Dirac-Fermion-Induced Parity Mixing in Superconducting Topological Insulators. Nagoya University Masatoshi Sato

Transcription

1 Dirac-Fermion-Induced Parity Mixing in Superconducting Topological Insulators Nagoya University Masatoshi Sato

2 In collaboration with Yukio Tanaka (Nagoya University) Keiji Yada (Nagoya University) Ai Yamakage (Nagoya University) Takeshi Mizushima (Okayama University) Experiments Yoichi Ando (Osaka University) Kouji Segawa (Osaka University) Sasaki Sasaki (Osaka University) Review paper Y. Tanaka, MS, N. Nagaosa, Symmetry and Topology in SCs Journal of Physical Society of Japan, 81 (2012) (open access) 2

3 Outline 1. Surface Majorana fermions in superconducting topological insulator Cu x Bi 2 Se 3 2. Dirac-fermion-induced parity mixing in s-wave superconducting topological insulator Sasaki, Kriener, Segawa, Yada, Tanaka, MS, Ando, Phys. Rev. Lett. 107, (11) Yamakage, Yada, MS, Tanaka, Phys. Rev. B85, (R) (12) Mizushima, Yamakage, MS, Tanaka, arxiv:

4 How to realize isolated MFs? MFs are naturally realized when the spin rotation symmetry is broken p-wave superconductor Read-Green (00), MS(09, 10), Fu-Berg(10) Dirac fermion + s-wave condensate MS(03), Fu-Kane (08) Hsieh et al S-wave superconducting state with Rashba SO + Zeeman field MS-Takahashi-Fujimoto (09), J. Sau et al (10), Y. Oreg et al (10) 4

5 Isolated MFs are realized under a strong magnetic field satisfying 1D Nanowire MF nanowire Zeeman field MS-Takahashi-Fujimoto (09) Lutchyn et al (10), Oreg et al (10) Mourik et al., Science (2012) InSb/ NbTiN Majorana Fermion 5

6 Question Are there any other candidate experiments suggesting MFs in solid state physics? Answer Yes Cu x Bi 2 Se 3 Cu x Bi 2 Se 3 Fu-Berg (10) Sasaki-Kriener-Segawa- Yada-Tanaka-MS -Ando(11) 6

7 An interesting feature of this material is the existence of Dirac fermions in the normal state Dirac fermion 7

8 In this talk, I would like to show that surface Dirac fermions in the normal state play a very important role in the surface state in the superconducting state If the superconducting state is topological Spectrum transition of Majorana fermion Yamakage, Yada, MS, Tanaka, Phys. Rev. B85, (R) (12) If the superconducting state is non-topological Dirac fermion induced enhancement of surface gap Mizushima, Yamakage, MS, Tanaka, arxiv: Both phenomena are very relevant to surface experiments 8

9 Surface Majorana fermions in superconducting topological insulator Cu x Bi 2 Se 3 Sasaki, Kriener, Segawa, Yada, Tanaka, MS, Ando, Phys. Rev. Lett. 107, (11) Yamakage, Yada, MS, Tanaka, Phys. Rev. B85, (R) (12) 9

10 3D time-reversal invariant topological SC [Sasaki, Kriener, Segawa, Yada, Tanaka, MS, Ando PRL (11)] Cu x Bi 2 Se 3 Superconducting only for 0.10 x 0.30 Wray et al., Nat. Phys. (2010) Hor et al., PRL (2010) Dirac fermion in the normal state (Remnant of topological insulator) Superconducting Topological Insulator (STI) 10

11 Due to strong SOC, odd-parity pairing can compete against s-wave pairing. [Fu-Berg (10) ] σ μ : Pauli matrices in orbital space (two p z -orbitals of Se) s μ : Pauli matrices in spin space Quintuple Layer k y orbital 1 orbital 2 SO int. induces helical spin structure on the Fermi surface 11

12 Intra-orbital Cooper Spin-singlet pairing (s-wave ) Inter-orbital Cooper Spin-triplet pairing [Fu-Berg (10) ] Topological SC [Fu-Berg (10), MS(10) ] If inter-orbit pairing is realized, topological SC is realized 12

13 Measurement of tunneling conductance has been done for this STI. [Sasaki, Kriener, Segawa, Yada, Tanaka, MS, Ando PRL (11)] Cu x Bi 2 Se 3 Sn Z mev Robust zero-bias peak appears in the tunneling conductance Evidence of Majorana fermion 13

14 But the story is not so simple cf.) Superconducting analogue of 3 He B-phase The simplest 3D TRI topological SC [Schnyder et al. (08), Qi et al. (09), ] It supports helical Majorana fermions on its surface with Spin-triplet 14

15 Tunneling conductance for the superconducting analogue of 3 He-B [Y.Asano et al. PRB (03)] conductance There exist surface helical Majorana fermions. But the tunneling conductance shows no single peak structure 15

16 Actually, the zero-bias dip is likely a general feature of 3D TSCs. Tunnel barrier Volume factor electron hole SC Metal When the tunnel barrier is high, Nonzero only at θ = 0 Surface DOS 16

17 Is the single peak structure of the tunneling conductance really explained by helical Majorana fermions? 17

18 Our answer: Yes Surface Dirac fermions in the normal states is a key to solve this problem Yamakage, Yada, MS, Tanaka PRB (12) Dirac fermion in the normal state (Remnant of topological insulator) 18

19 Model Hamiltonian parent topological insulator Z 2 invariant σ μ : Pauli matrices in orbital space (two p z -orbitals of Se) s μ : Pauli matrices in spin space For Surface bound state = Dirac Fermion 19

20 Superconducting TI Nambu rep. Two possible full gapped Cooper pairs [Fu-Berg (10)] Intra-orbital spin-singlet (s-wave ) Inter-orbital spin-triplet ( odd-parity) Topological SC hosting MFs 20

21 Chemical potential Our result Yamakage, Yada, MS, Tanaka PRB (12) For superconducting TI, Majorana fermions have a transition in the energy dispersion, due to Dirac fermions in the normal state. The transition make it possible to have a robust zero bias peak large μ small μ Effective mass of conduction band 21

22 Chemical potential Energy E Why the transition occurs? large μ large μ Momentum k small μ No Dirac fermion near the Fermi surface Surface Dirac fermion near the Fermi surface! small μ 22

23 More details For small μ, the surface Dirac fermion exists near the FS. The surface Dirac fermion remains gapless even in the superconducting state since no s-wave Cooper pair is induced. Dirac fermion + Majorana cone = Caldera shape E The bulk spin-triplet Cooper pair has a completely different symmetry than s-wave one Majorana cone Dirac fermion k Hao and Lee, PRB (11) Hsieh and Fu, PRL (12) Yamakage et al PRB (12) 23

24 We have two different spectra of MF small μ E Transition large μ E k k Caldera Transition occurs when Cone critical chemical pot. Positive only when Dirac fermions exist (Z2 non-trivial ) 24

25 Near the transition, we have enhancement of the surface DOS at zero energy Surface density of states at E=0 Singular at the critical chemical potential Zero-bias peak of the tunneling conductance [Sasaki et al PRL (11)] eriment Yamakage, Yada, MS, Tanaka PRB (12) 25

26 Summary I Recent measurements of tunneling conductance for the superconducting TI Cu x Bi 2 Se 3 show a pronounced zero-bias conductance peak. In conventional 3D TSCs, helical Majorana fermions show zero bias dip rather than zero-bias peak in the tunneling conductance. But the superconducting topological insulator Cu x Bi 2 Se 3 may support helical Majorana fermions that are consistent with recent experiments of tunneling conductance. But the story did not end. 26

27 Very recently, STM experiments reported a conflicting result of tunneling spectroscopy No zero bias peak 27

28 Motivated by this experiment, we self-consistently solve the surface gap function and study what happens if s-wave pairing is realized in STI. We found Even if s-wave pairing, STI shows an interesting phenomena on the surface. Mizushima, Yamakage, MS, Tanaka, arxiv:

29 Main result Contrary to the claim of the NIST group, we found that s-wave pairing does not naturally explain their results. Our result NIST experiment Double-peak structure 29

30 Why such a double peak appears? Dirac-fermion of STI in the normal state may induce large enhancement of surface gap function in the superconducting state Key Point Dirac fermion Cu x Bi 2 Se 3 Wave function of Dirac fermion is polarized surface in orbital space Orbital 2 dominates the surface state 30

31 Mechanism of enhancement Near the surface, intra orbit odd-parity pairing can be induced by breaking of inversion symmetry. s-wave Odd-parity Orbitals 1 and 2 may have different gaps. Bulk quasiparicles Dirac fermions Gap in orbital 2 is enhanced in order to gain the condensation energy of Dirac fermion Gap in orbital 1 changes smoothly Mizushima, Yamakage, MS, Tanaka, arxiv:

32 The enhancement of the surface gap function gives an extra structure of LDOS LDOS of orbital 1 LDOS of orbital 2 Extra gap by Dirac fermion Surface DOS We have an additional coherent peak at the surface gap as well as the peak at the bulk gap Double-peak structure 32

33 We have also confirmed that such an enhancement of surface gap function does not occur if the interorbital odd-parity SC is realized in the bulk Surface gap function LDOS 33

34 Summary II If s-wave pairing is realized in STI, the surface DOS shows a double peak structure, unlike a simple U-shaped spectrum of conventional s-wave SCs The data of the NIST STM experiment does not establish an s- wave pairing symmetry of STI What happen in reality? 34

35 Possible explanation = topology change of FS Cu-doped E. Lahoud et al, arxiv: Fermi surface criterion MS(9,10), Fu-Berg(10) Strong TSC MF on (111)surface Not Strong TSC No MF on (111)surface Bulk odd-parity pairing might be consistent with experiments 35

36 Summary III Conflicting results of tunneling conductance could be related to the topology change of Fermi surface. To establish the existence of Majorana fermions, we need to establish the bulk pairing symmetry by using bulk measurements such as NMR measurements. 36