Shunsuke A. Sato, Angel Rubio, arXiv:2310.08875 [cond-mat.mtrl-sci]

Limitations of time-dependent mean-field approximations
to second-order nonlinear optical phenomena
Shunsuke A. Sato
Center for Computational Sciences, University of Tsukuba

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Introduction
Strong field physics (including attosecond physics)
Intense and short laser pulses induce nonlinear ultrafast phenomena in solids.
Opt-electronic device (PetaHertz electronics)

T. Higuchi, et al, Nature 550,224 (2017)

Our research aim- To understand the microscopic mechanism of such strongly-nonlinear ultrafast phenomena in solids.
- For this aim, we employ the first-principles calculation based ontime-dependent density functional theory (TDDFT).
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Lowest order nonlinear current injection
Second-order nonlinear optical
Second-order nonlinear polarization (time-domain)

Second-order nonlinear polarization (frequency domain)

Second-order susceptibility (Low frequency response limit; 𝜔Σ = 𝜔′ + 𝜔′′ → 0)
J. E. Sipe et al., PRB 61, 5337 (2000)

Optical rectification(光整流効果)

Shift current(シフト電流)

Injection current
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Second-order nonlinear optical response in time domain
Current

Electric field

Polarization

Acceleration

Timetime
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Mean-field artifact?
Photo-induced current in BaTiO3
under linearly polarized light pulse

Current

Time• TDDFT (mean-field) calculations shows the residual current even after the irradiation of linearly polarized light.
• The residual DC current is classified as the injection current, and it is usually observed under circular/ellipticallypolarized light• The residual DC current indicates a breakdown of the time-reversal symmetry. Artifact?
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Perturbation analysis (Exact many-body Schrödinger eq.)
Many-body Schrödinger eq.

Perturbative expansion & eigen function expansion

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DC current after the pulse ends (with exact many-body TDSE)
We assume the laser-fields vanish after the time, 𝑡𝑓 :𝑨 𝑡 = 0 for 𝑡 > 𝑡𝑓

TimeAssuming the Hermiteness of the problem, we can analytically prove thatthe residual current is ZERO under linearly polarized light.
=> Exact many-body Schrodinger equation forbids the injection current
under linearly polarized light.
Shunsuke A. Sato, Angel Rubio, arXiv:2310.08875 [cond-mat.mtrl-sci]

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Mean-field artifact
Photo-induced current in BaTiO3Current

Time

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Injection current under circularly polarized light
Circularly polarized light

Mechanism of injection current

𝑬 𝑡 = 𝒆𝑥 𝐸𝑥 𝑡 + 𝒆𝑦 𝐸𝑦 𝑡
Conduction band

Energy−𝒌𝐸𝑥 𝑡

𝐸𝑦 𝑡

𝒌electron

𝐸𝑦 𝑡

𝐸𝑥 𝑡

Valence band

1. Circularly polarized lightcauses the quantum
interference between two
excitation paths.
2. Due to the interference,different photo-carrier
population can be created at𝒌 and −𝒌 points.
3. The population imbalancecauses the residual current.

hole

Bloch wave-vector,𝑘9/11

Injection current in the mean-field approximation
Linearly polarized light

Mechanism of injection current

𝑬 𝑡 = 𝒆𝑥 𝐸𝑥 𝑡
Conduction band

Energy−𝒌𝐸𝑥 𝑡

𝛿𝑣 𝑡𝒌electron

𝛿𝑣 𝑡

𝐸𝑥 𝑡

Valence band

Bloch wave-vector,𝑘hole

1. An excitation path caused by
the electric field is interferedwith a self-excitation path via
the induced field.
2. Due to the interference,different
photo-carrier
population can be created at
𝒌 and −𝒌 points.
3. The population imbalancecauses the residual current.

Spontaneous symmetry breaking?
The mean field spontaneously breaks
the time-reversal symmetry of thesystem via the self-excitation path.
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Conclusion

Shunsuke A. Sato, Angel Rubio, arXiv:2310.08875 [cond-mat.mtrl-sci]• We analyzed the shift-current (second-order nonlinear optical effect) for BaTiO3 from the TDDFT
calculation, and we found the injection current induced by linearly polarized light.
• We analyzed the exact many-body Schrodinger equation with perturbation theory, and we found thatthe generation of the injection current by linearly polarized light is forbidden. Hence, the abovefindings are mean-field artifacts.
• Further analysis clarified that the unphysical injection current in the mean-field theories aregenerated by the quantum interference opened via the self-excitation path through the timedependent mean-field.

Current

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