Bulk Topological Superconductor Possible Topological Superconductors l Periodic
Bulk Topological Superconductor
Possible Topological Superconductors l “Periodic Table” of topological invariant Schnyder-Ryu-Furusaki-Ludwig (2008) Kitaev (2009) SC in TI surface Chiral p-wave 1 D 2 D 3 D Time-Reversal Broken (TRB) Z 2 Z - (D) Time-Reversal Invariant (TRI) Z 2 Z (DIII) l Surface State of TIs f=p f=0 SC SC TI Fu & Kane (2008) l Sr 2 Ru. O 4 Bogoliubov qp EF 2 D EF Majorana Edge State
Possible Topological Superconductors l “Periodic Table” of topological invariant Schnyder-Ryu-Furusaki-Ludwig (2008) Kitaev (2009) Kitaev model SC in TI surface Chiral p-wave 1 D 2 D 3 D Time-Reversal Broken (TRB) Z 2 Z - (D) Time-Reversal Invariant (TRI) Z 2 Z (DIII) In. Sb/ Nb. Ti. N Mourik et al. , Science (2012) In. As/Al Das et al. , Nature Phys. (2012) Oreg et al. , PRL (2010) Lutchyn et al. , PRL (2010) 1 D Nanowire of In. Sb or In. As Majorana End-State Alicea, RPP (2012)
Possible Topological Superconductors l “Periodic Table” of topological invariant Schnyder-Ryu-Furusaki-Ludwig (2008) Kitaev (2009) Kitaev model SC in TI surface Chiral p-wave 1 D 2 D 3 D Time-Reversal Broken (TRB) Z 2 Z - (D) Time-Reversal Invariant (TRI) Z 2 Z (DIII) Superfluid 3 He-B phase • New 3 D topological state of matter • The surface state may host Helical Majorana Fermions that are itinerant and massless E EF ky
SC in Cux. Bi 2 Se 3 Hor et al. , PRL (2010) l Four-component Hamiltonian of Bi 2 Se 3 with the basis ( P 1 z+ , P 2 z- ) E Topological SC State in the bulk Fu & Berg, PRL (2010) Helical Majorana fermions EF k E Conventional SC State in the bulk Proximity SC EF k Majorana zero mode in vortices Hosur et al. , PRL (2011)
SC in Cux. Bi 2 Se 3 Hor et al. , PRL (2010) Problem: Sample is difficult to prepare, shielding fraction is low. Zero Resistivity E Topological SC State in the bulk Fu & Berg, PRL (2010) Helical Majorana fermions EF Specific Heat Jump SC V. F. 70% k E Conventional SC State in the bulk Proximity SC EF k Majorana zero mode in vortices Hosur et al. , PRL (2011)
“Soft” Point Contact Ag particles on the surface Sasaki, Ando et al. , PRL (2011) SEM image of an actual sample B-dep. (Ag particle size ~50 nm) Sn Cux. Bi 2 Se 3 T-dep.
Effects of Heating and/or Critical Currents? T = 0. 35 K Example of a spurious ZBCP Sheet et al. , PRB (2004) H-dep. G(V)/Gn ue to d e t a t ds n u o tate b s v C e e S r l d An tiona n e v n o an unc V (m. V) l Dip position moves with H l H dependence is completely different! l Peak height is insensitive to H 1 T 0. 75 T 0 0. 5 T 0 T Reflectionless tunneling would be governed by Lf ~ 1 mm and suppressed with ~1 m. T.
Possible SC States in Cux. Bi 2 Se 3 l Four-component Hamiltonian of Bi 2 Se 3 ( P 1 z+ , P 2 z- ) Sasaki, Ando et al. , PRL (2011) Fu & Berg, PRL (2010) All odd-parity states are topologically non-trivial and host helical Majorana fermions on the surface
Unconventional SC States in Cux. Bi 2 Se 3 D 2 : Odd parity, full gap Helical Majorana A Yamakage et al. , PRB (2012) Helical Majorana B Hsieh & Fu, PRL(2012) D 4 (D 3) : Odd parity, point node Helical Majorana C d. I/d. V for A d. I/d. V for B cal i l e h o due t P s? C n B o Z i m r na fe a r o j a M Sasaki, Ando et al. , PRL (2011)
Controversy in Cux. Bi 2 Se 3 STM Levy et al. , PRL (2013) ? Conventional s-wave ? If the bulk is BCS s-wave Parity mixing of pair potential is anomalously enhanced by surface Dirac fermions Opening of an additional surface gap which is larger than the bulk gap EF Mizushima, Yamakage, Sato & Tanaka, PRB (2014)
Controversy in Cux. Bi 2 Se 3 Lahoud et al. , PRB (2013) Mizushima et al. , ar. Xiv: 1311. 2768 Levy et al. , PRL (2013) n 1017 cm-3 1019 cm-3 1020 cm-3 Qua ? C S T si-2 D n = 4 1017 cm-3 n = 2 1020 cm-3
Superconducting Doped TCI
Topological Crystalline Insulator Sn. Te : contribution from Te p-orbital Sn. Te Pb. Te Band inversion + Mirror symmetry Nontrivial Mirror Chern number ky Sn. Te p 0 Pb. Te L 3 L 4 L 1 L 2 - + + p - k x Tanaka, Sato, Ando et Z 2 invariant n = 0 al. , Nature Physics (2012) Sn. Te Hsieh et al. , Nature Commun. (2012)
In-doped Sn. Te Superconductor Rhombohedral Cubic Erickson et al. , PRB (2009) Novak, Ando et al. , PRB (2013) Sn 1 -x. Inx. Te Ferroelectric Sn 2+/In 3+ Te 2 - Topological SS is present in Sn 1 x. Inx. Te. Na. Cl Structure n = 2 – 8 1020 cm-3 Sato, Ando et al. , PRL (2013)
In-doped Sn. Te Sasaki, Fu, Ando et al. , PRL (2012) Point-Contact Spectroscopy 0. 24 me. V 2 D Sn 1 -x. Inx. Te T- dep. (x = 0. 045) Tc = 1. 2 K Normalized ZBCP height is > 2 !! Faceted (001) surface B- dep. tate S d n u Bo v e e r d n l SC A a n e o c i t a f n Sur nve o c n U due to Peak suppression corresponds to Hc 2
Sn. Te vs. Pb. Te Similar FS structures, but the band parities are different. Sn 1 -x. Inx. Te Pb 1 -x. Tlx. Te l iona t n e v on Unc T- dep. Tanaka, Ando et al. , Nature Phys. (2012) al tion n e v n Co T- dep.
Possible SC States in Sn 1 -x. Inx. Te l k p Hamiltonian of Sn. Te around each L point SC? l a c i g opolo sz = 1 p orbitals of Sn and Te with opposite parity T ( k 3: along GL, k 1: along LK ) l k p Hamiltonian of Bi 2 Se 3 around G point sz = 1 Se pz orbitals on the top and bottom layer Possible Pairing Symmetry Sasaki, Fu, Ando et al. , PRL (2012) (representations of D 3 d group) A 1 g A 1 u A 2 u Eu Parity even odd odd Topologically non-trivial
Possible SC States in Sn 1 -x. Inx. Te Rhombohedral Cubic Novak, Ando et al. , PRB (2013) SC? l a c i g opolo T Sasaki, Fu, Ando et al. , PRL (2012) Possible Pairing Symmetry (representations of D 3 d group) A 1 g A 1 u A 2 u Eu Parity even odd odd Topologically non-trivial
Majorana Zero Mode in Vortices? If the bulk SC is conventional: Cux. Bi 2 Se 3 Majorana zero mode in vortices Hosur et al. , PRL (2011) Sn 1 -x. Inx. Te Multiple Majorana zero modes can coexist due to additional symmetry to protect them from hybridization
Natural Heterostructure
Natural Heterostructure PSBS [(Pb. Se)5]n[(Bi 2 Se 3)3]m n = 1 m = 1 “Quintuple Layer” (Bi 2 Se 3) Nakayama, Sato, Ando et al. , PRL (2012) (Bi 2 Se 3) m = 2 m =
Natural Heterostructure PSBS Nakayama, Sato, Ando et al. , PRL (2012) m = 1 m = 2 m = Surface states are encapsulated by the insulating Pb. Se layer “Surface states” in every (Bi 2 Se 3)m units? Ultra-thin Bi 2 Se 3 Films Y. Zhang, Q. K. Xue et al. , Nat. Phys. (2010) Quasi-2 D system with topological “bulk” state !!
Cu-intercalation to PSBS m = 2 Sasaki, Segawa, Ando, PRB (2014)
Nearly 100% Volume Fraction Sasaki, Segawa, Ando PRB (2014) Specific-heat behavior is very different from BCS, suggesting a gap with line nodes
Reproducibility Sasaki, Segawa, Ando PRB (2014) Cel(T) is reproducible in two high-volume-fraction samples.
Magnetic-Field Dependence of Cel Sasaki, Segawa, Ando PRB (2014)
Implications of Cu-PSBS l Nodal Gap Unconventional SC None of the previously known superconducting TI presented clear bulk signature of unconventional SC l Sign Changing Gap + Strong Spin-Orbit Coupling Spin-split surface Andreev bound state (i. e. Helical Majorana fermions) d-wave gap l Quasi 2 D-Fermi surface Majoranas are on the side surface or terrace edge
Sr. Pt. As
Sr. Pt. As
Stronger relaxation in the SC state Appearance of spontaneous magnetic field TRS breaking T-dependence of penetration depth Full gap d+id (chiral d-wave) pairing ?
Thank you!
- Slides: 32