Anomalous Temperature Dependence of High-Harmonic Generation in Mott Insulators

Yuta Murakami, Kento Uchida, Akihisa Koga, Koichiro Tanaka, and Philipp Werner

Phys. Rev. Lett. 129, 157401 – Published 3 October 2022

Abstract

We reveal the crucial effect of strong spin-charge coupling on high-harmonic generation (HHG) in Mott insulators. In a system with antiferromagnetic correlations, the HHG signal is drastically enhanced with decreasing temperature, even though the gap increases and the production of charge carriers is suppressed. This anomalous behavior, which has also been observed in recent HHG experiments on ${Ca}_{2} {RuO}_{4}$ , originates from a cooperative effect between the spin-charge coupling and the thermal ensemble, as well as the strongly temperature-dependent coherence between charge carriers. We argue that the peculiar temperature dependence of HHG is a generic feature of Mott insulators, which can be controlled via the Coulomb interaction and dimensionality of the system. Our results demonstrate that correlations between different degrees of freedom, which are a characteristic feature of strongly correlated solids, have significant and nontrivial effects on nonlinear optical responses.

Received 14 April 2022
Accepted 12 September 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.157401

Physics Subject Headings (PhySH)

High-order harmonic generation Nonlinear optics Ultrafast phenomena

Antiferromagnets Mott insulators Strongly correlated systems

Dynamical mean field theory Electron-correlation calculations High-harmonic generation Hubbard model Matrix product states

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yuta Murakami ^1,2, Kento Uchida³, Akihisa Koga ¹, Koichiro Tanaka^3,4, and Philipp Werner⁵

¹Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan
²Center for Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan
³Department of Physics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
⁴Institute for Integrated Cell-Material Sciences, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan
⁵Department of Physics, University of Fribourg, 1700 Fribourg, Switzerland

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Issue

Vol. 129, Iss. 15 — 7 October 2022

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Images

Figure 1
(a) Experimental HHG intensity at the indicated HHG peaks as a function of the optical gap for ${Ca}_{2} {RuO}_{4}$ (Mott insulator) and InAs (semiconductor), reproduced from Ref. [56]. The temperature $T$ is modified in the range $T \in [290, 50] K$ . (b) DMFT results for the intensity at the indicated HHG peaks as a function of the Mott gap ( $Δ_{Mott}$ ) for the single-band Hubbard model in the Mott insulating phase.
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Figure 2
(a) Local spectral functions $A_{loc} (ω)$ in equilibrium. (b) HHG spectra of the Mott insulator computed with DMFT for various $T$ . (c) The intensity at the peaks of the HHG spectra as a function of $T$ . The peak intensity is normalized by the value at $T = 0.2$ (PM phase). For (a)–(c), we use $U = 6$ . (d) $U$ dependence of the increase ratio of the HHG peaks. In order to take into account the change of the Mott gap, we compare the $(2 U + n)$ th HHG peaks. We use $T = 0.2$ for the PM phase, while we use $T = 0.3 / U$ for the AF state to take account of the change of $J_{ex} \propto (1 / U)$ . The excitation parameters are $E_{0} = 0.8$ , $Ω = 0.5$ , $t_{0} = 75$ , and $σ = 15$ .
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Figure 3
(a) and (b) Subcycle spectra $I_{HHG} (ω, t_{p})$ for $U = 6$ at (a) $T = 0.2$ (PM phase) and at (b) $T = 0.05$ (AF phase). A Gaussian window with standard deviation $σ^{'} = 0.9$ is used. The red dashed (blue dot-dashed) lines indicate the maxima of $I_{HHG} (ω, t_{p})$ at $T = 0.05$ ( $T = 0.2$ ) at a given $ω$ as a function of $t_{p}$ around $t_{p} = 80$ , which defines the function $f_{ω} (t_{p})$ . The vertical dashed lines indicate the times when the electric field $E (t) = 0$ . (c) Intensity $I_{HHG} (ω, t_{p})$ along the lines $f_{ω} (t_{p})$ for $U = 6$ . (d) Normalized intensity $I_{HHG} (ω, t_{p})$ along the lines $f_{ω} (t_{p})$ for the indicated values of $U$ . We use $T = 0.2$ for the PM phase and $T = 0.3 / U$ for the AF states to take account of the change of $J_{ex} \propto (1 / U)$ . $I_{HHG} (f_{ω} (t_{p}), t_{p})$ is renormalized by the value at $t_{p} = 79.5$ in each case. The excitation parameters are the same as in Fig. 2.
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Figure 4
(a) $I_{HHG}$ for different $B_{stagg}^{z}$ and subcycle analysis for (b) $B_{stagg}^{z} = 0.001$ and (c) $B_{stagg}^{z} = 0.2$ . A Gaussian window with $σ^{'} = 0.9$ is used. The colored markers indicate the energy emitted at $t_{p}$ by the recombination of a doublon-holon pair, which is predicted from the three-step model using the doublon and holon dispersions from the Bethe ansatz [51]. The color indicates the time interval between the recombination and the creation of the doublon-holon pair $t_{pair}$ , and $T_{p} = (2 π / Ω)$ . (d) Phase of the Fourier component of $J (ω)$ at $ω = n Ω$ ( $n$ is an integer). In all panels, we set $U = 8$ , and the excitation parameters are $Ω = 0.5$ , $E_{0} = 0.8$ , $t_{0} = 60$ , and $σ = 15$ .
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