Exotic Superconductivity Exotic Superconductivity A matter of - - PowerPoint PPT Presentation

Exotic Superconductivity Exotic Superconductivity A matter of Symmetry and Topology A matter of Symmetry and Topology

Feb 2013 Manfred Sigrist

B A

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temperature resistivity

Tc

Phenomenon ''Superconductivity''

vanishing electrical resistance

1911

normal metal

superconductor

Meissner-Ochsenfeld effect B B=0 B

temperature resistivity

Tc

Phenomenon ''Superconductivity''

vanishing electrical resistance

1911

normal metal

superconductor

1933

normal metal superconductor

London equation

screening of magnetic field

Meissner-Ochsenfeld effect B B=0 B

temperature resistivity

Tc

Phenomenon ''Superconductivity''

vanishing electrical resistance

1911

normal metal

superconductor

1933

normal metal superconductor

flux quantization London equation

screening of magnetic field

Ginzburg-Landau theory

spontaneously broken U(1) - gauge symmetry complex macroscopic condensate wavefunction

Superconducting Condensate

Bardeen-Cooper-Schrieffer

superconductivity as a Fermi surface instability

electrons of opposite momenta correlate to form a coherent state of Cooper pairs

Cooper pair

Superconducting Condensate

Bardeen-Cooper-Schrieffer

superconductivity as a Fermi surface instability

electrons of opposite momenta correlate to form a coherent state of Cooper pairs

Cooper pair add/remove freely Cooper pairs

coherence

Superconducting Condensate

Bardeen-Cooper-Schrieffer

superconductivity as a Fermi surface instability

electrons of opposite momenta correlate to form a coherent state of Cooper pairs

Cooper pair

pair wave function

add/remove freely Cooper pairs

coherence

Superconducting Condensate

Bardeen-Cooper-Schrieffer

superconductivity as a Fermi surface instability

electrons of opposite momenta correlate to form a coherent state of Cooper pairs

Cooper pair add/remove freely Cooper pairs ''hard'' to add/remove low-energy electron eV +Δ

• Δ

electron tunneling

normal metal

gap

coherence

Superconducting Condensate

Bardeen-Cooper-Schrieffer

superconductivity as a Fermi surface instability

electrons of opposite momenta correlate to form a coherent state of Cooper pairs

Cooper pair

pair wave function

• rbital & spin symmetry
• rbital

angular momentum parity

spin spin singlet spin triplet

Superconducting Condensate

Bardeen-Cooper-Schrieffer

superconductivity as a Fermi surface instability

electrons of opposite momenta correlate to form a coherent state of Cooper pairs

Cooper pair

• rbital

angular momentum parity

spin spin singlet spin triplet spin singlet even parity spin triplet

• dd parity

Pauli principle

Superconducting Condensate

Bardeen-Cooper-Schrieffer

superconductivity as a Fermi surface instability

electrons of opposite momenta correlate to form a coherent state of Cooper pairs

Cooper pair

spin singlet even parity spin triplet

• dd parity

Pauli principle

most symmetric

''conventional conventional''

lower symmetry

''unconventional unconventional''

B

A

Helium-3 - unconventional superfluid

superfluid A- and B- phase

superfluid Helium 3

B A

Helium-3 - unconventional superfluid A-phase:

broken time reversal symmetry

chiral phase

pair wave function

normal state symmetry

superfluid Helium 3

B A

B-phase: A-phase:

broken time reversal symmetry

chiral phase

dynamical spin-orbit coupling

helical phase Helium-3 - unconventional superfluid

normal state symmetry

pair wave function

superfluid Helium 3

B A Sr2RuO4 Maeno et al. (1994)

transition metal oxide quasi-two-dimensional metal

chiral p-wave phase

CePt3Si Bauer et al. (2004)

heavy Fermion compound non-centrosymmetric crystal

mixed-parity phase Helium-3 - unconventional superfluid

Sr Sr2

2RuO

RuO4

4

chiral p-wave superconductor chiral p-wave superconductor

Maeno et al 1994

broken time reversal symmetry

angular momentum

spin

Sr2RuO4 - chiral p-wave superconductor

Deguchi & Maeno

analog to 3He A-phase

Maeno et al 1994

broken time reversal symmetry

angular momentum

spin spin rotation

• rbital rotation

Sr2RuO4 - chiral p-wave superconductor

Deguchi & Maeno

broken time reversal symmetry

Sr2RuO4 - chiral p-wave superconductor

Maeno et al 1994

rotation U(1)-gauge

angular momentum charge

Sr2RuO4 - chiral p-wave superconductor

Maeno et al 1994

rotation U(1)-gauge

angular momentum charge conserved ''charge''

Volovik

Sr2RuO4 - chiral p-wave superconductor

Maeno et al 1994

conserved ''charge''

Volovik

magnetic moment for charge particles

M

• M

Cooper pair

anomalous electromagnetism SC

charge fluctuation generate magnetic flux currents generate transverse electric field

Sr2RuO4 - chiral p-wave superconductor

magnetic moment for charge particles

M

• M

Cooper pair

anomalous electromagnetism SC

Sr2RuO4 - chiral p-wave superconductor

analogy to the integer quantum Hall state

2-dim. electron gas

B

cyclotron

• rbits

Sr2RuO4 - chiral p-wave superconductor

B Andreev bound states

electron hole

θ

eiθ

''bouncing cyclotron orbits''

edge states

Quantum Hall state

cyclotron

• rbits

chiral p-wave SC

electron-hole hybridized Bohr-Sommerfeld-orbits

continuum continuum

chiral edge state

energy gap 2Δ

surface surface

surface surface

Sr2RuO4 - chiral p-wave superconductor

B Andreev bound states

electron hole

θ

eiθ

''bouncing cyclotron orbits''

edge states

Quantum Hall state

cyclotron

• rbits

chiral p-wave SC

electron-hole hybridized Bohr-Sommerfeld-orbits

continuum continuum

chiral edge state

energy gap 2Δ

states with topological nature edge states topologically protected

Sr2RuO4 - chiral p-wave superconductor

B Andreev bound states

electron hole

θ

eiθ

edge states

Quantum Hall state

cyclotron

• rbits

chiral p-wave SC

electron-hole hybridized Bohr-Sommerfeld-orbits

driving current screening current

Bz

spontaneous edge currents

surface

''bouncing cyclotron orbits''

Sr2RuO4 - chiral p-wave superconductor

B Andreev bound states

electron hole

θ

eiθ

edge states

Quantum Hall state

cyclotron

• rbits

chiral p-wave SC

electron-hole hybridized Bohr-Sommerfeld-orbits

driving current

Bz

spontaneous edge currents

surface

''bouncing cyclotron orbits''

spontaneous Hall effect but no Quantum Hall effect

intrinsic magnetism ? intrinsic magnetism ?

random local magnetism

Luke et al (1998)

µSR - zero-field relaxtion ''edge currents'' around inhomogeneities & defects muon-spin depolarization intrinsic magnetism

edge state currents

Hicks et al (2010)

data

scanning probes at sample boundaries scanning Hall Tamegai et al scanning SQUID Kirtley, Moler et al

magnetic signal clearly below expected bounds no edge states ?

edge states ? edge states ?

continuum continuum

chiral edge state

energy gap 2Δ

tunneling conductance

eV +Δ

1

• Δ

conventional superconductor

1

eV +Δ

• Δ

chiral p-wave superconductor

local quasiparticle spectrum

tunneling through edge states

edge states ? edge states ?

tunneling conductance

eV +Δ

1

• Δ

conventional superconductor

1

eV +Δ

• Δ

chiral p-wave superconductor

local quasiparticle spectrum

tunnel-contact

normal metal

dI/dV Goll, von Löhneysen et al. Kashiwaya et al.

zero-bias anomaly

Mao, Liu et al. Sr2RuO4

edge states ? edge states ?

tunneling conductance

eV +Δ

1

• Δ

conventional superconductor

1

eV +Δ

• Δ

chiral p-wave superconductor

local quasiparticle spectrum

dI/dV Goll, von Löhneysen et al. Kashiwaya et al.

Mao, Liu et al.

tunnel-contact

normal metal

Sr2RuO4

chirality ? chirality ?

subtle Doppler-shift effects through coupling to a magnetic field

chirality ? chirality ?

polar Kerr effect

x y

θK

in

• ut

Kapitulnik et al. (2006)

polarization axis of reflected light is rotated

chirality ? chirality ?

polar Kerr effect

x y

θK

in

• ut

Kapitulnik et al. (2006)

polarization axis of reflected light is rotated

mSR: random intrinsic magnetism scanning probes: chiral surface currents polar Kerr effect: optical property - chirality Josephson interference effect: chiral domains positive negative compatible

Anomalous Josephson effect Anomalous Josephson effect

Pb Sr2RuO4

current source

V

3 Kelvin phase - signatures of topology 3 Kelvin phase - signatures of topology

µm - size Ru-inclusion

Maeno et al (1997)

• nset of inhomogeneous

superconductivity at

"3-Kelvin phase"

Ru Ru

Sr2RuO4 Pb

z

Josephson coupling via Ru-inclusions

Pb Sr2RuO4

current source

V Nakamura et al

(2010)

Ru Ru

Sr2RuO4 Pb

z Pb Sr2RuO4

current source

V Nakamura et al

(2010)

Nakamura et al (2010)

3 Kelvin phase - signatures of topology 3 Kelvin phase - signatures of topology

µm - size Ru-inclusion

Maeno et al (1997)

• nset of inhomogeneous

superconductivity at

"3-Kelvin phase"

Josephson coupling via Ru-inclusions

T (K) Ic (mA)

Tc

Josephson critical current

Ru Ru

Sr2RuO4 Pb

z Pb Sr2RuO4

current source

V Nakamura et al

(2010)

Nakamura et al (2010)

3 Kelvin phase - signatures of topology 3 Kelvin phase - signatures of topology

µm - size Ru-inclusion

Maeno et al (1997)

• nset of inhomogeneous

superconductivity at

"3-Kelvin phase"

Josephson coupling via Ru-inclusions

T (K) Ic (mA)

Tc

topologically incompatible topologically compatible

Josephson critical current

conventional + chiral p-wave conventional + 3-K-phase

Ru Ru

Sr2RuO4 Pb

z Pb Sr2RuO4

current source

V Nakamura et al

(2010)

Nakamura et al (2010)

3 Kelvin phase - signatures of topology 3 Kelvin phase - signatures of topology

µm - size Ru-inclusion

Maeno et al (1997)

• nset of inhomogeneous

superconductivity at

"3-Kelvin phase"

Josephson coupling via Ru-inclusions

T (K) Ic (mA)

Tc

topologically incompatible topologically compatible

Josephson critical current

conventional + chiral p-wave conventional + 3-K-phase

GCOE team

• Y. Maeno T. Nakamura S. Yonezawa T. Terashima
• R. Nakagawa
• T. Sumi
• T. Yamagishi

…..

Non-centrosymmetric Non-centrosymmetric Superconductors Superconductors

time reversal & inversion symmetry time reversal & inversion symmetry

Cooper pair

electrons which can be paired

spin singlet even parity spin triplet

• dd parity

time reversal & inversion symmetry ensure presence of degenerate pairing partners

time reversal & inversion symmetry time reversal & inversion symmetry

Cooper pair

electrons which can be paired

spin singlet even parity spin triplet

• dd parity

time reversal & inversion symmetry ensure presence of degenerate pairing partners

lack of time reversal or inversion symmetry Cooper pairs with mixed parity / spin

Non-centrosymmetric superconductors Non-centrosymmetric superconductors

Ce-based heavy Fermion superconductor CePt3Si

Bauer et al (2004)

Non-centrosymmetric superconductors Non-centrosymmetric superconductors

Ce-based heavy Fermion superconductor CePt3Si

Bauer et al (2004)

inversion

Non-centrosymmetric superconductors Non-centrosymmetric superconductors

Ce-based heavy Fermion superconductor CePt3Si

Bauer et al (2004)

inversion

consequence: Rashba spin-orbit coupling

spin splitting of electron states

k

E

electronic spin structure determines Cooper pairing symmetry

Non-centrosymmetric superconductors Non-centrosymmetric superconductors

electronic spin structure determines Cooper pairing symmetry ''conventional'' parity-mixed pairing state

• dd parity

even parity

Non-centrosymmetric superconductors Non-centrosymmetric superconductors "s+p-wave"

analog to 3He B-phase

electronic spin structure determines Cooper pairing symmetry ''conventional'' parity-mixed pairing state

• dd parity

even parity

Non-centrosymmetric superconductors Non-centrosymmetric superconductors

analog to 3He B-phase

"s+p-wave"

spin-orbit coupling

electronic spin structure determines Cooper pairing symmetry ''conventional'' parity-mixed pairing state

• dd parity

even parity

Non-centrosymmetric superconductors Non-centrosymmetric superconductors

analog to 3He B-phase

helical (chirality coupled to spin)

Helical edge states - Helical edge states - Andreev bound states

Andreev bound states

dominant even parity topologically trivial dominant odd parity topologically non-trivial non-trivial

continuum continuum helical edge states

Helical edge states - Helical edge states - Andreev bound states

Andreev bound states

dominant even parity topologically trivial dominant odd parity topologically non-trivial

continuum continuum

spin current at edges Quantum Spin Hall effect

for topologically non-trivial state

analogy to topological insulators

spin current

helical edge states

dominant even parity topologically trivial dominant odd parity topologically non-trivial

continuum continuum

conductance

tunnel-contact

normal metal

NCSC

quasiparticle spectra - tunneling

CePt3Si

good candidate for but no experiments so far theory

Helical edge states - Helical edge states - Andreev bound states

Andreev bound states

Helical phase

magneto-electric effects magneto-electric effects

H

shift of Fermi surface centers

Cooper pairing with finite momentum

with

analog to Fulde-Ferrel phase (different mechanism)

helical phase:

Kaur et al, Dimitrova et al

Magneto-electric effects - helical phase Magneto-electric effects - helical phase

effect of magnetic field on the Fermi surfaces

H

shift of Fermi surface centers

Cooper pairing with finite momentum

with

analog to Fulde-Ferrel phase (different mechanism)

helical phase:

Kaur et al, Dimitrova et al

effect of magnetic field on the Fermi surfaces

Magneto-electric effects - helical phase Magneto-electric effects - helical phase

H

shift of Fermi surface centers

Cooper pairing with finite momentum

with

analog to Fulde-Ferrel phase (different mechanism)

helical phase:

Kaur et al, Dimitrova et al

effect of magnetic field on the Fermi surfaces

gauge freedom

phase gradient ''removable'' no currents induced

Magneto-electric effects - helical phase Magneto-electric effects - helical phase

non-centrosymmetric crystals can be twinned

inversion

Crystal twin domains

non-centrosymmetric crystals can be twinned

inversion

H H

Crystal twin domains Crystal twin domains

non-centrosymmetric crystals can be twinned

inversion

Crystal twin domains Crystal twin domains

• pposite

helical phases

H

inhomogeneous helical states inhomogeneous helical states

+

_

matching at twin boundary

small fields

''wave function machting''

x y

H

inhomogeneous helical states inhomogeneous helical states

+

_

small fields

x y

magnetic field on twin boundary ''wave function machting''

H

inhomogeneous helical states inhomogeneous helical states

+

_

large fields

reduction magnetic flux

x y

wave function phase mismatch

solitons - flux lines

as a field screening effect

first-order transition in a magnetic field

1 2

inhomogeneous helical states inhomogeneous helical states

energy

external magnetic field induced magnetic field

first-order transition in a magnetic field

1 2

inhomogeneous helical states inhomogeneous helical states

energy GCOE collaboration

Kazushi Aoyama

Conclusion Conclusion

symmetry and topology classification of superconductors class SU(2) TRS D DIII A AIII C CI no no restricted restricted yes yes no yes no yes no yes

Schnyder, Ryu, Furusaki & Ludwig (2008)

Conclusion Conclusion

class SU(2) TRS D DIII A AIII C CI no no restricted restricted yes yes no yes no yes no yes

Schnyder, Ryu, Furusaki & Ludwig (2008)

mixed-parity ''s+p-wave''

helical edge states spin current

symmetry and topology classification of superconductors

Conclusion Conclusion

class SU(2) TRS D DIII A AIII C CI no no restricted restricted yes yes no yes no yes no yes

Schnyder, Ryu, Furusaki & Ludwig (2008)

mixed-parity ''s+p-wave''

helical edge states spin current

''chiral p-wave''

chiral edge states charge current

symmetry and topology classification of superconductors

Collaborators & Acknowledgement Collaborators & Acknowledgement

Theory:

• D. Agterberg, K. Aoyama, S. Etter, P. Frigeri, S. Fujimoto,
• A. Furusaki, J. Goryo, B. Gut, N. Hayashi, Y. Imai, C. Iniotakis,
• H. Kaneyasu, R. Kaur, A. Koga, F. Loder, M. Matsumoto,
• D. Perez, T.M. Rice, L. Savary, Y. Tanaka, K. Wakabayashi,
• Y. Yokoyama, Y. Yanase

Experimental groups:

• Y. Maeno, E. Bauer, A. Mackenzie, J. Kirtley, K. Moler,
• Q. Mao, Y. Liu, H. Yaguchi, T. Nakamura, Y. Onuki,
• R. Settai, N. Kimura, I. Bonalde, A. Kapitulnik, …

Unconventional Superconductors Unconventional Superconductors

strongly correlated electron systems

heavy Fermion compounds

CeCu2(Si1-xGex)2

cuprate high-Tc superconductors

since 1979 since 1986

AF

SC La2-xSrxCuO4

4f-electrons 3d-electrons

strongly correlated electron systems

heavy Fermion compounds

CeCu2(Si1-xGex)2

cuprate high-Tc superconductors

since 1979 since 1986

AF

SC La2-xSrxCuO4

4f-electrons 3d-electrons

magnetism

Unconventional Superconductors Unconventional Superconductors

strongly correlated electron systems

pnictide superconductors

(Ba,K)Fe2As2 since 2008 3d-electrons

''essential !?''

AF

SC

superconductivity connected with magnetism

Competion Cooperation Coexistence

Unconventional Superconductors Unconventional Superconductors