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Quantum transport phenomena with the edge channels in topological superconductors

@Nagoya U. Sept. 5, 2009. Quantum transport phenomena with the edge channels in topological superconductors. 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

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Quantum transport phenomena with the edge channels in topological superconductors

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  1. @Nagoya U. Sept. 5, 2009 Quantum transport phenomena with the edge channels in topological superconductors 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. 79 060505 (2009) Phys. Rev. Lett. Vol.102 166801 (2009) Phys. Rev. Lett. Vol.103 107002 (2009)

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

  3. Sr2RuO4 Chiral p-wave superconductors 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 symmetricsystem 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 Helical SC Ferro wire QSHS Q-wire Ladder 1/3 FQH

  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. 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. 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. 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. 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) y 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. Normal metal Helical superconductor Angle resolved Andreev reflection

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

  23. Split electrons into fractions L R 8 pieces of fractions !! R L 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 Helical SC Ferro wire QSHS Q-wire Ladder 1/3 FQH

  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

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