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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. 79 060505 (2009) Phys. Rev. Lett. Vol.102 166801 (2009) Phys. Rev. Lett. Vol.103 107002 (2009) Analogy between chiral superconductor and QHS Quantum Hall system Chiral superconductor Spontaneous T-symmetry breaking e2 H n h n : Topological integer Chiral edge channels ?? 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 H Andreev bound state in SRO Maeno et al. (01) voltage V charge accumulation e2 1 compressible 2 h (k F ) ground state s H Furusaki-Matsumoto-Sigrist (2000) Current I Majorana (real) Fermions f , f Usual (complex) fermions ( f f )/ 2 2 1 “half” of the usual (complex) fermion “real” fermion 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 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 3D Topological insulator 3D generalization of QSH system Topological insulator helical edge channels H ( p) odd number of 2D Dirac surface metal - Robust against disorder - New state of matter From C.L.Kane’s homepage Proximity effect of SC and topological insulator Fu-Kane A B A B SC Ferro Ferro up SC 0 Ferro Ferro down channels Chiral Majorana Chiral Fermion SC Helical Majorana Metal No channel Non-centrosymmetric Superconductors CePt3Si LaAlO3/SrTiO3 interface Bauer-Sigrist et al. H 0 ck ( k (k ) )ck k (k ) (k ) Time-reversal (k ) (k ) Space-inversion Mixture of spin singlet and triplet pairings Possible helical superconductivity M. Reyren et al 2007 Edge modes of various systems Majorana fermion k k robust susceptible Chiral Chiral Helical Spinless Majorana Fermion Majorana Fermion p+ip SC 5/2 FQH STI+SC 1/3 FQH Helical SC Ferro wire Helical Fermion Spinful Fermion 2-Spinful Fermion QSHS Q-wire Ladder 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 m plays the role of vector potential N/TI/S N/TI/S Chiral Majorana mode N/FI/S junction on top of TI (1) z x y x Dispersion of CMM a b Sign change by the direction of mz c Chiral Majorana mode (CMM) appears as an Andreev bound state Change of velocity of Chiral Majorana mode (CMM) by m/mz Chiral Majorana mode N/FI/S junction on top of TI(2) z y x a b c Normalized conductance has a peak at zero voltage x Chiral Majorana mode N/FI/S junction on top of TI (3) z y x c a b c CMM is also influence by my/mz x Chiral Majorana mode S/FI/S junction on top of TI (1) y x N: Transparency of the junction j: Phase difference CMMs a b c 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 Non-centrosymmetric Superconductors CePt3Si LaAlO3/SrTiO3 interface Bauer-Sigrist et al. H 0 ck ( k (k ) )ck k (k ) (k ) Time-reversal (k ) (k ) Space-inversion Mixture of spin singlet and triplet pairings Possible helical superconductivity M. Reyren et al 2007 Rashba superconductor H k (k k 2 D ) k s ki y k p ki(d (k ) ) y k h.c. k Chiral base k 1 1 i k (ck e ck ), k (ck e i k ck ) 2 2 H (k | k |)ckck ( s p )eik ckck ( s p )eik ckck h.c. k Both + and – bands are p+ip superconductor ky k k Frigeri et al. 2004 kx Fu-Kane, 2008 Proximity effect of 3D topological insulator and s-wave SC Andreev bound state energy dispersion Low energy limit Helical edge modes appear only when Kramer’s pair of Majorana edge modes Angle resolved Andreev reflection Normal metal Helical superconductor Doppler shift induces spin current Ay (0) H z Super current Normal metal Doppler/Zeeman kF 1 Helical SC Magnetic field -0.4 a : H 0, b : H 0.2H 0 , c : H 0.2H 0 , d : H 0.4H 0 0.4 H0 h e 0.02T Split electrons into fractions L R R or L or positiveor negativeenergy 8 pieces of fractions !! R xR R L harmonic oscillator etc. Various combination of ' s can be fixed by el - el interaction Recombination of pieces robust susceptible Chiral Chiral Helical Spinless Majorana Fermion Majorana Fermion p+ip SC 5/2 FQH STI+SC 1/3 FQH Helical SC Ferro wire Helical Fermion Spinful Fermion 2-Spinful Fermion QSHS Q-wire Ladder 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