nonlinear and ultrafast responses in mott insulators · 2018. 11. 15. · nonlinear and ultrafast...

Nonlinear and ultrafast responses

in Mott insulators

H. Okamoto (Univ. of Tokyo, CREST-JST)

○ Terahertz-electric-field-induced

Mott insulator to metal transition

Dielectric breakdown mechanism

H. Yamakawa et al., Nature Materials (2017)

○ Photoinduced Mott insulator to metal

transition

Probing of ultrafast spin dynamics

coupled with charge excitations

T. Miyamoto et al., in preparation

THz

pulse

Cu

O

7 fs

pulse

ET

Collaborators

● Femtosecond pump probe spectroscopy

H. Yamakawa T. Morimoto T. Miyamoto N. Kida

● Sample preparationsM. Suda, H.M. Yamamoto (IMS), and R. Kato (RIKEN)

K. Miyagawa and K. Kanoda (UT)

T. Ito, A. Sawa (AIST)

● Theory S. Ishihara (Tohoku Univ.)

T. Terashige, H. Tobe, Y. Kinoshita N. Asada (UT)

Acknowledgements

T. Tohyama (Tokyo Univ. Science) and T. Oka (Max Planck)

Towards the understanding of strong electric field effects

on correlated electron materials

1 THz

⇔ ~4 meV⇔ ~300 m

>> 100 kV/cm

1 psex. Pulse front tilting

J. Hebling et al., Opt. Express 10, 1161 (2002).

A nearly mono-cyclic THz pulse

New possibilities for rapid

controls of physical properties

in solids

carrier number

M. C. Hoffmann et al., PRB (2009)

H. Hirori et al., Nat. Commun. (2013)

e

e

Phonon exciton

magnon

I. Katayama et al., PRL (2012) H. Hirori et al.,

Phys. Rev. B (2010)

T. Kampfrath et al.,

Nature Photonics (2010)

superconducting

order parameter

R. Matsunaga, N. Tsuji, R. Shimano et al.,

Science (2014)

electro-magnon

Attempts to control solids by a nearly monocyclic strong THz pulse

T. Kubacka et al., Science (2014)

Polarization control by a terahertz field in electronic ferroelectrics

Paraelectric

(neutral)

maxETHz

415 kV/cm

a

b

c

TTFCA

Ferroelectric

(ionic)

P

neutral-ionic

transition

Tc=81K

TTF-CA

TTF (Donor : D)

S

S

S

S

CA (Acceptor : A)

O O

Cl

Cl

Cl

Cl

Coercive field is 5 kV/cm

for 100-Hz electric fields

Pvs E

Electric field E or ETHz

P

5 5200 400 kV/cm

Pvs ETHz

P/P 7%-1 0 1-0.1

0

0.1

-200

0

200

400

Delay time (ps)

= 1.3 eV2 = 2.6 eV

65 K

I S

HG

/ I S

HG

maxETHz

415 kV/cm

ETHz

P/P7%@ 400 kV/cm

Nature Commun. 4, 2586 (2013), Sci. Rep. 6, 20571 (2016), PRL 118, 107602 (2017)

Ferroelectric

P

P+P

’ ’ ’ ’ ’ ’

SHG 2ω

(2.6 eV)

THz pulse (400 kV/cm)

P

probe

ω (1.3 eV)

Terahertz-pump SHG-probe method

Filed-induced intermolecular charge transfers

Polarization control by a terahertz field in electronic ferroelectrics

insulator-metal transition

VO2

To achieve an ultrafast phase control in a sub-picosecond time scale

by a smaller electric field, focus on electronic phase transitions

without large structural changes.

A large structural change

・A terahertz electric field enhancedin a metamaterial resonator 2 MV/cm

・Slow dynamics >> 1 ps

M. Liu, R. Averitt, K.A. Nelson et al., Nature (2012)

Attempts to drive a phase transition by a strong THz pulse

Mott insulator Metal

To drive a MI to metal transition

by a lower electric field,

a narrow-gap Mott insulator

is advantageous.

T. Oka, Phys. Rev. B 86, 075148 (2012)

Theory ΔMott (eV) Eth (MV/cm)

ET-F2TCNQ 0.7 3

Sr2CuO3 1.5 9

ΔMott

Upper Hubbard band

Lower Hubbard bandETHz

Carrier generations

through quantum tunneling

(Zener tunneling)

A system with one electron per site (half-filled band)

Large U

Terahertz-field-induced Mott insulator to metal transition

Mott

insulatormetal

Anion

X

K. Kanoda, JPSJ 75, 051007 (2006)

ET

a

c

+0.5ET

(ET)2

X

A unit is an ET dimer.

The nominal valence

of each ET is 0.5.

A dimer has one hole.

2D half-filled band

Bandwidth

Insulator-metal transition in κ-(ET)2X

Anion

X

bulk On diamond

metal

K. Kanoda, JPSJ 75, 051007 (2006)

Bandwidth

Mott

insulator

d-Br

-(ET)2Cu[N(CN)2]Br

diamond

d-Br 0.6 m

Suda,

Yamamoto

(IMS)

bulk

0 0.2 0.4 0.6 0.8

0

1

2

3

4

E // c

OD

Photon Energy (eV)

bulk

metal

insulator

on diamond

10 K


Absorption (OD: optical density) spectra

0 0.2 0.4 0.6 0.8

0

1

2

3

4

E // c

OD

Photon Energy (eV)

bulk

metal

insulator

on diamond

10 K

-2 -1 0 1 2

-100

0

100

200

Time (ps)

ET

Hz

(kV

/cm

)

THz pulse

The sample is completely transparent

for the THz pulse.

No carriers are excited beyond the gap.


Absorption (OD: optical density) spectra

diamond

d-Br 0.6 m

Suda,

Yamamoto

(IMS)

Terahertz-pump

optical-absorption-probe

spectroscopy

OD

Frequency (THz)

Photon Energy (eV)

Mott gap

Mott30 meV

insulator

on diamond

0.001 0.01 0.1 1

0

1

2

3

40.1 1 10 100

THz pump (180 kV/cm)

ΔO

DO

D

E // c

10 K

Insulator on diamond

Photon Energy (eV)

td = 0.7 ps

0

1

2

3

4

0 0.2 0.4 0.6 0.8

-0.05

0

0.05

0.1

0.15

Metal (bulk)

(ODmetalODMott)

×0.11

THz-pump optical-absorption-probe spectroscopy (180kV/cm)

Delay Time (ps)

ΔO

D

0.124 eV

0.14 eV

0.16 eV

0.273 eV

0.36 eV

0.65 eV

E // c

0 5 10

0

0.05

0.1

-2 -1 0 1 2

-100

0

100

200

ET

Hz

(kV

/cm

)

Delay Time (ps)

THzpulseETHz

10

-4 (E

TH

z)2

(kV

2/c

m2)

0.7 ps

(Eth)2

0

1

2

3

4

Electric-field-induced

Mott-insulator to metal transition

(the carrier density 0.055/dimer)

THz pump (180 kV/cm)

ΔO

DO

D

E // c

10 K

Insulator on diamond

Photon Energy (eV)

td = 0.7 ps

0

1

2

3

4

0 0.2 0.4 0.6 0.8

-0.05

0

0.05

0.1

0.15

Metal (bulk)

THz electric-field dependence of absorption changes in IR region

-2 -1 0 1 2 3 4

0

0.05

0.1

ΔO

D

Delay Time (ps)

180 kV/cm147 kV/cm120 kV/cm


td = 0 ps

0 50 100 150 2000

0.02

0.04

0.06

ETHz (kV/cm)

ΔO

D

td = 0 ps


-2 -1 0 1 2 3 4

0

0.05

0.1

ΔO

D

Delay Time (ps)



td = 0 ps

ΔO

D

ETHzexp(π Eth/ETHz)⇔ OD

Probability of quantum tunneling

The I-M transition is driven bycarrier generations via the

quantum tunneling mechanism.

T. Oka, Phys. Rev. B 86, 075148 (2012)

ETHz (kV/cm)

td = 0 ps

0 50 100 150 2000

0.02

0.04

0.06ETHzexp(πEth /ETHz)

Eth=64 kV/cm

ΔMott

Upper Hubbard band

Lower Hubbard band

ξ

ETHz

Carrier generation via quantum tunneling


-2 -1 0 1 2 3 4

0

0.05

0.1

ΔO

D

Delay Time (ps)



td = 0 ps

ETHz (kV/cm)

td = 0 ps

0 50 100 150 2000

0.02

0.04

0.06

td = 0.7 ps

td = 0.7 ps

40 100 2000.0001

0.001

0.01

0.1

ETHz (kV/cm)

ΔO

D

td = 0 ps

td = 0.7 ps

ΔO

D

ΔMott

Upper Hubbard band

Lower Hubbard band

ξ

ETHz


ETHz exp(π Eth / ETHz)

Eth=64 kV/cm

0

0.05

0.1

-0.4 -0.2 0 0.2 0.4 0.6

0

0.001

0.002


ΔMott

Upper Hubbard band

Lower Hubbard band

ξ

ETHz


Mott transition

180 kV/cm

ΔO

DΔ

OD

Rise time:

0 ps

45 kV/cm

(×45)Rise time:

0.13 ps

Delay Time (ps)

|ETHz|exp(π Eth/|ETHz|)

0.13 ps

0.13 ps

Rise time 0.13 ps

is the characteristic

time of the Mott

transition.

40 100 2000.0001

0.001

0.01

0.1

ETHz (kV/cm)

ΔO

D

td = 0 ps

td = 0.7 ps

ETHz exp(π Eth / ETHz)

Eth=64 kV/cm

Mott transition


ΔMott

Upper Hubbard band

Lower Hubbard band

ξ

ETHz


Mott transition

180 kV/cm

ΔO

DΔ

OD

Rise time:

0 ps

45 kV/cm

(×45)Rise time:

0.13 ps

Delay Time (ps)

|ETHz|exp(π Eth/|ETHz|)

0.13 ps

a

c t

t

t = 78 meV⇔ 0.051 ps

t’ = 33 meV⇔ 0.12 ps

t '

0.13 ps

0

0.05

0.1

-0.4 -0.2 0 0.2 0.4 0.6

0

0.001

0.002

D. Faltermeier et al., PRB 76, 165113 (2007).

Rise time 0.13 ps

is the characteristic

time of the Mott

transition.

170 kV/cm

ΔO

D

ΔO

Do

sc

THz pulse exc.

Inte

nsity

THz pulse exc.

ETHz2

0.124 eV

28

cm-1

37

cm-146

cm-1

a

c


0

0.05

0.1

0

0.1

0.2

0.3

0.4

-0.01

0

0.01

Delay Time (ps) Wavenumber (cm-1)Delay Time (ps)0 2 4 6 0 20 40 600 5 10

Analyses of the coherent oscillations on the absorption changes

Metal (lattice relaxed)

0.13 ps 0.5 ps

Molecular displacements increase U on

each dimer and stabilize the Mott phase.Releases of molecular displacements

stabilizing the Mott insulator state


ETHz

ΔMott

Upper Hubbard band

Lower Hubbard band

ξ

Impulsive

dielectric

breakdown

Mott

transition

td = 0.7 ps

0 0.2 0.4 0.6 0.8

-0.05

0

0.05

0.1

0.15

ΔO

D

Photon energy (eV)

THz pulse (180 kV/cm)κ-(ET)2Cu2(N(CN)2)Br

Summary : the electric-field-induced Mott-insulator to metal transition

Terahertz-pump optical-probe spectroscopy

on κ-(ET)2Cu2(N(CN)2)Br

・ A characteristic time for the electronic state changes in the Mott transition is evaluated

to be 0.1 ps.

・ Electric-field-induced carrier generationsby an impulsive dielectric breakdown and

a subsequent Mott transition are detected.

○ Terahertz-electric-field-induced

Mott insulator to metal transition

Dielectric breakdown mechanism


○ Photoinduced Mott insulator to metal

transition

Probing of ultrafast spin dynamics

coupled with charge excitations

T. Miyamoto et al., in preparation

THz

pulse

Cu

O

7 fs

pulse

ET

py(O)

px(O)

dx2-y2 (Cu)

Cu2+ :d 9

unpaired electron in dx2-y2

Cu 3d

Cu2+

dx2-y2

Mott insulator

U

Cu 3d

Cu 3d

Coulomb

Repulsion

U

On-site Coulomb repulsion

U

Electronic structure of undoped cuprate Nd2CuO4 (NCO)

Nd2CuO4(NCO)

:Cu

:O

:Nd

:Cu

:O

:La

Mott insulatorInjection of

electron and hole carriers

(doublons and holons)

Metal

Ultrafast photoinduced Mott-insulator to metal transition

:Cu

:O

:Nd

:Cu

:O

:La

Nd2CuO4

ab

c


H. Okamoto et al., PRB 82, 060513R (2010), PRB 83, 125102 (2011).

Photoinduced Mott-insulator to metal transition in Nd2CuO4 (180 fs res.)

Photon energy (eV)

Norm

aliz

ed

OD


0 0.5 1.00

1

20.1 ps

5.0 ps (x 50)2.0 ps (x 14.5)

Midgap absorption

Drude

component

Low-energy spectra (normalized)



Charge dynamics in half-filled 2D Mott insulators with large U

Introduction of carriers produces midgap

absorption (incoherent part).

spin-charge coupling

holon

Energy

Energy

Incoherent part

Drude comp.

Small carrierdensity

Intermediate carrier density

ex. LSCO, NCCO

low carrier density

Drude weight is small as compared to

the incoherent part.S. Uchida et al., PRB 43, 7942 (1991)

Y. Onose et al., PRB 69, 024504 (2004)ex. E. Dagotto Rev. Mod. Phys. 66, 763 (1994)

spin-charge coupling

doublon

Energy

Energy

Incoherent part

Drude comp.



ex. LSCO, NCCODrude weight is small as compared to

the incoherent part.

Introduction of carriers produces midgap

absorption (incoherent part).

Charge dynamics in half-filled 2D Mott insulators with large U

low carrier density

S. Uchida et al., PRB 43, 7942 (1991)

Y. Onose et al., PRB 69, 024504 (2004)ex. E. Dagotto Rev. Mod. Phys. 66, 763 (1994)

doublonholon

Photon energy (eV)

Norm

aliz

ed

OD

Midgap absorption

0 0.5 1.00

1

20.1 ps

5.0 ps (x 50)2.0 ps (x 14.5)

Drude

component

Low-energy spectra (normalized)



Mid-gap state Mott insulator Metal

h

d

Pump-probe experiments with the time resolution of 10 fs

t

7 fs

pump

probesample

photo-detector

Pulse width 7 fs

Delay Time (fs)

Inte

nsity

-20 -10 0 10 20

0

1

Cross correlation profile

FWHM10 fs

○ 7 fs pulse is divided to two beams.→ a pump and a probe pulse

Reflection-type pump-probe system

using 7 fs pulses generated from

a non-collinear OPA

Pulse width 7 fs

Delay Time (fs)

Inte

nsity

-20 -10 0 10 20

0

1

Cross correlation profile

FWHM10 fs

○ 7 fs pulse is divided to two beams.→ a pump and a probe pulse

○ The spectral weight transfer between the Mott gap transition and the low

energy components occurs.

Time evolutions of bleaching signals

→ dynamics of photoexcited states

1 2 30

0.1

0.2

0.3

0

0.5

1

1.5

Photon Energy (eV)

Re

fle

ctivity

103

(S/c

m)

Nd2CuO4

7 fspulse

Energy

Midgapabs.

Drudecomp.

Pump-probe experiments with the time resolution of 10 fs

ΔR

/R

-100

-0.2

-0.1

0

Iex (ph/Cu)

Delay time (fs)

-50 0 50

0.0016

0.0032

0.0049

0.0065

0.0081

0.012

0.016

0.024

0.032

0.049

0.065

0.079

100

Iex (ph/Cu)

Perturbed free induction decay of probe-pulse-induced polarization C.H. Brito Cruz et. al., IEEE J. Quantum Electron. 24 261 (1988)

Response function

Time evolutions of bleaching signals at various excitation photon density

Iex (ph/Cu)

Delay time (fs)

-100 -50 0 50

-0.2

-0.1

0

0.0016

0.0032

0.0049

0.0065

0.0081

0.012

0.016

0.024

0.032

0.049

0.065

0.079

100

Iex (ph/Cu)

Low photon density 0.003 ph/Cu

High photon density 0.079 ph/Cu

Excitation photon density dependence of bleaching signals in Nd2CuO4Δ

R/R

ΔR

/R

Delay time (fs)-100 0 100

-0.02

-0.01

0

ΔR

/R


-0.2

-0.1

0

20 fs

10 fs

10 fs



ΔR

/R


-0.02

-0.01

0

ΔR

/R


-0.2

-0.1

0

Excitation photon density dependence of bleaching signals in Nd2CuO4

Energy

Energy

Incoherent part

Drude comp.



ex. LSCO, NCCO

low carrier density

Mid-gap

absorption

Mid-gap

absorption

Drude

component

Mid-gap

absorption

Chemical carrier doping

20 fs

ΔR

/R


-0.2

-0.1

0

ΔR

/R


-0.02

-0.01

0




Mid-gap

absorption

Drude

component

Mid-gap

absorption

∆𝑅

𝑅= 𝐴1 + 𝐴2 1 − exp −

𝑡

𝜏𝑟exp −

𝑡

𝜏1

∆𝑅

𝑅= 𝐴1 + 𝐴2 1 − exp −

𝑡

𝜏𝑟exp −

𝑡

𝜏1

Midgap absorption

+ 𝐴3exp −𝑡

𝜏2

Midgap absorption

Drude component

slow rise 18 fs

11 fs


Time scale of phonon : ħ 500 cm-1 ⇔ 60 fsTime scale of spin : J 0.13 eV ⇔ 30 fs

18 fs

Spin relaxation

11 fs

Decay of Metallic (Drude) component

ΔR

/R


-0.2

-0.1

0

ΔR

/R


-0.02

-0.01

0



Mid-gap

absorption

Drude

component

Mid-gap

absorption

18 fs

11 fs

Charge-spin coupling

0 0.02 0.04 0.06 0.080

10

20

30

40

Excitation photon density xph (ph/Cu)

Decay t

ime

(fs

)

Strong e-e interaction

Decrease in the decay time

of Drude component

Auger recombination of carriers

Drude comp.

Excitation photon density dependence of the Drude component

Excitation photon density xph (ph/Cu)

Δ

R/R

(A1

A2, A

3)

Drude comp.

0 0.02 0.04 0.06 0.080

0.1

0.2 Midgap absorption(spin-relaxed)

Amplitude Decay time

Threshold behavior

of the Drude component

Localization of carriers

0

1

2

0

1

2

0

1

2

0

1

2

0 0.2 0.40

1

2

-100 0 100 200

-14

-12

-10

-8

-6

-4

-2

0

1.5 20

0.5

1

0

0.1

0.2

0.3

0.4

-1

0

1

-1

0

1

-4

0

4

-4

0

4

0 80 160-1

0

1

1.80 eV

1.88 eV

1.94 eV

2.03 eV

2.10 eV

Delay time (fs)

10

2Δ

R/R

0.008 ph/Cu

probe

energy

SampleProbe Pulse

Photo-

Detector

Bandpass

Filter

1.5 20

0.5

1

Pulse

Photon Energy (eV)

294 K

103

(S/c

m)

Probe energy dependence

0

1

2

0

1

2

0

1

2

0

1

2

0 0.2 0.40

1

2

-100 0 100 200

-14

-12

-10

-8

-6

-4

-2

0

1.5 20

0.5

1

0

0.1

0.2

0.3

0.4

-1

0

1

-1

0

1

-4

0

4

-4

0

4

0 80 160-1

0

1

Fourier

Pow

er

Spectr

a (

arb

. units)

2.03 eV

1.94 eV

1.88 eV

1.80 eV

1.80 eV

1.88 eV

1.94 eV

2.03 eV

2.10 eV

Delay time (fs)

10

2Δ

R/R

0.008 ph/Cu

Delay time (fs)

10

3Δ

R/R

1.80 eV

1.88 eV

1.94 eV

2.03 eV

2.10 eV

Coherent oscillations

Oscillation energy EOSC (eV)

probe

energy

2.10 eV

Probe

2758

cm-1

2339

cm-1

2758

cm-1

1597

cm-1

789

cm-1

0 0.1 0.2 0.3 0.4 0.50

0.1

0.2

0.3

0.4

Momentum q

En

erg

y (

eV

)

K. Ishii et al.,

Nat. Commun.

5, 3714 (2014).

2. EOSC is very high.

8002800 cm-1

Optical phonon:

・large dispersion・large energy

magnon:

0

1

2

0

1

2

0

1

2

0

1

2

0 0.2 0.40

1

2

-100 0 100 200

-14

-12

-10

-8

-6

-4

-2

0

1.5 20

0.5

1

0

0.1

0.2

0.3

0.4

-1

0

1

-1

0

1

-4

0

4

-4

0

4

0 80 160-1

0

1

2.03 eV

1.94 eV

1.88 eV

1.80 eV

Oscillation energy EOSC (eV)Delay time (fs)

10

3Δ

R/R

1.80 eV

1.88 eV

1.94 eV

2.03 eV

2.10 eV


2.10 eV

Probe 1. EOSC depends on

the probe energy.

(large dispersion)

・small energy

Characteristics

・no dispersion

Fourier

Pow

er

Spectr

a (

arb

. units)

Inelastic X-ray

scattering

2758

cm-1

2339

cm-1

2758

cm-1

1597

cm-1

789

cm-1

0

1000

2000

3000

-100 0 100 200

-14

-12

-10

-8

-6

-4

-2

0

1.5 20

0.5

1

0

0.1

0.2

0.3

0.4

Probe energy ℏprobe (eV)

103

(S/c

m)

EO

SC

(eV

)

EOSC ℏprobe ℏg

Raman Scattering：Y. Tokura et al.

PRB 41, 11657 (1990).

2-magnon excitation


2ℏ𝜔𝑘

q

energy

/2 /2

Magnon

dispersion

ℏ𝜔𝑘

k k

ℏg

2-magnon

sideband

ℏg

ℏr (eV)

(a

rb .

unit)

0

0.5

1

0

0.5

1

0

0.5

1

0

0.5

1

0 0.2 0.40

0.5

1

-100 0 100 200

-14

-12

-10

-8

-6

-4

-2

0

1.5 20

0.5

1

0

0.1

0.2

0.3

0.4

EO

SC

(cm

-1)

The oscillations

may be related to

the emission

of two magnons.

EOSC 2ℏk

Raman spectra of cuprates

-100 0 100 200

-14

-12

-10

-8

-6

-4

-2

0

1.5 20

0.5

1

0

0.1

0.2

0.3

0.4


103

(S/c

m)

EO

SC

(eV

)

EOSC ℏprobe ℏg

ℏg

2-magnon

sideband

ℏg

ℏr (eV)

(a

rb .

unit)

0

0.5

1

0

0.5

1

0

0.5

1

0

0.5

1

0 0.2 0.40

0.5

1

-100 0 100 200

-14

-12

-10

-8

-6

-4

-2

0

1.5 20

0.5

1

0

0.1

0.2

0.3

0.4

A probe pulse causes a transition to

| 2, 𝑘 : two D-H pairs + 2magnons

2D-H+2mag.| 2, 𝑘

D-H+2mag.| 1, 𝑘

D-H | 1, 0

G.S.| 0, 0

pump probe

interference

2ℏ𝜔𝑘

A pump pulse produces two states;

| 1, 0 : a D-H pair| 1, 𝑘 : a D-H pair + 2magnons

A possible mechanism of coherent oscillations (S. Ishihara et al.)

These two transitions can interfere

with each other.

A coherent oscillation with

2ℏk (2magnon frequency).

via the two transition paths

| 1, 0 + “a D-H pair + 2magnons”| 1, 𝑘 + “a D-H pair”.

D-H pair excitation One mode of two magnon (2ℏ𝜔𝑘)

𝐻0 = ℏ𝜔g𝑋†𝑋 +

𝑖=𝑘,𝑞

ℏ𝜔𝑖𝑏𝑖† 𝑏𝑖

holon-doublon pair magnon

・Hamiltonian

・Electronic and spin state: | 𝑁, 𝑘 and | 𝑁, 𝑞

𝑁 : 𝑁 holon-doublon pair excitations

𝑘 : a two-magnon excitation with a frequency of 2ℏ𝜔𝑘

𝑞 : a two-magnon excitation with a frequency of 2ℏ𝜔𝑞

𝐻′ = 𝐴𝜔g𝑋† + 𝑔

𝑖=𝑘,𝑞

𝐴𝜔g+2𝜔𝑖𝑋†𝑏𝑖

†𝑏−𝑖† + 𝐻. 𝑐.

・Interactions with photons

𝐴𝜔： the vector potential with frequency

magnon sidebandMott gap transition

(2ℏ𝜔𝑘 < 2ℏ𝜔𝑞)-100 0 100 200

-14

-12

-10

-8

-6

-4

-2

0

1.5 20

0.5

1

0

0.1

0.2

0.3

0.4

ℏprobe (eV)

103

(S/c

m)

EO

SC

(e

V)

EOSC ℏprobe ℏg

ℏg

2-magnon

sideband

ℏg

(a

rb .

unit)

0

0.5

1

0

0.5

1

0

0.5

1

0

0.5

1

0 0.2 0.40

0.5

1

-100 0 100 200

-14

-12

-10

-8

-6

-4

-2

0

1.5 20

0.5

1

0

0.1

0.2

0.3

0.4

2ℏ𝜔𝑘

D-H

| 1, 0ℏ𝜔g

(a

rb .

unit)

ℏprobe (eV)

2ℏ𝜔𝑞

D-H + 2magnons

| 1, 𝑘

| 1, 𝑞

Magnon

sideband

A possible mechanism of coherent oscillations (S. Ishihara et al.)

・ The expectation value of electronic current

・ Three excited states | 1, 0 , | 1, 𝑘 and | 1, 𝑞are simultaneously generated at 𝑡 = 0by a broadband pump pulse.

𝑗 𝑡 = 𝛹 𝑡 𝑗 𝛹 𝑡 ~ 0

𝑡

𝑑𝑡’𝐹 𝑡′

𝐹 𝑡′ = 𝐹0 𝑡′

+ sin 𝜔g + 2𝜔k 𝑡 − 𝜔g𝑡′ 𝐴𝜔g

′ 𝑡′

+𝑤k sin 𝜔g𝑡 − 𝜔g + 2𝜔k 𝑡′ 𝐴𝜔g+2𝜔k

′ 𝑡′

+𝑤q sin 𝜔g𝑡 − 𝜔g + 2𝜔q 𝑡′ 𝐴𝜔g+2𝜔q

′ 𝑡′

+ sin 𝜔g + 2𝜔q 𝑡 − 𝜔g𝑡′ 𝐴𝜔g

′ 𝑡′

Interference of constituent terms

trivial term

A simplified model of coherent oscillations (S. Ishihara et al.)

-100 0 100 200

-14

-12

-10

-8

-6

-4

-2

0

1.5 20

0.5

1

0

0.1

0.2

0.3

0.4

ℏprobe (eV)

103

(S/c

m)

EO

SC

(e

V)

EOSC ℏprobe ℏg

ℏg

2-magnon

sideband

ℏg

(a

rb .

unit)

0

0.5

1

0

0.5

1

0

0.5

1

0

0.5

1

0 0.2 0.40

0.5

1

-100 0 100 200

-14

-12

-10

-8

-6

-4

-2

0

1.5 20

0.5

1

0

0.1

0.2

0.3

0.4

2ℏ𝜔𝑘

D-H

| 1, 0ℏ𝜔g

(a

rb .

unit)

ℏprobe (eV)

2ℏ𝜔𝑞

D-H + 2magnons

| 1, 𝑘

| 1, 𝑞

Magnon

sideband

𝜔probe = 𝜔g + 2𝜔𝑘 𝜔probe = 𝜔g + 2𝜔𝑞

0 20 40 60 80

-2

-1

0

1

2

0 20 40 60 80

-2

-1

0

1

2

0 1 2 30

0.5

1

0 1 2 30

0.5

1

wk term

wq term

Delay Time t

Pow

er

Spectr

a

Frequency

Curr

ent j

Delay Time t

Frequency

2𝜔𝑘

wk term

wq term

wkterm wq

term

wkterm

wqterm

2𝜔𝑘2𝜔𝑞

2𝜔𝑞Intensity near 2𝜔𝑘(2𝜔𝑞)

is larger at

ℏ𝜔probe = ℏ𝜔g+2ℏ𝜔𝑘(ℏ𝜔probe = ℏ𝜔g + 2ℏ𝜔𝑞).

(a

rb .u

nit)

ℏprobe (eV)

(a

rb .u

nit)

ℏprobe (eV)

| 1, 𝑘 state | 1, 𝑞 state

A simplified model of coherent oscillations (S. Ishihara et al.)

Pump-probe spectroscopy with the

time resolution of 10 fs on Nd2CuO4

・ Frequency of the coherent oscillations depends on the probe energy.

Strong coupling of charge and spin degrees of freedom in a 2D Mott insulator

Summary : the photoinduced Mott-insulator to metal transition

Theoretical calculation

・ Quantum interference of the optical transitions between

charge-spin coupled excited states

doublon

holon

・ Spin-relaxation time in magnetic-polaron formations 18 fs

-100 0 100 200

-14

-12

-10

-8

-6

-4

-2

0

1.5 20

0.5

1

0

0.1

0.2

0.3

0.4


103

(S/c

m)

EO

SC

2ℏ

k(e

V)

2-magnon

sideband

ℏCT

ℏprobe (eV)

(a

rb .u

nit)

0

0.5

1

0

0.5

1

0

0.5

1

0

0.5

1

0 0.2 0.40

0.5

1

-100 0 100 200

-14

-12

-10

-8

-6

-4

-2

0

1.5 20

0.5

1

0

0.1

0.2

0.3

0.4

EOSC ℏprobe ℏg

18 fs

18 fs

nonlinear and ultrafast responses in mott insulators · 2018. 11. 15. · nonlinear and ultrafast...

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