1. Quantum transport phenomena with the edge channels in topological superconductors
@Nagoya U. Sept. 5, 2009
Naoto Nagaosa
Department of Applied Physics
The University of Tokyo
and
Cross-Correlated Materials Research Group, RIKEN
Collaborators:
Y. Tanaka, T. Yokoyama, A.V. Balatsky
Phys. Rev. B (Rapid Communications)　Vol (2009)
Phys. Rev. Lett. Vol (2009)
Phys. Rev. Lett. Vol (2009)

2. Analogy between chiral superconductor and QHS
Quantum Hall system
Chiral superconductor
Spontaneous
T-symmetry breaking
Topological integer ??
Chiral edge channels

3. Chiral p-wave superconductors
Sr2RuO4
Maeno (1994),
Sigrist-Rice
Spin-triplet p-wave
Time-reversal
symmetry broken
Topological index for chirality
Volovik
related to the # of edge channels but not to

4. Andreev bound state in SRO
Maeno et al. (01)
voltage
compressible
ground state V
charge
accumulation
Furusaki-Matsumoto-Sigrist (2000)
Current I

5. Majorana (real) Fermions
Usual (complex) fermions
“half” of the usual (complex) fermion
“real” fermion
Chiral Majorana mode at the edge of spinless p+ip SC (A.Furusaki)
c.f. Majorna zero energy bound state at vortex
(Read-Green, Kitaev, Ivanov, D.H.Lee etc.)

6. 2D topological insulator (Quantum Spin Hall system)
Time-reversal symmetric system
Spin current instead of charge current
Spin-orbit interaction
helical edge channels
Kane-Mele New topological matter
Quantum Well of HgTe system
Molenkamp-SC.Zhang

7. 3D Topological insulator
3D generalization
of QSH system
Topological insulator
helical edge channels
odd number of 2D
Dirac surface metal
Robust against
disorder
- New state of matter
From C.L.Kane’s homepage

8. Proximity effect of SC and topological insulator
Fu-Kane A B A B
channels SC
Ferro
Chiral Majorana
Ferro up
Ferro down
Chiral Fermion SC SC
Helical Majorana
Ferro
Metal
No channel

9. Non-centrosymmetric Superconductors
CePt3Si
LaAlO3/SrTiO3 interface
Bauer-Sigrist et al.
Time-reversal
Space-inversion
Mixture of spin singlet
and triplet pairings
Possible helical
superconductivity
M. Reyren et al 2007

10. Edge modes of various systems
Majorana
fermion
robust
susceptible
Chiral
Majorana
Chiral
Fermion
Helical
Majorana
Spinless
Fermion
Helical
Fermion
Spinful
Fermion
2-Spinful
Fermion
p+ip SC
5/2 FQH
STI+SC
1/3
FQH
Helical SC
Ferro
wire
QSHS
Q-wire
Ladder

11. 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

12. Hamiltonian for the surface state of Topological insulator
m plays the role of vector potential
N/TI/S
N/TI/S

13. N/FI/S junction on top of TI (1) Dispersion of CMM a b c
Chiral Majorana mode
N/FI/S junction
on top of TI (1) x z y x
Dispersion of CMM a
Sign change by the direction of mz b c
Chiral Majorana mode　(CMM) appears as an Andreev bound state
Change of velocity of Chiral Majorana mode　(CMM) by m/mz

14. Normalized conductance has a peak at zero voltage
Chiral Majorana mode
N/FI/S junction
on top of TI(2) x z y x a b c
Normalized conductance has a peak at zero voltage

15. CMM is also influence by my/mz
Chiral Majorana mode
N/FI/S junction
on top of TI (3) x z y x a b c c
CMM is also influence by my/mz

16. S/FI/S junction on top of TI (1) CMMs a b c y x
Chiral Majorana mode
S/FI/S junction
on top of TI (1) y x
sN: Transparency of the junction
CMMs
j: Phase difference a b c

17. S/FI/S junction on top of TI (2) a b cy
Anomalous current phase relation by mx a b c
Anomalous current phase relation can be detected by interferometer

18. Non-centrosymmetric Superconductors
CePt3Si
LaAlO3/SrTiO3 interface
Bauer-Sigrist et al.
Time-reversal
Space-inversion
Mixture of spin singlet
and triplet pairings
Possible helical
superconductivity
M. Reyren et al 2007

19. Rashba superconductor
Chiral base
Both + and – bands are p+ip superconductor
Frigeri et al. 2004
Fu-Kane, 2008
Proximity effect of 3D topological insulator and s-wave SC

20. Andreev bound state energy dispersion
Low energy limit
Kramer’s pair of
Majorana edge modes
Helical edge modes appear only when

21. Angle resolved Andreev reflection
Normal metal
Helical
superconductor

22. Doppler shift induces spin current
Super current
Normal metal
Helical SC
Magnetic field
-0.4
0.4

23. Split electrons into fractions
8 pieces of fractions !! L R
etc.
harmonic
oscillator
Recombination of pieces
robust
susceptible
Chiral
Majorana
Chiral
Fermion
Helical
Majorana
Spinless
Fermion
Helical
Fermion
Spinful
Fermion
2-Spinful
Fermion
p+ip SC
5/2 FQH
STI+SC
1/3
FQH
Helical SC
Ferro
wire
QSHS
Q-wire
Ladder

24. Conclusions
Topological insulators and non-centrosymmetric SC
with T-symmetry as new comers
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