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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
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