Dynamical phase transitions in the photodriven
charge-ordered Dirac-electron system
Yasuhiro Tanaka
Math. and Science Education Research Center,
Kanazawa Institute of Technology

Masahito Mochizuki
Department of Applied Physics, Waseda University
YT and M. Mochizuki, Phys. Rev. B 104, 085123 (2021)
YT and M. Mochizuki, Phys. Rev. Lett. 129, 047402 (2022)

Outline
1. Introduction
Photoinduced phase transitions
Physical properties of a-(BEDT-TTF)2I3
2. Model and Method
Interacting Dirac electron system
Time dependent Schödinger eq. + Floquet theory
3. Results
Successive dynamical phase transitions

4. Summary

Photoinduced Insulator to Metal transition

Correlated electron systems

Mott insulator(Charge Ordered Insulator)

Photoinduced Metallic State

S. Iwai, Crystals 2, 590 (2012)
K. Yonemitsu and K. Nasu, Phys. Rep. 465, 1 (2008)
H. Aoki et al., Rev. Mod. Phys. 86, 779 (2014)

Photoinduced topological phase transition
Floquet Chern insulator

Dirac fermion system
Irradiation withcircularly polarized light

Topologicalgap

Floquet theory
T. Oka and H. Aoki, Phys. Rev. B 79, 081406(R) (2009)
T. Kitagawa et al., Phys. Rev. B 84, 235108 (2011)

Light-induced anomalous Hall effect in graphene
J. W. McIver et al., Nat. Phys. 16, 38 (2020)
S. A. Sato et al., Phys. Rev. B 99, 214302 (2019)

Interacting Dirac fermion systems (honeycomb lattice)

S. Sorella, Y. Otsuka, and S. Yunoki, Sci. Rep. 2, 992 (2012)
S. Raghu et al., Phys. Rev. Lett. 100, 156401 (2008)

Photoirradaition to interacting Dirac fermion system ?
a-(BEDT-TTF)2I3 : Correlated Dirac fermion system with charge orderPhysical properties of a-(BEDT-TTF)2I3

Crystal structureCharge order➢ quasi-2d structure➢ 3/4-filling➢ 1st order transition TCO=135 K➢ Spin gap (nonmagnetic) below TCO(1 hole/2 molecules)

TCO

N. Tajima, et al.
J. Phys Soc. Jpn. 75, 051010 (2006)

Dirac semimetal phase under pressure
CO → Dirac semimetal (DS)DS
➢ P-T phase diagram

CODS

S. Katayama, et al., J. Phys. Soc. Jpn. 75, 054705 (2006)
D. Liu et al., Phys. Rev. Lett. 116, 226401 (2016)
N. Tajima, et al., J. Phys Soc. Jpn. 75, 051010 (2006)

Photoinduced melting of charge orderphotoexcitationFemtosecond Pump-probe spectroscopy
S. Iwai, et al., Phys. Rev. Lett. 98, 097402 (2007)

Theories for photodriven a-(BEDT-TTF)2I3 : CO melting• Interacting model (Extended Hubbard model)• Linearly polarized lightmelting of CO by photoexcitation• Time-dependent Schrödinger eq.

CA
B

A’

Hartree-Fock appr.
YT and K. Yonemitsu, J. Phys. Soc. Jpn. 79, 024712 (2010)

Exact diagonalization
S. Miyashita, YT, S. Iwai, and K. Yonemitsu, J. Phys. Soc. Jpn. 79, 034708 (2010)

Theories for photodriven a-(BEDT-TTF)2I3 : DS phase• Noninteracting model + Floquet theory➢ Circularly polarized light

K. Kitayama and M. Mochizuki, Phys. Rev. Res. 2, 023229 (2020)
K. Kitayama, YT, M. Ogata, and M. Mochizuki, J. Phys. Soc. Jpn. 90, 104705 (2021)

Photoinduced topological phase transition➢ Linearly polarized light

K. Kitayama, M. Mochizuki, YT, and M. Ogata, Phys. Rev. B 104, 075127 (2021)

Photoinduced pair annihilation of magnetic charges➢ Elliptically polarized light

K. Kitayama, M. Ogata, M. Mochizuki, and YT, J. Phys. Soc. Jpn. 91, 104704 (2022)

Collision and Collapse of the Dirac cones

Theories for photodriven a-(BEDT-TTF)2I3 : DS phase• Noninteracting model + time dependent Schrödinger eq.

➢ DS

Floquet Chern ins. (Circularly polarized light)

Transient spectra, Hall conductivity

CO

YT and M. Mochizuki, Phys. Rev. B 104, 085123 (2021)

DS

At ambient pressure, CO appears
CODS ?
COFloquet Chern insulator ?

Interacting model + CPL

Model and Method
Hamiltonian

H. Kino and H. Fukuyama, J. Phys. Soc. Jpn. 64, 1877 (1995)
H. Seo, J. Phys. Soc. Jpn. 69, 805 (2000)

Interaction terms

Hartree-Fock approximation

Transfer integrals
b1=0.127(eV), b2=0.145, b3=0.062, b4=0.025
a1=-0.035, a2=-0.046, a3 =0.018

ab

A. Kobayashi et al., J. Phys. Soc. Jpn. 73, 3135 (2004)

Time evolution (Time-dependent Schrodinger eq.)
Photoexcitation : Peierls phase: Vector potential for circularly polarized light

A. Terai and Y. Ono, Prog. Theor. Phys. Suppl. 113, 177 (1993)
M. Kuwabara and Y. Ono, J. Phys. Soc. Jpn. 64, 2106 (1995)

Parameters➢ HF solutions• horizontal CO with no spin order• DS (no CO)

DSCO

Energy difference
CCO gap

A

B

A'=

=
Initial state before the photoexcitation

Parameters➢ Pump pulse➢ Light frequency :Pulse width :Pulse center :➢ Spectral function :J. K. Freericks et al., Phys. Rev. Lett. 102, 136401 (2009)
M. A. Sentef et al., Nat. Commun. 6, 7047 (2015)

Floquet theory (noninteracting model)
K. Kitayama and M. Mochizuki, Phys. Rev. Res. 2, 023229 (2020)

Probe pulse:
Pulse width :Pulse center :Transient band and time evolution of electron density

CO gap > 0

CO melting

DS band➢ Floquet theory
K. Kitayama and M. Mochizuki,Phys. Rev. Res. (2020)➢ Real-time dynamics

Topologicalgap opens

YT and M. Mochizuki,
Phys. Rev. B (2021)

YT and M. Mochizuki, Phys. Rev. Lett. 129, 047402 (2022)

Slow oscillation of charge densities
slow-oscillation components ofandthe same oscillation centers
A and A’ sites are equivalentoscillation centers slightly differ between
andA and A’ sites are NOT equivalentFloquet theory➢ Floquet theorem

K. Kitagawa et al., Phys. Rev. B 82, 235114 (2010)
M. Burkov et al., Adv. Phys. 64, 139 (2015)

time-periodic Hamiltonian: Floquet state

FFT with respect to time

Static eigenvalue equation

Floquet analysis with mean-field order parameters➢ time profiles of mean-field order parameters
FFT within a time domainaround the pulse centerin our mean-field treatment: n-th Bessel’s function

Chern number :T. Fukui et al., J. Phys. Soc. Jpn. 74, 1674 (2005)

Floquet bands and transient bands
2p00

Floquet bands
coincide with2p

w

E dependence of charge gap and Chern number

staggered site potential

andhoneycomb lattice+ staggerd sublattice potential Δ + CPL
L D’Alessio and M. Rigol, Nat. Commun. 6. 8336 (2014)

Floquet theory

Time evolution of transient bands

YT and M. Mochizuki, Phys. Rev. Lett. 129, 047402 (2022)

Summary
Melting of CO and topological phase transition induced bycircularly polarized light in organic conductor a-(BEDT-TTF)2I3➢ Combined method of numerical simulation based on time-dependent
Schrodinger eq. and Floquet theory➢ Transient spectral function and time evolution of electron densities
Effects of CPL
Closing the charge gap through melting the CO
Opening the topological gap at the Dirac point

Successive dynamical phase transitions
CO melting

gapless DF band

Floquet Chern ins.

YT and M. Mochizuki, Phys. Rev. Lett. 129, 047402 (2022)