Quantum transport phenomena with the edge channels in topological superconductors Naoto Nagaosa...
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Transcript of Quantum transport phenomena with the edge channels in topological superconductors Naoto Nagaosa...
Quantum transport phenomena with the edge channels in topological
superconductors
Naoto Nagaosa Department of Applied Physics
The University of Tokyoand
Cross-Correlated Materials Research Group, RIKEN
Collaborators: Y. Tanaka, T. Yokoyama, A.V. Balatsky
Phys. Rev. B (Rapid Communications) Vol. 79 060505 (2009)
Phys. Rev. Lett. Vol.102 166801 (2009) Phys. Rev. Lett. Vol.103 107002 (2009)
@Nagoya U. Sept. 5, 2009
Quantum Hall system
Analogy between chiral superconductor and QHS
Chiral superconductor
SpontaneousT-symmetry breaking
nh
eH
2
:n
Chiral edge channels??
Topological integer
Chiral p-wave superconductors Sr2RuO4Maeno (1994), Sigrist-Rice
Spin-triplet p-wave
Time-reversal symmetry broken
Volovik
Topological index for chirality
related to the # of edge channels but not to H
Maeno et al. (01)
Andreev bound state in SRO
Current I
V charge accumulation
voltage
2
2
)(
1
F
sH kh
e compressible
ground state
Furusaki-Matsumoto-Sigrist (2000)
“half” of the usual (complex) fermion“real” fermion
Majorana (real) Fermions
ff ,Usual (complex) fermions
2/)( ff 1 2
Chiral Majorana mode at the edge of spinless p+ip SC (A.Furusaki)
k
c.f. Majorna zero energy bound state at vortex (Read-Green, Kitaev, Ivanov, D.H.Lee etc.)
2D topological insulator (Quantum Spin Hall system)
Time-reversal symmetric systemSpin current instead of charge currentSpin-orbit interaction
Kane-Mele New topological matter
Molenkamp-SC.Zhang
helical edge channels
Quantum Well of HgTe system
From C.L.Kane’s homepage
3D generalization of QSH systemTopological insulator
helical edge channels
)( pH
odd number of 2D Dirac surface metal- Robust against disorder- New state of matter
3D Topological insulator
A B
Proximity effect of SC and topological insulator
Fu-Kane
A B channels
SC Ferro Chiral Majorana
Ferro up Ferro down Chiral Fermion
SC SC Helical Majorana 0
Ferro Metal No channel
M. Reyren et al 2007
Non-centrosymmetric Superconductors
CePt3Si LaAlO3/SrTiO3 interface
Bauer-Sigrist et al.
kkkk ckcH ))((0
)()( kk
)()( kk
Time-reversal
Space-inversion
Mixture of spin singlet and triplet pairings
Possible helical superconductivity
Edge modes of various systems
Majorana fermion
kk
ChiralMajorana
p+ip SC 5/2 FQHSTI+SC
ChiralFermion
1/3FQH
Helical Majorana
HelicalSC
SpinlessFermion
HelicalFermion
Ferrowire
QSHS
SpinfulFermion
Q-wire Ladder
2-SpinfulFermion
robust susceptible
Purpose of this work
• Charge transport on the surface of topological insulator via chiral Majorana edge mode(CMM).
• Influence of magnetization on CMM.
• Tunneling conductance in N/FI/S junction
• Josephson current in S/FI/S junctions
• Helical Majorana edge modes in non-centrosymmetric SC
Hamiltonian for the surface state of Topological insulator
N/TI/S
N/TI/S
m plays the role of vector potential
N/FI/S junction on top of TI (1)
ab
c
Change of velocity of Chiral Majorana mode (CMM) by /mz
xz
Chiral Majorana
mode
x
y
Chiral Majorana mode (CMM) appears as an Andreev bound state
Dispersion of CMM
Sign change by the direction of mz
N/FI/S junction on top of TI(2)
ab
c
Normalized conductance has a peak at zero voltage
xz
Chiral Majorana
mode
x
y
S/FI/S junction on top of TI (1)
bc
a
Chiral Majorana mode
x
y
CMMs N: Transparency of the junction
: Phase difference
Anomalous current phase relation can be detected by interferometer
bc
a
S/FI/S junction on top of TI (2)
y
Anomalous current phase relation by mx
M. Reyren et al 2007
Non-centrosymmetric Superconductors
CePt3Si LaAlO3/SrTiO3 interface
Bauer-Sigrist et al.
kkkk ckcH ))((0
)()( kk
)()( kk
Time-reversal
Space-inversion
Mixture of spin singlet and triplet pairings
Possible helical superconductivity
..))(()( 2 chkdiikH kykpkykskD
kkk
)(2
1 ),(
2
1
k
ikkk
ikk
ceccec kk Chiral base
..)()(|)|( chcceccecckH kki
pskki
pskkk
kkk
Rashba superconductor
Frigeri et al. 2004
Both + and – bands are p+ip superconductor
xk
yk
k
k Fu-Kane, 2008Proximity effect of 3D topological insulator and s-wave SC
Andreev bound state energy dispersion
Low energy limit Kramer’s pair of
Majorana edge modes
Helical edge modes appear only when
Normal metalHelical
SC
00
0
4.0 :d ,2.0 :c
,2.0 :b ,0 :a
HHHH
HHH
Doppler shift induces spin current
Magnetic field
Super current
Te
hH 02.00
zy HA )0(
1emanDoppler/Ze Fk
0.4-0.4
Split electrons into fractions
or or LR
energy negativeor positive
8 pieces of fractions !!
R
L
RxR etc.
ninteractio el-elby fixed becan
s' ofn combinatio Various
Recombination of pieces
ChiralMajorana
p+ip SC 5/2 FQHSTI+SC
ChiralFermion
1/3FQH
Helical Majorana
HelicalSC
SpinlessFermion
HelicalFermion
Ferrowire
QSHS
SpinfulFermion
Q-wire Ladder
2-SpinfulFermion
R
L
harmonic oscillator
robust susceptible
Conclusions
1. Topological insulators and non-centrosymmetric SC with T-symmetry as new comers
2. Manipulation of the Majorana fermion, Andreev reflection, and Josephson junction by magnetization
direction transport perpendicular to edge
3. Spintronics functions in superconductors using helical edge channels
4. All kinds of edge channels - chiral, helical, Majorana, etc - electrons are split into 8 pieces - Recombine some of the pieces to produce a new
state