Topological current at an interfacebetween superfluid 3He A-phases

APS March Meeting, 3/22/2013

RIKEN Yasumasa Tsutsumi

Z22.00002

Edge state and domain wallhigh-temperature and high-pressureA-phase

point node

Anderson-Brinkman-Morel (ABM) state

spin state

orbital statedz(kx + iky)

broken time-reversal symmetry

Domain wall

topological mass current-1 0 1-1

0

1

-0.8-0.4 0 0.4 0.8

ky

kz

E LR

Edge state

: density of 3He atoms: number of 3He atoms

macroscopic intrinsic angular momentum

Quasi-classical Eilenberger theory

Eilenberger equation

Gap equation

�(kF , r) = N0�kBT�

��c��n��c

�V (kF ,k�F )f(k�F , r,�n)

�

k�F

�/EF � 1

�

V (kF ,k�F ) = 3g1kF · k�

Fpair potential :

mass current:

dispersion:

Riccati method

Riccati equationstoward

toward

�g if�if �g

�=

�(1 + ab)�1 0

0 (1 + ba)�1

� �1� ab 2ia�2ib �(1� ba)

�

left state right state

Result (edge state)same with edge state

-0.8

-0.4

0

0.4

0.8

-20 -10 0 10 20

0 1 2 3 4 5

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1

dispersion at domain wall

-3-2-1 0 1 2 3

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1

energy spectrum of mass current

0

0.01

0.02

0.03

0.04

0.05

-20 -10 0 10 20

mass current

Result (lowest energy domain)

0 1 2 3 4 5

-1

-0.5

0

0.5

1

dispersion at domain wall

-0.8

-0.4

0

0.4

0.8

lowest energySalomaa and Volovik, JLTP 74, 319 (1989).

-20 -10 0 10 20

-1 -0.5 0 0.5 1

0 1 2 3 4 5

-1

-0.5

0

0.5

1

0 1 2 3 4 5

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1

-0.1

-0.08

-0.06

-0.04

-0.02

0

-20 -10 0 10 20

mass current

0 1 2 3 4 5

-1

-0.5

0

0.5

1

Summary and remark

M. A. Silaev and G. E. Volovik, PRB 86, 214511 (2012).

quasiclassical theory

Bogoliubov-de Gennestheory

by normal reflection-1 -0.5 0 0.5 1

Topological mass current has no relation to intrinsic angular momentum.