Novel properties of the optical conductivity due to electric-dipole-induced magnetic transitions in the Hubbard model

Adrien Bolens, Hosho Katsura, Masao Ogata +1 more

We study how the synergetic effect of spin-orbit coupling (SOC) and Zeeman splitting (ZS) affects the optical conductivity in the one-dimensional Hubbard model using the Kubo formula. We focus on two phenomena: (1) the electric dipole spin resonance (EDSR) in the metallic regime and (2) the optical conductivity in the Mott-insulating phase above the optical gap. In both cases, we calculate qualitatively the effects of SOC and ZS and how they depend on the relative angle between the SOC vector and the magnetic field direction. First, we investigate the spin resonance without electron correlation (the Hubbard parameter $U=0$). Although, neither SOC nor ZS causes any resonance by itself in the optical conductivity, the EDSR becomes possible when both of them exist. The resulting contribution to the optical conductivity is analyzed analytically. The effect of $U$ on the spin resonance is also studied with a numerical method. It is found that at half filling, the resonance is first enhanced for small $U$ and then suppressed when the optical gap is large enough. In the strong coupling limit $U\ensuremath{\rightarrow}\ensuremath{\infty}$ at half filling, we also refer to the resonance between the lower and upper Hubbard bands appearing at $\ensuremath{\omega}\ensuremath{\sim}U$, above the optical gap. A large magnetic field tends to suppress the signal while it is recovered thanks to SOC depending on the relative angle of the magnetic field.

Jaroslav Fabian

W. Brenig

Zijun Wang, Tim J. Senden, Andries Meijerink

Abstract The radiative transition probability is a fundamental property for optical transitions. Extensive research, theoretical and experimental, has been conducted to establish the relation between the photonic environment and electric dipole (ED) transition probabilities. Recent work shows that the nanocrystal (NC)-cavity model accurately describes the influence of the refractive index n on ED transition rates for emitters in NCs. For magnetic dipole (MD) transitions, theory predicts a simple n3 dependence. However, experimental evidence is sparse and difficult to obtain. Here we report Eu3+-(with distinct ED+MD transitions) and Gd3+-(MD transitions) doped β-NaYF4 NC model systems to probe the influence of n on ED and MD transition probabilities through luminescence lifetime and ED/MD intensity ratio measurements. The results provide strong experimental evidence for an n3 dependence of MD transition probabilities. This insight is important for understanding and controlling the variation of spectral distribution in emission spectra by photonic effects.

J. J. Vicente Alvarez, C. A. Balseiro, Hermenegildo Alejandro Ceccatto

We study the response to a static electric field (charge stiffness) and the frequency-dependent conductivity of the Hubbard model in a resonant-valence-bond-type paramagnetic phase. This phase is described by means of a charge and spin rotational-invariant approach, based on a mixed fermion-boson representation of the original strongly correlated electrons. We found that the Mott transition at half filling is well described by the charge stiffness behavior, and that the values for this quantity off half filling agree reasonably well with numerical results. Furthermore, for the frequency-dependent conductivity we trace back to the origin of the band that appears inside the Hubbard gap to magnetic pair breaking. This points to a magnetic origin of the midinfrared band in high-${T}_{c}$ compounds.

Giang H. Bach, Jorge G. Hirsch, F. Marsiglio