ϕ = B

A

C = AT + BT 3 T2

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de Haas-van Alphen Effect (dHvA)

S ε

SF

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Heavy Fermion Compounds

s-p-d

s-p-d 5f

4f

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Models: Kondo Lattice H =

∑ ε (k )c

+ k ,σ

k

c k ,σ + J

∑ i

→ →

S i si +







I ij S i S

j

ij

→ →

H Kondo = J ∑ Si si i

→ →

H RKKY = ∑ I ij Si S j i, j

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Kondo-Effect

→ →

H Kondo = J ∑ Si si i

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Resistance at low temperatures

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Kondo Cloud

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Kondo-Screening

U. S. DEPARTMENT OF ENERGY 35

Ruderman-Kittel-Kasuya-Yosida (RKKY) Wechselwirkung

→ →

H RKKY = ∑ I ij Si S j i, j

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I RKKY

Ferromagnetic Ordering

2p F R Antiferromagnetic Ordering

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Antiferromagnetic Ordering

T > Tc

T < Tc OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 38

Spin Liquid

Resonating Valence Bonds

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Heavy Fermions: Phase Diagram

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Strongly Correlated Systems: Organic Conductors

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Bechgaard salts

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Molecular Superconductors

ET=BEDT-TTF

Bis(EthyleneDiThio) TetraThiaFulvalene OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY

J.A.Schlueter et al, 2004

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Conducting/Magnetic Hybrid Molecular Solids

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY

J.A.Schlueter et al, 2004

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X[Pd(dmit)2]2 Pd

S

C

One free electron spin on each vertex of a triangular lattice OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY

46 M. Tamura et al., J. Phys. Soc. Jpn. 75, 093701 (2006)

Spin Ladders

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Phase Diagram

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and Nanostructures …

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