unconventional superconductivity (the phenomenon) and
TRANSCRIPT
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Pedagogical Overview
Unconventional Superconductivity (The Phenomenon) and Unconventional Superconductors (The Materials)
• Conventional Superconductivity • Unconventional Superconductivity and Superconductors • Some Personal Favorites
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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 = ......!"..... =!
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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
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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
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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
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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*
Unconventional Superconductivity
!(k) = dk 3" V (k,k ')!(k ')
! " !vF / kTpTc = min T! ,Tp{ }
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Conventional Classic BCS and
Extensions
Unconventional Superconductivity
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
Unconventional Superconductivity
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Adapted from a DoE Report
Pr(O-‐F)FeAs BC
S Theory
Conven6onal Era Unconven6onal Era
Unconven5onal Superconduc5vity Along the El-‐Ph Line
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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
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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)
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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
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Heavy Fermions and Magnetic Mechanisms
Adapted from a DoE Report
Pr(O-‐F)FeAs BC
S Theory
Conven6onal Era Unconven6onal Era
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Cuprates and Strong Correlation – A Mixed Blessing
Adapted from a DoE Report
Pr(O-‐F)FeAs BC
S Theory
Conven6onal Era Unconven6onal Era
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In Nature the Transition Temperature Can Be “Astronomically” High
Alfred and Schmitt RMP 80 (2008)
Quark-‐Gluon Plasma
Color-‐Flavor Locked Quark Ma^er
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With Some Experimental Evidence
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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
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If you want to find something unconventional, don’t look under the street light.
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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
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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
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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.
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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