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Superconductivity in strongly coupled multi-band systems
Predrag Nikolić
W.M.Keck Program inQuantum Materials
In collaboration with:Pallab Goswami, Qimiao Si
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2/19
Iron-pnictide materials
Superconductivity in strongly coupled multi-band systems
New high-temperature superconductors
discovery: LaFeAsO1-x
Fx (February 2008)
highest Tc~55K … SmFeAsO
1-xF
x
Features 4 types: 1111, 122, 111, 11 Fe-As layers parent compounds: AF metals structural transition SC upon doping multiple electron bands
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3/19
Electron correlations
Superconductivity in strongly coupled multi-band systems
Fermiology two hole pockets near Γ-point two electron pockets near M-points orbital content:
Fe d-orbitals (xz, yz, xy, x2-y2, z2) hybridize with As p-orbitals (x,y)
Fermi surface nesting AF at k=(π,0) s-wave SC: k=(π,0) d-wave SC: k=(π,π)
Coulomb interactions Coupling to the lattice
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4/19
Phase diagram
Superconductivity in strongly coupled multi-band systems
Anti-ferromagnet (AF) SDW at (π,0) + multi-band FS
small Fe magnetic moment 0.3-0.9 μB
orthorhombic lattice structure
Superconductor (SC) fully gapped, s-wave pseudogap?
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5/19
Theories of pnictides
Superconductivity in strongly coupled multi-band systems
Itinerant electron picture undoped parent compound is a metal SDW has small magnetic moment despite S=2 of Iron electrons are not localized start from a Fermi liquid, look for SDW and SC instability challenge: SC is beyond mean-field
Localized electron picture electron correlations are appreciable (Drude weight...) approximate pnictides with Mott insulators look for short-range spin and pairing correlations disadvantage: forget about metallic behavior and quasiparticles advantage: amenable to mean-field treatment of SC
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6/19
Localized electron picture
Superconductivity in strongly coupled multi-band systems
Both itinerant and localized approached assume that pairing and magnetism originate from the same physics (Coulomb repulsion)
Problem in itinerant picture natural description of Fermi liquid and SDW states
(exciton condensates from repulsive interactions) SC has to defeat repulsive forces
… does not happen at short length-scales, mean-field useless state-of-art: functional RG
“Solution” in localized electron picture doped anti-ferromagnet motion of isolated holes leaves trail of frustrated spins frustration is avoided by pairing, there is kinetic energy gain qualitatively captured by slave-boson theories
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7/19
Microscopic model
Superconductivity in strongly coupled multi-band systems
2-band t-J model:
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8/19
Slave boson approach
Superconductivity in strongly coupled multi-band systems
Introduce doping (electron or hole) Obtain superconductivity from spin-exchange
electron = holon + spinon
constraint at each site and orbital:
hole doping:
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9/19
Mean-field theory
Superconductivity in strongly coupled multi-band systems
Mean-field order parameters:
Neglect fluctuations about the mean-field Hamiltonian becomes quadratic for spinons diagonalize => Bogoliubov - de Gennes quasiparticles Obtain BdG spectrum:
Free energy density for non-interacting BdG quasiparticles:
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10/19
Symmetries
Superconductivity in strongly coupled multi-band systems
Minimize free energy density with respect to order parameters 1) fix chemical potential, ignore constraints 2) fix average spinon density , enforce
Eight microscopic order parameters:
Reorganize by point-group symmetry:
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11/19
Symmetries
Superconductivity in strongly coupled multi-band systems
Symmetry classes .... symmetric under all transformations .... sign-change under 90o rotation and reflection through diag. .... the same as above, but rotated by 45o
.... higher orbtal harmonic (g-wave)
Orbital harmonics .... .... .... ....
Symmetries are fundamental. Orbital harmonics mix by fluctuations.
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12/19
Order Parameter
Superconductivity in strongly coupled multi-band systems
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13/19
Order Parameter
Superconductivity in strongly coupled multi-band systems
grey
red
green
light grey
cyan
purple
yellow white
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14/19Superconductivity in strongly coupled multi-band systems
Phase diagram
A1: A2:
B1: B2:
C1: C2:
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15/19
Phases
Superconductivity in strongly coupled multi-band systems
A … A1g
+iB2g
=> broken time-reversal symmetry (J1<J
2)
B … A1g
(s-d) = sign-changing extended s-wave (s±) (J1~J
2)
C … A1g
+iB1g
=> broken time-reversal symmetry (J1>>J
2)
Coexisting symmetry classes => time-reversal symmetry breaking follows from Landau-Ginzburg theory: W-C. Lee, S-C. Zhang and C. Wu, PRL 102, 217002 (2009)
Coexisting orbital harmonics => relative minus sign inter-band pair tunneling & pairing despite repulsive Coulomb interactions
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16/19
Critical temperature
Superconductivity in strongly coupled multi-band systems
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17/19
Fixed density: δ = 0.5
Superconductivity in strongly coupled multi-band systems
Free energy density
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Superconductivity in strongly coupled multi-band systems 18/19
Strongly coupled multi-band superconductivity
Orbital degrees of freedom + symmetries multi-component order parameter... multiple superconducting states? translational, rotational & time-reversal symmetry breaking? vortex core structure?
Quasiparticles fully gapped, nodal, or coexisting quasiparticle Fermi surfaces? breached or “FFLO” superconductor? can affect vortex lattice structure affects vortex dynamics (is there a “pseudogap” state?)
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19/19
Conclusions
Tractable by slave-boson mean-field theory classification of states by symmetries and orbital content T=0 phase diagram
Is there a tractable effective theory for pnictides which contains: metallic SDW with low magnetic moment superconductors created by Coulomb interactions structural transitions (coupling to phonons)?
What if pnictides were Mott insulators... 2-band t-J model low magnetic moment from spin frustration superconductivity from spin-exchange
Superconductivity in strongly coupled multi-band systems