Higher harmonics in Mott-Hubbard insulators as sensors

Abstract

Using strong-coupling time-dependent perturbation theory, we study the response of Mott and charge-transfer insulators to an oscillating electric field. We derive analytical expressions for the resulting higher-harmonic currents and show that they encode information about spin order and microscopic hopping pathways. The results demonstrate that higher harmonics can serve as probes of correlated materials and as sensors of the applied driving field.

Figures (3)

• Figure 1: Odd-harmonic spectrum showing the maximum current for each harmonic order $m$ for two electric-field strengths: weak field $Er_{\mu\nu}/U=0.05$ (top) and strong field $Er_{\mu\nu}/U=0.5$ (bottom). Parameters: $U=15\omega$, producing a resonance at harmonic $m=15$.
• Figure 2: Two-band Fermi-Hubbard setup with lower Mott band at energy $U^{ss}_{11}$ and empty upper band at energy $U^{ss}_{22}$. The dotted ellipse shows the on-site Coulomb repulsion. Having two electrons in the same lattice site and the same band, would result in a Coulomb repulsion $U^{ss'}_{11}$ or $U^{ss'}_{22}$. Intra- and inter-band hoppings are denoted by $T_{\mu\nu}^{AB}(t)$.
• Figure 3: Ground state of charge-transfer insulator with a filled $p$ band and a Mott-localized $d$ band. The dotted circle represents the Coulomb repulsion when two electrons occupy the same lattice site in the $d$-band.