E or J

KT, et al. PRB 2017; PRB 2017 KT and M.Sato arXiv 2018 Z. Gong, …, KT, … PRX 2018

Poster-12 兎子尾 Poster-31 山本KT et al. in preparation

01/20

Lightning (雷) Zener diode Plasma displayLichtenberg figure

Figures from Wikipedia

02/20

Gap

Gap

Zener diode

Tunneling between Bloch bands

c.f. Bloch’s theorem, 1928

03/20

Yamakawa et al.,

Nat. Mat. 2017Y. Taguchi et al., PRB 2000

Experimental observation

Oka, Arita and Aoki, PRL 2003

Theoretical studies

E Electric field

Cu

rren

t

Mott E

U

Bias Voltage

04/20

E

E

p e

E

Schwinger機構(電子-陽電子対生成)

C. Sow et al., Science 2017

Current

T

05/20

・

・

・

Kondo insulators

c

f

Bose Mott insulatorsCDW insulatorsFermionic Mott ins.

Universality in breakdown (Noneq. phase transition)… ?

Fermionic Hubbard (1D)

Integrable (Bethe ansatz)

: Numerical(DMRG)

: Analytical

Oka and Aoki, PRB 2010

c.f.

06/20

・

・

・

Kondo insulators

c

f

Bose Mott insulatorsCDW insulatorsFermionic Mott ins.

Universality in breakdown (Noneq. phase transition)… ?

Fermionic Hubbard (1D)

Integrable (Bethe ansatz)

: Numerical(DMRG)

: Analytical

Oka and Aoki, PRB 2010

c.f.

06/20

KT, M. Nakagawa, N. Kawakami, in prep.

I

FFth

Insulator Metal

Threshold

07/20

G.S.

Excited states

G.S.

1st ex.

c.f. T. Oka and H. Aoki, PRB 2010

08/20

Outline

Outline

H(t)

“Critical time”

Dykhne-Davis-Pechukas (DDP) 公式 Dykhne, Sov. Phys. JETP 1962

Davis and Pechukas, J. Chem. Phys. 1976

09/20

: Landau-Zener model

“Critical time”

LZ formula

Re t Im t

tc

ReE

t

E

10/20

Outline

Setup:

,

A= ih

FFth

Threshold

11/20

A= ih

e+h

e -h

Gap closing

Energy gap

h (Asymmetry)

hc

=Mott breakdown

c.f. Hubbard case: (proposed by Fukui and Kawakami)

Fukui and Kawakami, PRB 1998

c.f. Random potential → Hatano-Nelson model Hatano and Nelson, PRL 1996

12/20

A= ih

e+h

e -h

Gap closing

Energy gap

h (Asymmetry)

hc

=Mott breakdown

c.f. Hubbard case: (proposed by Fukui and Kawakami)

Fukui and Kawakami, PRB 1997

c.f. Random potential → Hatano-Nelson model Hatano and Nelson, PRL 1996・非対称ホッピングの冷却原子系での実現提案・非エルミート系におけるトポロジカル相

[Ref. Z. Gong, …, KT, … ,M. Ueda, Phys. Rev. X 8 031079 (2018)]

12/20

Outline

h (Asymmetry)

hc

c.f. Giamarchi’s text book

13/20

Sine-Gordon

|g|

14/20

Main result

15/20

ドープされたエルミートな絶縁体へマップされた

16/20

hhc

*Schematic figures

,

17/20

Analytic formula of threshold field

Landau-Zener

t

E

β=2 : Band insulator

velocity interaction

2. 具体的な模型ではなく有効場の理論にのみ依る

18/20

Fermionic Mott (Hubbard)CDW insulator (XXZ)Band insulator (SSH)

/Δ0

Check:

弱結合領域で幅広く成立している

19/20

KT, M. Nakagawa, N. Kawakami, in prep.

I

FFth

Insulator Metal

Threshold

20/20