Surface Andreev Bound States and Surface Majorana States on the - PowerPoint PPT Presentation

Surface Andreev Bound States and Surface Majorana States on the Superfluid 3 He B Phase Tokyo Institute of Technology R. Nomura S. Murakawa, M. Wasai, K. Akiyama, Y. Wada, Y. Tamura, M. Saitoh, Y. Aoki and Y. Okuda Collaboration with Y. Nagato, M. Yamamoto, S. Higashitani and K. Nagai at Hiroshima Univ.

Andreev Bound States (ABS) N S e h h e L z/  Resonant states L ~  in normal metal. SABS are intrinsic to surface of anisotropic BCS states.

Zero bias conductance peak in unconventional superconductors tunneling of YBCO junction Sr2RuO4 Kashiwaya et al . PRB 70 , 094501 Laube et al . ( 2004 ) PRL 84, 1595 (2000)

By Yukio Tanaka, superclean (2005)

superfluid phases of 3He           A phase p ip A x y l anisotropic gap                  B phase p ip p ip p B x y x y z In the BW state, anti-symmetry of the order parameter is broken. isotropic gap

Theoretically calculated SDOS in BW state on specular surface angle averaged ( Natato 1998) angle resolved 4 T = 0.2 T c S = 1.0 3 SDOS 2 1 0 0 0.5 1 1.5 E /   ( ) N E E E  c // p // No sharp peak at zero energy but a broad SABS band appears within the bulk energy gap  . “Dirac” cone on 3He-B

p        ( ) ( ) p p // 0 z z  p F  0 E     E // sin c p // //    0 0   ∥     d  0 0 ∥ i      0 0 

particel = anti-particel SABS: Majorana Fermion “Majorana cone” Chun, Zhan, PRL09

Recent theories on Majorana surface state in 3He-B (1)Classification of topological insulators and superconductors in three spatial dimensions A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, Phys. Rev. B 78, 195125 2008 (2)Topological superfluids with time reversal symmetry R. Roy, arXiv:0803.2868v1, 19 Mar 2008 (3)Time-Reversal-Invariant Topological Superconductors and Superfluids in Two and Three Dimensions Xiao-Liang Qi, Taylor L. Hughes, S. Raghu, and Shou-Cheng Zhang, PRL 102, 187001 (2009) (4) Detecting the Majorana fermion surface state of 3He-B through spin relaxation S. B. Chung and S. C. Zhang, PRL 103, 235301 (2009) (5) Fermion zero modes at the boundary of superfluid 3He-B G.E. Volovik, Pis'ma ZhETF 90, 440-442 (2009) (6) Topological invariant for superfluid 3He-B and quantum phase transitions G.E. Volovik, Pis'ma ZhETF (7) Fermi Surface Topological Invariants for Time Reversal Invariant Superconductors X. L. Qi, Taylor, L. Hughes and S. C. Zhang, arXiv:0908.3550v1, 25 Aug 2009 (8) Strong Anisotropy in Spin Suceptibility of Superfluid 3He-B Film Caused by Surface Bound States Y. Nagato, S. Higashitani and K. Nagai, J. Phys. Soc. Jpn., 78, 123603 (2009)

Quasiparticles scattering off a wall Specular limit Partially specular Diffusive limit 1 > S > 0 S = 1 S = 0 S =0.5 S can be controlled continuously by thin 4 He layers on a wall.

Theoretically calculated SDOS in BW state at various S 4 T = 0.2 T c s = 0.0 N (  , z = 0) / N (0) s = 0.2 3 s = 0.5 s = 1.0  * 2 E F Δ 1 0 0 0.5 1 1.5  bulk Zero energy state is intrinsically suppressed at S > 0. Bandwidth (  *) is broader at S > 0. Flat surface bound states band at S = 0. Nagato et al . JLTP 1998

Measurements Transverse acoustic impedance of AC-cut quartz in liquid 3 He      Stress tensor of liquid on the wall xz Z Z ' iZ " xz u Oscillation velocity u x x   1 1 1       Superfluid 3 He Z ' Z ' n Z   0 q   4 Q Q 0  1 f f    0 Z " Z " n Z  0 q 2 f 0 u Wall   Z c q q q Superfluid 3 He 0.5mm Transducer

Hydrodynamics region  << 1, high temperature a y      Z 1 i 2 Equivalent to  viscosity measurements x critically damped Collisionless region  >> 1, low temperature     xz Z Z ' iZ " u x Quasiparticle scattering Pair breaking  ~  Spectroscopy of SDOS

Diffusive limit, S = 0 Pure 3 He without 4 He coating 4 3   SDOS  * 2 1 0 0 1 2  /  bulk

T pb 100 2  ( T ) [MHz] Pair breaking edge temperature T pb 50     2 ( ) T pb 0 0.85 0.9 0.95 1 T/Tc T / T c In s-wave BCS superfluid (no SABS) Drop in Z ’ at T pb   0 : 0 T Z Small frequency dependence Only  n responses

T * T * T pb T pb T c 1000 1000 1000 In B phase ( Z' - Z' 0 ) /  [cm /sec] ( Z' - Z' 0 ) /  [cm /sec] ( Z' - Z' 0 ) /  [cm /sec] No change in Z at T c 0 0 0 No drop in Z’ at T pb . P = 10.0 bar P = 10.0 bar P = 10.0 bar -1000 -1000 -1000 peak in Z” and kink ( Z" - Z" 0 ) /  [cm /sec] ( Z" - Z" 0 ) /  [cm /sec] ( Z" - Z" 0 ) /  [cm /sec] 0 0 0 in Z’ at T* -500 -500 -500 Structure appears below T pb. -1000 -1000 -1000 29 MHz Low lying 28.7 MHz 28.7 MHz 28.7 MHz 48 MHz 47.8 MHz 47.8 MHz 47.8 MHz excitations !! -1500 -1500 -1500 0.85 0.85 0.9 0.9 0.95 0.95 1 1 0.85 0.9 0.95 1 T / T c T / T c T / T c

Z(T) at S = 0 experiment theory T* T* T* T* 実験 理論 5 ( Z' - Z' 0 ) /  [m /sec] 1.2 Z' / Z N 0 1 -5 P = 1.7 MPa 0.8 27.8 MHz ( Z" - Z" 0 ) /  [m /sec] 0 46.4 MHz 0 Z" / Z N -5 -0.2 28 MHz 27.8 MHz 46 MHz 46.4 MHz -10 -0.4 0.9 0.92 0.94 0.96 0.98 1 0.9 0.92 0.94 0.96 0.98 1 T / T c T / T c Aoki et al . PRL (2005)

Z(  ) theory kink Z’ with SABS Z/Z N peak Kink and peak Z are anomaly ”       * when    4 First experimental confirmation 3   SDOS of the sub-gap structure.  * 2 Aoki et al . PRL (2005) 1 0 0 1 2  /  bulk

Partially specular wall; 0 < S <1 Coat a wall with 4 He layers 3 He 4 He wall Cartoon

Evaluate S from Z in normal fluid 10 bar 16 MHz 2000 Z' / ρ ( cm / s ) pure 2.7 層 Pure 3He 3.5 層 4He 2.7 layers F 2 = -0.5 S = 0.2 1000 4He 3.5 layers S = 0.84 0 10 1 10 2 10 3 T ( mK ) fitting at 16 MHz and 17 bar

S vs 4 He layers and P 1 0.8 10 bar 17 bar 25 bar 0.6 S 0.4 0.2 0 0 1 2 3 4 5 4 He layers S is larder for thicker 4 He. is smaller at higher P.

T* T* Z(T) in B phase 1000 ( Z' - Z' 0 ) /  [cm /sec] S = 0.17 、 2.7 layers 4 He, 10bar 0 P = 10.0 bar 4 He 2.7 layer Compared to S = 0, Pure -1000 T * shifts to higher. ( Z" - Z" 0 ) /  [cm /sec] 0 Smaller temperature dependence Z(T). -500       * ( *) T -1000 29 MHz 28.7 MHz 48 MHz 47.8 MHz -1500 0.85 0.9 0.95 1 T / T c

S dependence of  *(T)/  (T) 1 0.8  * ( T ) /  ( T ) 0.6    0.4 Specularity 0 0.04 0.07 Theory 0.2 0.17 Specularity 0.55 1.0 0.80 0.5 0 0.7 0.8 0.9 1 T / T c T/Tc Saitoh, et al. PRB(R) 2006 Wada, et al. PRB 2008

4 s = 1.0 s = 0.5 3 s = 0.0 SDOS  * 2 1 0 0 1 2  /  bulk Broadening at larger S Suppression of SDOS at zero-energy at larger S Nagato et al . JLTP 1998

New low temperature peak at S > 0. 2 ( Z' - Z' 0 ) /  (m / s) S = 0.53 0 -2 -4 -6 P = 1.7 MPa 1 ( Z" - Z" 0 ) /  (m / s) 0 -1 -2 -3 28.7 MHz 47.8 MHz -4 67.0 MHz 0.6 0.7 0.8 0.9 1 T / T c Murakawa et al ., PRL 09

Scaled energy dependence of Z(  ) at various S Low energy peak grows when S > 0 due to the formation of the Majorana cone.

Z(  ) theory by Nagato et al. for S = 0.5 total  +  * Z’/Z N  Scattering  -  * T=0.9T C Pair excitation  *       Two peaks in Z(  ) due to the formation of Majorana cone.

Z(  ) theory for S = 0 Z’  +  * Z/Z N Z’’    Flat below  * Single peak in Z(T)

Summary Surface Andreev bound states in 3 He-B are detected by Z(T,  ) measurement. Specularity S is controlled by 4 He layers. On a partially specular wall Bandwidth of bound states  * becomes broader. Growth of the low temperature peak in Z(T) as increasing S is due to the formation of the Majorana cone. Our observation is an experimental indication of the Majorana cone on 3He-B.