NQS2022, Nov.18 (Fri), 16:00-16:30 (JST) @Panasonic Hall, YITP

DC-driven Quantum Matter:
Electric Field, Normal Current, Supercurrent
Kazuaki Takasan

University of Tokyo

KT, M. Sato, Phys. Rev. B 100, 060408(R) (2019)
S. C. Furuya, KT, M. Sato, Phys. Rev. Res. 3, 033066 (2021)
KT, M. Tezuka, arXiv: 2111.03857
KT, T. Morimoto, J. Orenstein, J. E. Moore, Phys. Rev. B 104, L161202 (2021)
KT, S. Sumita, Y. Yanase, Phys. Rev. B 106, 014508 (2022)
S. Sumita, KT, J. Phys. Soc. Jpn. 91, 074703 (2022)

Collaborators
Masahiro Sato (Chiba U)
Magnetism

Shunsuke C. Furuya (U Tokyo)
Masaki Tezuka (Kyoto U)
Takahiro Morimoto (U Tokyo)

Optical response

Joseph Orenstein (UC Berkeley)
Joel E. Moore (UC Berkeley)

Superconductivity

Shuntaro Sumita (U Tokyo)

Youichi Yanase (Kyoto U)

02/21

Outline
Take-home message

DC-drive works as a good tool for controlling states of matter.
There is a rich physics of DC-driven quantum matter.

Introduction: AC-drive vs DC-drive, Why we study DC
Our studies about DC-driven quantum matter
1. Insulating magnets + DC electric field → Control magnetic interaction
2. Topological semimetals + DC electric current → Enhance optical responses

3. Superconductors + DC supercurrent → Topological phase transitions

Outlook, Summary

03/21

AC-drive control = Floquet engineering
Time-periodic (AC-driven) Hamiltonian

FloquettheoryEffective (static) Hamiltonian

𝐻 𝑡 = 𝐻(𝑡 + 𝑇)

𝐻 eff

Design driving protocol

Desired Hamiltonian

Topologically
non-trivial

Massless Dirac + Circularly pol. light

Massive Dirac (Chern ins.)

𝐻 𝑡 = [𝒌 − 𝑨 𝑡 ] ⋅ 𝝈

𝐻eff = 𝐻 0 + 𝑚eff(𝐴) 𝜎𝑧𝒌 = (𝑘𝑥 , 𝑘𝑦 , 0)Theory: Oka and Aoki, PRB(R) (2009)

𝑨 𝑡 = 𝐴 cos 𝜔𝑡, sin 𝜔𝑡, 0Experiment: McIver et al. Nat. Phys. (2020)04/21

AC-drive control = Floquet engineering
Topologically
non-trivial

Massless Dirac + Circularly pol. light

Massive Dirac (Chern ins.)

Add a new feature/functionality by external AC driveThis works as a good technique for realizing novel quantum states of matter
Chiral spin liquid

Classen et al. Nat. Comm. (2017); Kitamura et al. PRB (2017).

Topological SC

KT et al. PRB (2017); Chono, KT, Yanase PRB (2020).
*theoretical proposals

05/21

05/21AC-drive control = Floquet engineering
Topologically
non-trivial

Massless Dirac + Circularly pol. light

Massive Dirac (Chern ins.)

Add a new feature/functionality by external AC driveThis works as a good technique for realizing novel quantum states of matter
My question: Is AC drive necessary? Other external drive?
Engineering by “DC drive”
from AC/DC official website

06/21

Why DC drive?
There are reasons beyond just curiosity!

1. DC drive does NOT needsophisticated optical techniques
Time-resolved probe, Strong pump

Gedik and Vishik (2017)

McIver et al. Nat. Phys. (2020)

2. Developing techniques forgenerating a strong DC E-fieldTHz pulse, EDLT, STM-like devise, …
Kampfrath, et al. (2013)

3. Features not expected in thecase of AC drive

Birisi, et al. (2017)

Hsu, et al. (2016)

breakingfrom AC/DC official website inversion sym.

Our works: DC-driven quantum matter
Insulator

07/21

Theoretical proposals for controlling states of matter using DC drive

1. Insulating magnets + DC electric field → Control magnetic interaction
KT, M. Sato, Phys. Rev. B 100, 060408(R) (2019).
S. C. Furuya, KT, M. Sato, Phys. Rev. Res. 3, 033066 (2021).
KT, M. Tezuka, arXiv: 2111.03857

Metal

2. Topological semimetals + DC electric current → Enhance optical responses
KT, T. Morimoto, J. Orenstein, J. E. Moore, Phys. Rev. B 104, L161202 (2021).

3. Superconductors + DC supercurrent → Topological phase transitions
Supercond.

KT, S. Sumita, Y. Yanase, Phys. Rev. B 106, 014508 (2022).
S. Sumita, KT, J. Phys. Soc. Jpn. 91, 074703 (2022).

Our works show that DC drive also works as a good tool forcontrolling states of matter, like (beyond?) AC (Floquet) driveOur works: DC-driven quantum matter
Insulator

1. Insulating magnets + DC electric field → Control magnetic interaction
KT, M. Sato, Phys. Rev. B 100, 060408(R) (2019).
S. C. Furuya, KT, M. Sato, Phys. Rev. Res. 3, 033066 (2021).
KT, M. Tezuka, arXiv: 2111.03857

07/21

08/21

Magnetisim in Mott insulators (1D)

KT, M. Sato, Phys. Rev. B 100, 060408(R) (2019)

𝐻eff = ෍ 𝐽0 𝑺𝑖 ⋅ 𝑺𝑗⟨𝑖,𝑗⟩4𝑡ℎ2
𝐽0 =𝑈…

…
i.

energy cost

ii.

𝑈𝑈

09/21

Mott insulators + DC electric field (1D)

KT, M. Sato, Phys. Rev. B 100, 060408(R) (2019)

2𝑡ℎ2

𝐻eff = ෍ 𝐽eff 𝐸 𝑺𝑖 ⋅ 𝑺𝑗

2𝑡ℎ2
𝐽eff 𝐸 =+=𝑈−𝐸 𝑈−𝐸

⟨𝑖,𝑗⟩

𝐽0

𝐸 21−
𝑈

…

cf. Katsura et al. PRL (2007),
Eckstein et al. arXiv (2017).

𝐸i.

ii.

…
energy cost

𝑈+𝐸

𝑈−𝐸

breaking
inversion sym.

10/21

Mott insulators + DC electric field (General)

KT, M. Sato, Phys. Rev. B 100, 060408(R) (2019)

𝐻eff = ෍⟨𝑖,𝑗⟩

𝐽0𝑬 ⋅ 𝒓𝑖𝑗
1−𝑈𝑬2 𝑺(𝒓𝑖 ) ⋅ 𝑺(𝒓𝑗 )𝒓𝑖𝑗 ∥ 𝑬 → Enhance !

𝒓𝑗𝒓𝑖𝒓𝑖𝑗𝒓𝑖𝑗 ⊥ 𝑬 → No enhance

Spatial structure of the magnetic interaction can be controlled

Application: Control of dimensionality11/21

Control of dimensionality by DC E-field
AFM coupling is enhanced in E-field direction

1. Frustrated magnet

1D-like

120°spiral order

KT, M. Sato, Phys. Rev. B 100, 060408(R) (2019)

2. Quasi-1D magnets= Ensemble ofspin chains

2D-likeE ⊥ chain 2D-ness is enhanced
E || chain 1D-ness is enhanced

E || chainE ⊥ chain

Modulated spiralDC-field-induced Quantum spin liquid

DC-field-induced AFM order12/21

Recent development: Ferromagnetism
Ferromagnetism is alsoenhanced in a similar way

AFM-to-FM switch is possibleusing Wannier-Stark localization

S. C. Furuya, KT, M. Sato, PRR 3, 033066 (2021)

KT, M. Tezuka, arXiv: 2111.03857

Extension to superexchange mechanism
FM enhancement ∝ E (c.f. AFM ∝ E 2)

Extreme strong field induces localization→ Effective localized spin systems

AFMEFM

𝐽eff =𝐽0𝐸 21−𝑈UOur works: DC-driven quantum matter
Insulator

13/21

Theoretical proposals for controlling states of matter using DC drive

1. Insulating magnets + DC electric field → Control magnetic interaction
KT, M. Sato, Phys. Rev. B 100, 060408(R) (2019).
S. C. Furuya, KT, M. Sato, Phys. Rev. Res. 3, 033066 (2021).
KT, M. Tezuka, arXiv: 2111.03857

Metal

2. Topological semimetals + DC electric current → Enhance optical responses
KT, T. Morimoto, J. Orenstein, J. E. Moore, Phys. Rev. B 104, L161202 (2021).

3. Superconductors + DC supercurrent → Topological phase transitions
Supercond.

KT, S. Sumita, Y. Yanase, Phys. Rev. B 106, 014508 (2022).
S. Sumita, KT, J. Phys. Soc. Jpn. 91, 074703 (2022).

Our works show that DC drive also works as a good tool forcontrolling states of matter, like (beyond?) AC (Floquet) driveOur works: DC-driven quantum matter

13/21

Metal

2. Topological semimetals + DC electric current → Enhance optical responses
KT, T. Morimoto, J. Orenstein, J. E. Moore, Phys. Rev. B 104, L161202 (2021).

14/21Topological semimetals + DC electric current
cf.

Metal + DC electric field→ Nonequilibrium steady state w/ finite current

2𝑓
𝜕𝑓𝜕
𝑓 = 𝑓eq. + 𝜏𝐸𝑎+ 𝜏 2 𝐸𝑎 𝐸𝑏+⋯
𝜕𝑘𝑎𝜕𝑘𝑎 𝜕𝑘𝑏

𝑓(𝜀)

𝑓(𝜀)

Boltzmann equation + Relaxation time approximation𝑓 − 𝑓eq.
𝜕𝑓𝑑𝑓−𝑬 ⋅==−
𝜕𝒌𝑑𝑡 coll.
𝜏𝐻eff

𝑘2

𝑘1

breaking
inversion
𝑘1 sym.

Application : Current-induced nonlinear optical response

Application: Current-induced nonlinear optical response
Nonlinear response 𝑗 = 𝜎 (1) 𝐸 + 𝜎 (2) 𝐸 2 + 𝜎 (3) 𝐸 3 + ⋯Even order is prohibited under inversion symmetry
Break inv. sym. by current → Activate the even order responses

Ex: Second harmonic generation (SHG) 𝐸 2 → 𝑒 2𝑖𝜔𝑡
Dirac (Weyl) semimetal

Second order optical conductivity

Finite SHG response!
Very large!
e.g. Cd3As2, Co3Sn2S2

w/ inversion sym.

102-104 times larger
than typical ones

DC-driven topological SMs work as useful nonlinear optical materials
cf. HHG in DC-driven graphene, Kanega-san’s poster (B-1)

Our works: DC-driven quantum matter
Insulator

16/21

Theoretical proposals for controlling states of matter using DC drive

1. Insulating magnets + DC electric field → Control magnetic interaction
KT, M. Sato, Phys. Rev. B 100, 060408(R) (2019).
S. C. Furuya, KT, M. Sato, Phys. Rev. Res. 3, 033066 (2021).
KT, M. Tezuka, arXiv: 2111.03857

Metal

2. Topological semimetals + DC electric current → Enhance optical responses
KT, T. Morimoto, J. Orenstein, J. E. Moore, Phys. Rev. B 104, L161202 (2021).

3. Superconductors + DC supercurrent → Topological phase transitions
Supercond.

KT, S. Sumita, Y. Yanase, Phys. Rev. B 106, 014508 (2022).
S. Sumita, KT, J. Phys. Soc. Jpn. 91, 074703 (2022).

Our works show that DC drive also works as a good tool forcontrolling states of matter, like (beyond?) AC (Floquet) driveOur works: DC-driven quantum matter

3. Superconductors + DC supercurrent → Topological phase transitions
Supercond.

KT, S. Sumita, Y. Yanase, Phys. Rev. B 106, 014508 (2022).
S. Sumita, KT, J. Phys. Soc. Jpn. 91, 074703 (2022).

16/21

17/21Superconductors + DC supercurrent
Supercurrent is equilibrium current𝑓 𝜀 = Fermi dist.

Described as COM momentum of Cooper pairs
Mean-field Hamiltoniancf. 𝐻eff

Example: Kitaev chain (1D p-wave SC)
Bogoliubov spectrum becomes asymmetric!

breaking
inversion sym.

DC-current-induced topological superconductivity (2D)
KT, S. Sumita, Y. Yanase, Phys. Rev. B 106, 014508 (2022)
w/o supercurrent

2D D+p-wave SC with Rashba-Zeeman SOC

w/ supercurrent
Fully-gapped topological SC
is realized
Class D, characterized byChern number
Symmetry-protection is liftedDC-current-induced Weyl superconductivity (3D)

19/21

S. Sumita, KT, J. Phys. Soc. Jpn. 91, 074703 (2022)[Editor’s Choice, JPS Hot Topics]

3D

Higer-order SOC

Line node

Point node(Weyl SC)

Outlook: Experimentally-feasible proposal, Serious theory
Insulator + DC field

Metal + DC current

Superconductor + DC current

1. More experimentally-feasible proposals
find “tiny current makes a great change”, material-specific calculation

2. More serious theoretical treatments
Boltzmann → Keldysh, Q. master eq., Supercurrent → vortex dynamics, beyond m.f., and so on
Understanding of current-carrying nonequilibrium steady states is essential

It has just started. Many aspects are still remained to be explored !

Summary: DC-driven quantum matter

21/21

Insulating magnets+ DC electric field→ Control magnetic
interaction

Topological semimetals+ DC electric current→ Enhance opticalresponses

Superconductors+ DC supercurrent→ Topological phasetransitions

KT, M. Sato, Phys. Rev. B 100, 060408(R)(2019); S. C. Furuya, KT, M. Sato, Phys.
Rev. Res. 3, 033066 (2021); KT, M. Tezuka,
arXiv: 2111.03857

KT, T. Morimoto, J. Orenstein, J. E. Moore,
Phys. Rev. B 104, L161202 (2021).

KT, S. Sumita, Y. Yanase, Phys. Rev. B 106,014508 (2022); S. Sumita, KT, J. Phys. Soc.
Jpn. 91, 074703 (2022).

Kazuaki Takasan (University of Tokyo), E-mail: kazuaki.takasan@phys.s.u-tokyo.ac.jp, Feel free to contact me!