Exotic Phenomena in Topological Insulators and Superconductors
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1 SPICE Workshop on Spin Dynamics in the Dirac System Schloss Waldthausen, Mainz, 6 June 2017 Exotic Phenomena in Topological Insulators and Superconductors Yoichi Ando Physics Institute II, University of Cologne
2 Outline Topological Protection and Planar Hall Effect Topological Superconductivity in Cu x Bi 2 Se 3 Recent Efforts at Cologne Funding: DFG CRC1238 ERC Advanced Grant MajoranaTopIn
3 Collaborators University of Cologne University of Cologne A. Taskin, F. Yang, Z. Wang, S. Ghatak, O. Breunig, D. Fan, L. Andersen, A. Bliesener, M. Rößler, M. Bai, A. Salari, P. Janoschka Past members: K. Segawa, S. Sasaki, Z. Ren, M. Kriener, M. Novak, K. Eto Theory: Profs. Rosch, Altland (Cologne) Fab.: Prof. Matsumoto (Osaka) NMR: Prof. Zheng (Okayama) Magnetocaloric: Prof. Maeno (Kyoto)
4 Topological Protection and Planar Hall Effect
5 Topological Protection Protection is lifted by Gap Opening Energy Bulk Conduction Band down spin Bulk Valence Band k = 0 up spin E F Dirac point k Top-Bottom Surface Hybridization Quantum Anomalous Hall Effect Taskin, Ando et al., PRL (2012) Chang, Xue et al., Science (2013) Time-Reversal-Breaking Effect of Parallel Magnetic Field?
6 Parallel Magnetic Field For surface Dirac fermions, Zeeman field acts like the vector potential: kk σσ kk + ggμμ BB HH σσ Dirac Hamiltonian HH = vv FF kk σσ = vv FF 0 kk xx iikk yy kk xx + iikk yy 0 k y k x H HH = vv FF kk + ggμμ BB HH σσ = vv FF mm zz kk xx +mm xx ii(kk yy +mm yy ) kk xx +mm xx +ii(kk yy +mm yy ) mm zz Parallel magnetic field does not open a gap, and its effect can be gauged away by a simple shift of the frame. To first order, there is no effect on surface transport properties. k y H k x '
7 Planar Hall Effect & In-Plane Anisotropy When the resistivity tensor is anisotropic, AMR PHE M ϕ FM metal R // > R I Angular Magnetoresistance (AMR) Planar Hall Effect (PHE)
8 Bulk-Insulating TI in Parallel Field y Bulk-insulating Bi 2-x Sb x Te 3 film (17 nm thick) B = 9 T ϕ Magnetic-field-induced resistivity anisotropy I x PHE AMR
9 PHE from TI surface Dual-Gating Device Amplitude PHE signal is symmetric w.r.t. B
10 PHE from TI surface Double-peak structure is associated with the Dirac Point Amplitude
11 Theoretical Analysis of PHE Resonance energy TSS Impurity states in B hybridization Spin-polarization of monmagnetic impurities Anisotropic scattering Peak position l ~ 7 nm PHE amplitude l φφ ~ 70 nm
12 Topological Superconductor
13 1. Introduction 2. Concept of topology in quantum mechanics 3. Basics of superconductivity 4. Theory of topological superconductors 5. Majorana fermions 6. Routes to topological superconductivity 7. Materials realizations 8. Properties of topological superconductors 9. Outlook
14 Possible Topological Superconductors Periodic Table of topological invariant Schnyder-Ryu-Furusaki-Ludwig (2008) Kitaev (2009) SC in TI surface Chiral p-wave 1D 2D 3D Time-Reversal Broken (TRB) Z 2 Z - (D) Time-Reversal Invariant (TRI) Surface State of TIs Z 2 Z 2 Z (DIII) φ = π φ = 0 Bogoliubov qp SC TI SC E F 2 E F Majorana Edge State Fu & Kane (2008) Sr 2 RuO 4
15 Possible Topological Superconductors Periodic Table of topological invariant Schnyder-Ryu-Furusaki-Ludwig (2008) Kitaev (2009) Time-Reversal Broken (TRB) Kitaev model 1D 2D 3D Z 2 Z SC in TI surface Chiral p-wave - (D) Time-Reversal Invariant (TRI) Z 2 Z 2 Z (DIII) InSb/ NbTiN 1D Nanowire of InSb or InAs InAs/Al Mourik et al., Science (2012) Das et al., Nature Phys. (2012) Oreg et al., PRL (2010) Lutchyn et al., PRL (2010) Majorana End-State Alicea, RPP (2012)
16 Possible Topological Superconductors Periodic Table of topological invariant Schnyder-Ryu-Furusaki-Ludwig (2008) Kitaev (2009) Time-Reversal Broken (TRB) Kitaev model 1D 2D 3D Z 2 Z SC in TI surface Chiral p-wave - (D) Time-Reversal Invariant (TRI) Z 2 Z 2 Z (DIII) New 3D topological state of matter The surface state may host Helical Majorana Fermions that are itinerant and massless Superfluid 3 He-B phase E E F k y
17 SC in Cu x Bi 2 Se 3 Hor et al., PRL (2010) Four-component Hamiltonian of Bi 2 Se 3 with the basis ( P1 z+, P1 z+, P2 z-, P2 z- ) Topological SC State in the bulk Fu & Berg, PRL (2010) Conventional SC State in the bulk Proximity SC E E Helical Majorana fermions E F k E F k Majorana zero mode in vortices Hosur et al., PRL (2011)
18 SC in Cu x Bi 2 Se 3 Hor et al., PRL (2010) Point-contact spectroscopy Sasaki, Ando et al., PRL (2011) Sn Yamakage et al., PRB (2012) Topological SC State in the bulk Fu & Berg, PRL (2010) Conventional SC State in the bulk Proximity SC E E Helical Majorana fermions E F k E F k Majorana zero mode in vortices Hosur et al., PRL (2011)
19 NMR Experiment on Cu x Bi 2 Se 3 Matano, Ando, Zheng et al., Nat. Phys. (2016)
20 Specific-Heat of Cu x Bi 2 Se 3 Yonezawa, Ando, Maeno et al., Nat. Phys. (2016)
21 Cu-intercalated (PbSe) 5 (Bi 2 Se 3 ) 6 Sasaki, Segawa, Ando, PRB (2014)
22 Nearly 100% Volume Fraction Sasaki, Segawa, Ando PRB (2014) Specific-heat behavior is very different from BCS, suggesting a gap with line nodes
23 Magnetic-Field Dependence of C el CC eeee ~ BB Sasaki, Segawa, Ando PRB (2014) At low T, CC eeee BB behaves as ~ BB, pointing to the existence of line nodes.
24 Magnetic-Field Dependence of C el Nodal Gap Unconventional SC The nodes are most likely due to the 4 gap CC eeee ~ BB Same pairing as in Cu x Bi 2 Se 3 Nematic SC is also reported for Sr x Bi 2 Se 3 and Nb x Bi 2 Se 3 At low T, CC eeee BB behaves as ~ BB, pointing to the existence of line nodes. Sasaki, Segawa, Ando, PRB (2014)
25 Recent Efforts
26
27 Topological Josephson Junction Bi 2 Se 3 + Pt/Al/Au V (µv) mk 192 mk 404 mk 450 mk 600 mk 750 mk 1 K 1.35 K 1.35 K 48 mk -30 B= 0 Gauss R (Ω) Gap 600 nm I (µa) I dc (µa) 6 dv/di mk T (K) B (Gauss)
28 H Nanowire-based Majorana box qubit for surface code processor Cook & Franz, PRB (2011) Surface Code is a realistic architecture to realize practical quantum computations by built-in error corrections
29 Summary Planar Hall Effect probes the anisotropic lifting of the topological protection from backscattering Superconducting doped Bi 2 Se 3 realizes a Topological Nematic SC State
30 Students and Postdocs wanted!
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