Unconventional Superconductivity (The Phenomenon) and ...

Pedagogical Overview

Unconventional Superconductivity (The Phenomenon) and Unconventional Superconductors (The Materials)

• Conventional Superconductivity • Unconventional Superconductivity and Superconductors • Some Personal Favorites

The Essence of Superconductivity -- With the Benefit of Hindsight

! pi= "int #$( )% cm r$( ) = "int #$( )% cm r$( ) e&i

Internal structure of a pair

• q = 2 • Pairing symmetry, pair size • Single par6cle excita6ons • Density of states • Material parameters of GL theory • The mechanism

Microscopic Specific Proper-es

ri

e

e !"

!BCS•

CM wave func5on of pair

Macroscopic Emergent Proper-es

• GL Order parameter/GL theory • R = 0, B = 0, • Type II superconduc6vity • Josephson effect

! = !0 = hc / q

ith pair

Superconductivity arises when phases lock !1 =!2 =!3 = ......!"..... =!

Some History

Adapted from a DoE Report

Pr(O-‐F)FeAs

BCS Theory

Conven6onal Superconduc6vity GL Theory, BCS, Gorkov and Eliashberg

Conven6onal Era Unconven6onal Era

Key Results of BCS Theory

• Superconductivity arises when electrons bind into pairs and these pairs lock their mutual phases to form a macroscopic quantum state. • The single-particle excitations of a superconductor are comprised of a phase- coherent linear combinations of electrons and holes. • , which implies that if no other phases intervene, all normal metals will become superconductors as T -> 0. Here λ is the attractive interaction parameter (not necessarily the electron-phonon interaction). • Size of Cooper pair

Tc = !oe"1/#

(k !,"k #)

! ks = uk! k

e + vkei"! k

h

!

•k !

• ! k "

• !k "

•! "k #

(k !,"k #)$ ( %k !," %k #)FS

In general, time reversed pairs (Anderson)

! " !vF / kTc

The Triumvirate Defining Conventional Superconductivity A Complete Theory (BCS + Mechanism + Equations for the Material Parameters)

BCS

Elisashberg Ginzburg-‐Landau

Tc =!0e"1

#"µ*

µ*= µ

1+ µ !n !F"D

#$%

&'(

F(r) = d 3! r " # 2 + 1

2$ # 4 !2

2m*%i&% e*

!cA'

()*+,#

2

+ B2

8-./0

10

230

40

Conventional Superconductivity

Unconventional Superconductivity

Even More Unconventional

Superconductivity Weak coupling λ << 1

Strong coupling λ > 1 Maximum in Tc

Very strong coupling λ >> 1 Phase fluctua5ons – Tc à 0

Mean field theory Quantum fluctua5ons when ξ is small

Bose metal of pairs?

S-‐wave singlet Time reversed pairs

Higher angular momentum pairing

p, d, …… pairing

S-‐wave triplet odd-‐ frequency pairing Broken TRS pairs – s + is, d + is, etc

Retarded el-‐ph interac5on Any other mechanism: Electronic interac5ons -‐-‐

spin or charge

Non-‐Fermi liquid in normal state

Quantum cri5cal points Compe5ng ordered phases

Anderson’s theorem Tc independent of disorder

Enhanced coulomb repulsion due to disorder

Disorder driven Superconductor/Insulator

Transi5on

Tc =!0e"1!

Tc = e!1

!!µ*

Tc =!0e"1

#"µ*"$µ*


!(k) = dk 3" V (k,k ')!(k ')

! " !vF / kTpTc = min T! ,Tp{ }

Conventional Classic BCS and

Extensions


More Unconventional Superconductivity

Single band superconductivity

Weakly coupled bands/orbitals

Josephson effects in k space

Q = 0 pairing Finite Q pairing

Pair density waves

Quasi-particles Phase coherent

superposition of e’s and h’s

SN proximity effect In the presence of a

Dirac point

Majorana Fermions

Earthly Other worldly



Pr(O-‐F)FeAs BC

S Theory


Unconven5onal Superconduc5vity Along the El-‐Ph Line

BaPb1-‐xBixO3

12K

BaPb1-‐xBixO3

12K

SEMICONDU

CTING

SUPE

R-‐C

30K

Ba1-‐xKxBiO3

Ba

Nega5

ve-‐U CDW

Phase Diagrams of the Superconducting Bismuthates

Nega5

ve-‐U CDW

Note similarity to the phase diagrams of the cuprate superconductors but where the ordered insulating state is in the charge sector

BaBiO3

Pb Doping Ba

BiO3

K Doping

Charge-Disproportionated (Negative U) Superconductors (e.g., BaBiO3) A Failure of LDA Theory à A new class of correlated insulator

Bi4+ Bi4+ Bi4+ Bi4+ Bi4+

Bi3+ Bi3+ Bi3+ Bi5+ Bi5+

Metal

Oxygen

2Bi4+ (4s1)! Bi3+ (4s2 ) + Bi5+ (4s0 )and

Oxygen atoms move to screen charge (Breathing mode)

Nega6ve U -‐-‐ Involves both charge and laZce

Insulator

e e e e e

ee ee ee U

Superconductivity arises upon doping (Ba1-xKxBO3 and BaPb1-xBixO3)

Tc0 =!0e"1

#"µ*

Tcd =!0e"1

!"µ*""µ*

Disorder in the High Tc Bismuthates

BaPb1-xBixO3

Neg

ativ

e-U

CD

W

Orth

orho

mbi

c

Orth

orho

mbi

c

Mon

oclin

ic

BaPb1-xBixO3

Tetra

gona

l/O

rthor

hom

bic

λ = el-‐ph interac6on parameter μ* = retarded coulomb repulsion

• Clean limit (BCS/Eliashberg):

Conven5onal theory for Tc

• Dirty limit (BCS/Eliashburg/Fukuyama):

!µ * = increase in μ* due to disorder-‐induced localiza6on

Measured Tc = Tcd and independently es6mated permits es6mate of Tc0 !µ *

Disorder ma^ers in region of highest Tc

Heavy Fermions and Magnetic Mechanisms


Pr(O-‐F)FeAs BC

S Theory


Cuprates and Strong Correlation – A Mixed Blessing


Pr(O-‐F)FeAs BC

S Theory


In Nature the Transition Temperature Can Be “Astronomically” High

Alfred and Schmitt RMP 80 (2008)

Quark-‐Gluon Plasma

Color-‐Flavor Locked Quark Ma^er

With Some Experimental Evidence

Local pairing,small unit cell and 3D (to minimize phase fluctuations), strong interactions, mean-field breakdown, not a single band.

Any Room Temperature Superconductor Will be Extremely Unconventional Σιζε οφ

Χοοπερ παιρσ

Room Temperature

Superconductor Room Temperature

Pairing Temperature TP (K)

Siz

e of

Coo

per P

air ξ

(Å)

Room Temperature

BCS Theory (vF const.) ! ! !vF / kTc

If you want to find something unconventional, don’t look under the street light.

Empirical Guidance on Specific Interactions Material Archetype

Tc Interac6on Guidance

Bismuthates (i.e., doped BaBiO3)

30K Charge + Lattice

Doped Negative U Insulator

Cs3C60

40K Lattice + Correlation (charge)

El-Ph Covalent Bonds

MgB2

40K Lattice El-Ph Covalent Bonds

Prediction

Fe-Based 50K Spin Antiferromagnetism Multiple orbitals

Cuprates 130K Spin

Doped Antiferromagnetic

Positive U Mott Insulator

Trace High Tc Anomalies

> Room Temperature

? Shouldn’t Ignore

Electronic (charge and spin) interactions look good

To Determine Tc There are Two Characteristic Temperatures to Consider

Superconductivity arises when electrons (or holes) form pairs and the quantum phases of these pairs order (lock) to form a coherent macroscopic quantum state with a single phase.

e e e e

e e e e

e e e e

e e e e

e e e e

! p = ! p ei"

! p!Pairs form

Pairing interaction

SC arises

Phase locking

! sc!

! pi

!i ! =!1 =!2 =!3 i i i

Each process has its own characteristic temperature

Phase locking

Macroscopic quantum state

Theoretical Guidance An always controversial subject

• How to op5mize the el-‐ph mechanism – Modern electronic structure calcula5ons (It is clear that theory could have predicted the high Tc superconduc5vity of Mg B2)

• New mechanisms • Electronic structure calcula5ons as a tool in the search • Strong interac5ons, but honor the “Goldilocks Principle”

E.g., from weak coupled BCS (delocalized) limit to strong coupled (local) limit. Typically also for doping.

H = !t cm† cm" !U np#np$" ! t% cm

† cp"Berg, Orgad and Kivelson PRB 78, 094509 (2008)

High Tc and High Pair Density Superconductor Using a Normal Metal/Negative-U Insulator Proximity Effect:

Normal Metal

Nega6ve-‐U Insulator

Tc

t!

…. And Maybe We Can Have Our Cake and Eat It Too

Unconventional Superconductivity (The Phenomenon) and ...

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