Exotic Superconductivity Exotic Superconductivity A matter of Symmetry and Topology A matter of Symmetry and Topology Feb 2013 Manfred Sigrist A B
Hunting the Higgs - finally a happy end LHC CERN Switzerland P. Higgs P.W. Anderson
Hunting the Higgs - finally a happy end LHC CERN Switzerland P. Higgs P.W. Anderson
Phenomenon ''Superconductivity'' vanishing electrical resistance 1911 resistivity superconductor normal metal T c temperature
Phenomenon ''Superconductivity'' vanishing electrical resistance Meissner-Ochsenfeld effect 1933 1911 resistivity superconductor B B=0 B normal metal superconductor normal metal T c temperature London equation screening of magnetic field
Phenomenon ''Superconductivity'' vanishing electrical resistance Meissner-Ochsenfeld effect 1933 1911 resistivity superconductor B B=0 B normal metal superconductor normal metal T c temperature London equation flux quantization screening of magnetic field Ginzburg-Landau theory spontaneously broken U(1) - gauge symmetry complex macroscopic condensate wavefunction
Superconducting Condensate Bardeen-Cooper-Schrieffer electrons of opposite momenta superconductivity as a correlate to form Fermi surface instability a coherent state of Cooper pairs Cooper pair
Superconducting Condensate Bardeen-Cooper-Schrieffer electrons of opposite momenta superconductivity as a correlate to form Fermi surface instability a coherent state of Cooper pairs Cooper pair add/remove freely Cooper pairs coherence
Superconducting Condensate Bardeen-Cooper-Schrieffer electrons of opposite momenta superconductivity as a correlate to form Fermi surface instability a coherent state of Cooper pairs Cooper pair pair wave function add/remove freely Cooper pairs coherence
Superconducting Condensate Bardeen-Cooper-Schrieffer electrons of opposite momenta superconductivity as a correlate to form Fermi surface instability a coherent state of Cooper pairs Cooper pair add/remove freely ''hard'' to add/remove electron tunneling Cooper pairs low-energy electron normal metal coherence gap eV - Δ + Δ
Superconducting Condensate Bardeen-Cooper-Schrieffer electrons of opposite momenta superconductivity as a correlate to form Fermi surface instability a coherent state of Cooper pairs Cooper pair pair wave function spin orbital angular momentum spin singlet parity spin triplet orbital & spin symmetry
Superconducting Condensate Bardeen-Cooper-Schrieffer electrons of opposite momenta superconductivity as a correlate to form Fermi surface instability a coherent state of Cooper pairs Cooper pair spin orbital Pauli principle angular spin singlet spin triplet momentum spin singlet parity spin triplet even parity odd parity
Superconducting Condensate Bardeen-Cooper-Schrieffer electrons of opposite momenta superconductivity as a correlate to form Fermi surface instability a coherent state of Cooper pairs Cooper pair Pauli principle most symmetric ''conventional conventional'' spin singlet spin triplet lower symmetry ''unconventional unconventional'' even parity odd parity
Helium-3 - unconventional superfluid superfluid A- and B- phase A B
Helium-3 - unconventional superfluid superfluid Helium 3 pair wave function normal state symmetry A B A-phase: broken time reversal symmetry chiral phase
Helium-3 - unconventional superfluid superfluid Helium 3 pair wave function normal state symmetry A B A-phase: B-phase: broken time reversal symmetry dynamical spin-orbit coupling chiral phase helical phase
Helium-3 - unconventional superfluid superfluid Helium 3 A B Sr 2 RuO 4 Maeno et al. (1994) CePt 3 Si Bauer et al. (2004) heavy Fermion compound transition metal oxide non-centrosymmetric quasi-two-dimensional crystal metal chiral p-wave phase mixed-parity phase
Sr 2 RuO 4 Sr 2 RuO 4 chiral p-wave superconductor chiral p-wave superconductor
Sr 2 RuO 4 - chiral p-wave superconductor Maeno et al 1994 broken time reversal symmetry angular momentum analog to 3 He A-phase spin Deguchi & Maeno
Sr 2 RuO 4 - chiral p-wave superconductor Maeno et al 1994 broken time reversal symmetry angular momentum orbital rotation spin spin rotation Deguchi & Maeno
Sr 2 RuO 4 - chiral p-wave superconductor Maeno et al 1994 broken time reversal symmetry
Sr 2 RuO 4 - chiral p-wave superconductor Maeno et al 1994 rotation angular momentum U(1) -gauge charge
Sr 2 RuO 4 - chiral p-wave superconductor Maeno et al 1994 rotation angular momentum U(1) -gauge conserved ''charge'' charge Volovik
Sr 2 RuO 4 - chiral p-wave superconductor magnetic moment for charge particles Cooper pair M - M SC anomalous electromagnetism charge fluctuation generate magnetic flux conserved currents generate ''charge'' transverse electric field Volovik
Sr 2 RuO 4 - chiral p-wave superconductor magnetic moment for charge particles Cooper pair M - M analogy to the integer quantum Hall state SC 2-dim. anomalous B electron gas electromagnetism cyclotron orbits
Sr 2 RuO 4 - chiral p-wave superconductor edge states B Quantum Hall state chiral edge state surface ''bouncing cyclotron orbits'' cyclotron continuum orbits chiral p-wave SC continuum surface Andreev bound states θ e i θ electron-hole hybridized energy gap 2 Δ Bohr-Sommerfeld-orbits hole electron
Sr 2 RuO 4 - chiral p-wave superconductor edge states B Quantum Hall state chiral edge state surface ''bouncing cyclotron orbits'' cyclotron continuum states with topological nature orbits edge states topologically chiral p-wave SC protected continuum surface Andreev bound states θ e i θ electron-hole hybridized energy gap 2 Δ Bohr-Sommerfeld-orbits hole electron
Sr 2 RuO 4 - chiral p-wave superconductor edge states spontaneous B edge currents Quantum Hall state driving current surface ''bouncing cyclotron orbits'' cyclotron orbits B z chiral p-wave SC Andreev bound states θ e i θ electron-hole hybridized Bohr-Sommerfeld-orbits hole screening current electron
Sr 2 RuO 4 - chiral p-wave superconductor edge states spontaneous B edge currents Quantum Hall state driving current surface ''bouncing cyclotron orbits'' cyclotron orbits B z chiral p-wave SC spontaneous Hall effect Andreev bound states θ but no e i θ electron-hole hybridized Bohr-Sommerfeld-orbits Quantum Hall effect hole electron
intrinsic magnetism ? intrinsic magnetism ? random local magnetism edge state currents ''edge currents'' around scanning probes at sample boundaries inhomogeneities & defects scanning Hall Tamegai et al µ SR - zero-field relaxtion scanning SQUID Kirtley, Moler et al Luke et al (1998) magnetic signal Hicks et al (2010) clearly below expected bounds data muon-spin depolarization no edge states ? intrinsic magnetism
edge states ? edge states ? tunneling conductance local quasiparticle spectrum chiral edge state conventional superconductor continuum 1 eV - Δ + Δ tunneling through edge states continuum chiral p-wave superconductor 1 energy gap 2 Δ - Δ + Δ eV
edge states ? edge states ? tunneling conductance local quasiparticle spectrum tunnel-contact normal Sr 2 RuO 4 conventional metal superconductor Mao, Liu et al. 1 zero-bias eV - Δ + Δ anomaly dI/dV chiral p-wave superconductor 1 - Δ + Δ eV Goll, von Löhneysen et al. Kashiwaya et al.
edge states ? edge states ? tunneling conductance local quasiparticle spectrum tunnel-contact normal Sr 2 RuO 4 conventional metal superconductor chirality ? chirality ? Mao, Liu et al. 1 subtle Doppler-shift eV effects through coupling - Δ + Δ to a magnetic field dI/dV chiral p-wave superconductor 1 - Δ + Δ eV Goll, von Löhneysen et al. Kashiwaya et al.
chirality ? chirality ? polar Kerr effect Kapitulnik et al. polarization axis of (2006) reflected light is rotated y x θ K out in
chirality ? chirality ? polar Kerr effect Kapitulnik et al. polarization axis of (2006) reflected light is rotated y x θ K out in positive mSR: random intrinsic magnetism negative scanning probes: chiral surface currents polar Kerr effect: optical property - chirality compatible Josephson interference effect: chiral domains
Anomalous Josephson effect Anomalous Josephson effect current source Pb V Sr 2 RuO 4
3 Kelvin phase - signatures of topology 3 Kelvin phase - signatures of topology Josephson coupling via Ru-inclusions current Nakamura et al Pb source (2010) z Ru Ru Pb Sr 2 RuO 4 V Sr 2 RuO 4 µ m - size Ru-inclusion Maeno et al (1997) onset of inhomogeneous superconductivity at "3-Kelvin phase"
3 Kelvin phase - signatures of topology 3 Kelvin phase - signatures of topology Josephson coupling via Ru-inclusions current Nakamura et al Pb source (2010) z Ru Ru Pb Sr 2 RuO 4 V Sr 2 RuO 4 Josephson critical current µ m - size Ru-inclusion Nakamura et al (2010) Maeno et al (1997) T c I c (mA) onset of inhomogeneous superconductivity at "3-Kelvin phase" T (K)
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