Nonreciprocal Phenomena in Chiral Materials - Left and Right in Quantum Dynamics –

Nonreciprocal Phenomena in Chiral Materials - Left and Right in Quantum Dynamics –

Naoto Nagaosa

RIKEN Center for Emergent Matter Science (CEMS) Dept. Applied Phys. Univ. Tokyoand

Collaborators

U.Tokyo: Ryohei Wakatsuki, Keita Hamamoto, Hiro Ishizuka, Motohiko Ezawa

Saitama Univ.: Shintaro Hoshino

Exp: Y. Tokura, Y. Iwasa, K.S. Takahashi, K. Yasuda, S. Koshikawa, S. Shimizu, Y. Kaneko, Y. Saito, T. Ideue, H. Yasuda, R. Yoshimi

Left and Right ( chirality ) is a crucial issue in sciences

From Wikipedia No Inversion I No Mirror M

Physics parity violation of weak interaction Chemistry chiral molecules

Biology chirality of DNA

M. Gardner, The Ambidextrous Universe. Left, Right and the Fall of Parity, Basic Books Inc. (1964)

http://quantumwise.com/

publications/tutorials/item /828‐silicon‐p‐n‐junction

http://www.optique‐ingenieur.org /en/courses/OPI_ang_M05_C02/

co/Contenu_09.html

Directional response is useful

pn junction optical isolator

V(x)

x

e

te

re

V(x)

x

e

e

t '

e

r'

2 2

| |

|'

| t  t | r |'

 | r |

Fundamental viewpoint from physics Right and Left directions of flow

Incident from left

Incident from right

t t ' 

Unitary nature of S matrix: conservation of prob.

Time-reversal symmetry T: S=S^Transpose Role of dissipation and classical nature

Asymmetry between t and -t

1. Microscopic time-reversal symmetry breaking external magnetic field B

magnetic ordering M

2. Macroscopic irreversibility dissipation of energy

diffusion

Non-reciprocal transport in non-centrosymmetric system

R (+I) ≠ R (‐I) ^+I

‐I

R = R₀ (1 + βB² + γBI)

Broken inversion symmetry ⇔ γ ≠ 0

”dichroism” of the electric current magnetochiral anisotropy

) ,

, ( )

, ,

( k  B    k   B



for linear response Magnetochiral optical effect

directional dichroism



( k ,  , B )  

  k  B I

k 

Nonlinear response

J   E   BE

e.g. electromagnon in multiferroics

A. Loidl, Y.Tokura

Time-reversal symmetry of microscopic dynamics vs irreversibility

K. Ishizaka et al. Nat. Mater. 10, 521 (2011).

Band structure in noncentrosymmetric crystal

) (

)

( k 

 k







Time-reversal symmetry

γ

10

10

10

G. L. J. A. Rikken et al.

PRL 87, 236602 (2001).

Bi helices Organics Si FET

F. Pop et al.

Nat. Commun. 5, 3757 (2014).

G. L. J. A. Rikken et al.

PRL 94, 016601 (2005).

I E B

Magnetochiral anisotropy – tiny effect

F SOI

B

B  

 ^{, }

R = R₀ (1 + βB² + γBI)

1 1

10

~ T

A



Enhanced magnetochiral anisotropy in BiTeBr

Y.Iwasa G, Y.Tokura G, NN G Nature Phys. 2017

2 _∥ 2 λ

Magnetochiral anisotropy in Rashba model

⋅ 1 ⋯ ,

Boltzmann equation Expand in E

increasing Fermi energy

B

 diverges as n  0 is zero when two FSs coexist

 is independent of  in the single relaxation time approx. like Hall coefficient

K. Hamamoto

 A

 '  _A

1

1

~ T

A



Chiral anomaly in Weyl semimetals

chemical potential difference in non-equilibrium steady state

B E B

J  (  )

 



negative magnetoresistance  due to chiral anomaly

X. Huang et al., PRX 2015

TaAs

K. Fukushima, D. Kharzeev

Weyl fermions in noncentrosymemtric semimetals

Magnetochial anisotropy in noncentrosymemtric Weyl semimetals

sec TaAs /

10 4

~

m

v  | 

|~ 10 meV

T. Morimoto, NN PRL2016

1

10

~ T

A



Giant enhancement of non-reciprocal response in superconductor

F SOI

B

SC

 B  ^ 

 ~ ,

Wakatsuki, Saito et al. Science Adv. 2017

Band structure and spin splitting in MoS²

ħ

2 3 ,

d ^∗

4 3

2 | | ,

93 5 28 3

16ħ 64

, 2

∼

Paraconductivity due to SC fluctuation in noncentrosymmetric MoS²

400

Tc

S. Hoshino et al. 2018

S. Hoshino et al. 2018

Number of vortices Dissipative dynamcis of vortices

Ratchet motion of vortex and nonreciprocal transport

A quantum particle in periodic potential

http://www.natural‐science.or.jp/article/20180529143612.php

Quantum dissipation

by coupling to heat bath

RG study

dimensionless dissipation strength

duality

  1 / 

Linear Mobility

1

 

) 1 (

~ 2

)

( ^



Fisher‐Zwerger PRB1985 Furusaki‐Nagaosa PRB1993 Kane‐Fisher PRB1992

-

- Time-reversal symmetry breaking plays an important role - Magnetochiral anisotropy

- dissipation

- quantum-classical crossover

- duality between bosons and vortices Summary

Symmetry Quantum Geometry Electron Correlation Irreversibility

For a review see Y.Tokura, N.Nagaosa, Nature Communications 2018