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

Surface Andreev Bound States and Surface Majorana States

• n the Superfluid 3He B Phase
• R. Nomura
• S. Murakawa, M. Wasai, K. Akiyama, Y. Wada,
• Y. Tamura, M. Saitoh, Y. Aoki and Y. Okuda

Tokyo Institute of Technology Collaboration with

• Y. Nagato, M. Yamamoto, S. Higashitani and K. Nagai

at Hiroshima Univ.

Andreev Bound States (ABS)

L ~  e e h h N S L Resonant states in normal metal. SABS are intrinsic to surface of anisotropic BCS states. z/

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

By Yukio Tanaka, superclean (2005)

   

 

          

z y x y x B

p ip p ip p phase B

 



     

y x A

ip p phase A

superfluid phases of 3He l anisotropic gap isotropic gap In the BW state, anti-symmetry of the

• rder parameter is broken.

No sharp peak at zero energy but a broad SABS band appears within the bulk energy gap . Theoretically calculated SDOS in BW state on specular surface

0.5 1 1.5 1 2 3 4

E /  SDOS

T = 0.2 Tc S = 1.0

E E N  ) (

// // p

c E 

“Dirac” cone on 3He-B angle resolved angle averaged (Natato 1998)



pF

//

p ) ( ) (

z z

p p       

 E

// // // sin

p c E    

             

 ∥ ∥ i

d

Chun, Zhan, PRL09

“Majorana cone” particel = anti-particel SABS: Majorana Fermion

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)

Diffusive limit S = 0 S can be controlled continuously by thin 4He layers on a wall.

Quasiparticles scattering off a wall

Specular limit S = 1 1 > S > 0 Partially specular S =0.5

Theoretically calculated SDOS in BW state at various S Zero energy state is intrinsically suppressed at S > 0. Flat surface bound states band at S = 0. Bandwidth (*) is broader at S > 0.

EF Δ Nagato et al. JLTP 1998

*

0.5 1 1.5 1 2 3 4

bulk N(,z = 0) / N(0)

T = 0.2 Tc s = 0.0 s = 0.2 s = 0.5 s = 1.0

Measurements

Transverse acoustic impedance of AC-cut quartz in liquid 3He

" ' iZ Z u Z

x xz

   

xz



x

u

Stress tensor of liquid on the wall Oscillation velocity

           1 1 4 1 ' ' Q Q Z n Z Z

q



2 1 " " f f f Z n Z Z

q

   

q q q

c Z  

Superfluid 3He  Wall u 0.5mm Transducer Superfluid 3He

Hydrodynamics region  << 1, high temperature

 

i Z   1 2 

x ay critically damped Equivalent to  viscosity measurements

" ' iZ Z u Z

x xz

   

Collisionless region  >> 1, low temperature Quasiparticle scattering Pair breaking  ~  Spectroscopy of SDOS

Diffusive limit, S = 0

Pure 3He without 4He coating

1 2 1 2 3 4

 / bulk SDOS

*



In s-wave BCS superfluid (no SABS)

) ( 2

pb

T    

:   Z T

Small frequency dependence Drop in Z’ at Tpb Pair breaking edge temperature Tpb Tpb Only n responses

0.85 0.9 0.95 1 50 100 T / Tc 2(T) [MHz]

T/Tc

0.85 0.9 0.95 1

• 1500
• 1000
• 500

(Z" - Z"0) /  [cm /sec] T /Tc

28.7 MHz 47.8 MHz

• 1000

1000 (Z' - Z'0) /  [cm /sec]

P = 10.0 bar

Tc

0.85 0.9 0.95 1

• 1500
• 1000
• 500

(Z" - Z"0) /  [cm /sec] T /Tc

28.7 MHz 47.8 MHz

• 1000

1000 (Z' - Z'0) /  [cm /sec]

P = 10.0 bar

No drop in Z’ at Tpb.

Tpb Tpb

0.85 0.9 0.95 1

• 1500
• 1000
• 500

(Z" - Z"0) /  [cm /sec] T /Tc

28.7 MHz 47.8 MHz

• 1000

1000 (Z' - Z'0) /  [cm /sec]

P = 10.0 bar

peak in Z” and kink in Z’ at T*

T* T*

No change in Z at Tc

In B phase

29 MHz 48 MHz Structure appears below Tpb.

Low lying excitations !!

Z(T) at S = 0

Aoki et al. PRL (2005)

実験

0.9 0.92 0.94 0.96 0.98 1

• 10
• 5

(Z" - Z"0) /  [m /sec] T /Tc 27.8 MHz 46.4 MHz

• 5

5 (Z' - Z'0) /  [m /sec] P = 1.7 MPa

T* T*

28 MHz 46 MHz 理論

0.9 0.92 0.94 0.96 0.98 1

• 0.4
• 0.2

Z" / ZN T /Tc

27.8 MHz 46.4 MHz

0.8 1 1.2 Z' / ZN

T* T* experiment theory

Z() theory with SABS

First experimental confirmation

• f the sub-gap structure.

kink peak   Z/ZN

1 2 1 2 3 4

 / bulk SDOS

*

 Z’ Z ”

*      

Kink and peak are anomaly when

Aoki et al. PRL (2005)

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

Cartoon

3He

wall

4He

fitting at 16 MHz and 17 bar

Evaluate S from Z in normal fluid

101 102 103 1000 2000 10 bar 16 MHz pure 2.7層 3.5層 Z' / ρ ( cm / s ) T ( mK ) F2 = -0.5 S = 0.2 S = 0.84

Pure 3He 4He 2.7 layers 4He 3.5 layers

S vs 4He layers and P

S is larder for thicker 4He. is smaller at higher P.

1 2 3 4 5 0.2 0.4 0.6 0.8 1

4He layers

S

10 bar 17 bar 25 bar

Z(T) in B phase

S = 0.17、 2.7 layers 4He, 10bar T* shifts to higher. Smaller temperature dependence Z(T). Compared to S = 0,

0.85 0.9 0.95 1

• 1500
• 1000
• 500

(Z" - Z"0) /  [cm /sec] T /Tc

28.7 MHz 47.8 MHz

• 1000

1000 (Z' - Z'0) /  [cm /sec]

P = 10.0 bar 4He 2.7 layer Pure

*) ( * T      

29 MHz 48 MHz T* T*

S dependence of *(T)/(T)

Wada, et al. PRB 2008

0.7 0.8 0.9 1 0.2 0.4 0.6 0.8 1 *(T) / (T) T / Tc

Specularity 0.04 0.07 0.17 0.55 0.80 Theory Specularity 1.0 0.5

T/Tc  Saitoh, et al. PRB(R) 2006

Nagato et al. JLTP 1998 1 2 1 2 3 4

 / bulk SDOS

s = 1.0 s = 0.5 s = 0.0

Broadening at larger S Suppression of SDOS at zero-energy at larger S *

• 6
• 4
• 2

2 (Z' - Z'0) /  (m / s)

P = 1.7 MPa

0.6 0.7 0.8 0.9 1

• 4
• 3
• 2
• 1

1

28.7 MHz 47.8 MHz 67.0 MHz

(Z" - Z"0) /  (m / s) T /Tc

S = 0.53

New low temperature peak at S > 0.

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

-* +* * 

Scattering Pair excitation total

   Z’/ZN



T=0.9TC

Two peaks in Z() due to the formation of Majorana cone.

Flat below * Single peak in Z(T) +*

Z() theory for S = 0

Z’’ Z’ Z/ZN  

Summary

Surface Andreev bound states in 3He-B are detected by Z(T, ) measurement. Specularity S is controlled by 4He layers. 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. On a partially specular wall