Inelastic light scattering

In this project, we are examining how light interacts with strongly correlated materials. Our focus is on inelastic light scattering, where the light changes color after interacting with the charge excitations of the material. Recently, there has been significant focus on inelastic x-ray scattering, where the photon is sensitive to structures on the nanoscale. There is very little theory for how such interactions take place when the material is strongly correlated. We examine both nonresonant scattering, where the response function depends only on the change of color of the photon (not its original color) and resonant scattering, where it depends on both the color and the change in color of the photon. Recently, we have discovered an interesting new sum rule for inelastic light scattering, which relates to the potential energy of the many-body system, much like the optical conductivity sum rule relates to the kinetic energy of the strongly correlated system.

Annotated list of publications

Raman scattering

A. M. Shvaika, O. Vorobyov, J. K. Freericks, and T. P. Devereaux, Electronic Raman scattering in correlated materials: A treatment of nonresonant, mixed, and resonant scattering with dynamical mean field theory Materials, Phys. Rev. B 71, 045120--1-17 (2005).
A. M. Shvaika, O. Vorobyov, J. K. Freericks, and T. P. Devereaux, Resonant Enhancement of Inelastic Light Scattering in Strongly Correlated Materials, Phys. Rev. Lett. 93, 137402--1-4 (2004).

A. M. Shvaika,

J. K. Freericks,

T. P. Devereaux,

Resonant Enhancement of Electronic Raman Scattering,

A. M. Shvaika, O. Vorobyov, J. K. Freericks, and T. P. Devereaux, Resonant electronic Raman scattering near a quantum critical point, (proceedings of the Strongly Correlated Electron Systems conference, Karlsruhe, Germany), Physica B 359--361C, 705--707 (2005).
J. K. Freericks, T. P. Devereaux, R. Bulla, and Th. Pruschke, Nonresonant inelastic light scattering in the Hubbard model, Phys. Rev. B 67, 155102--1-8 (2003).

This is the first work to calculate a Raman response for a system that undergoes a metal-insulator transition. We find that our results are universal on the insulating side of the metal-insulator transition and display the three fundamental features seen in experiment on strongly correlated materials: (i) a rapid loss of low-energy spectral weight and a gain of high-energy spectral weight as temperature is lowered; (ii) the appearance of an isosbestic point, where the Raman response is independent of temperature at a characteristic frequency; and (iii) the ratio of the range in frequency over which the Raman response is depleted at low temperature to the onset temperature where the depletion begins is large. This behavior has been seen SmB₆, FeSi, and the high-temperature superconductors. The extension of the nonresonant work to the resonant case represents one of the most complex solutions to a many-body problem with DMFT. We founmd three interesting results in the resonant regime as well: (i) the isosbestic behavior is now easily seen in all channels; (ii) there is a double resonance occuring when the transfered energy approaches the incident photon energy; and (iii) there is a joint resonance of the low-energy peak and the charge-transfer peak when the photon energy is on the order of U.

Inelastic x-ray scattering

T. P. Devereaux, G. E. D. McCormack and J. K. Freericks, Inelastic x-ray scattering as a probe of electronic correlations, Phys. Rev. B 68, 075105--1-11 (2003).
T. P. Devereaux, G. E. D. McCormack and J. K. Freericks, Inelastic x-ray scattering in correlated (Mott) insulators, Phys. Rev. Lett. 90, 067402--1-4 (2003).

The first series of papers examine the nonresonant inelastic X-ray scattering, which can resemble the resonant response (to a zeroth-order approximation). We find a number of interesting features of the response: (i) isosbestic behavior is seen in all symmetry channels for all transfered wavevectors; (ii) the nonresonant response is independent of the symmetry channel when we are at the Brillouin zone corner indicating that any polarization dependence there is a direct measure of nonlocal fluctuations; and (iii) the low-energy peak disperses, while the charge-transfer peak broadens through the Brillouin zone. Current work is focusing on examining resonant effects.

Sum rules for inelastic light scattering

J.K. Freericks and T.P. Devereaux, Sum rules for inelastic scattering in the Hubbard model, Physica B 378--380, 650--653 (2006) (Proceedings of the Strongly Correlated Electrons Systems 2005 conference, Vienna, Austria, July, 2005).
J.K. Freericks, T.P. Devereaux, M. Moraghebi, and S.L. Cooper, Optical sum rules that relate to the potential energy of strongly correlated systems, Phys. Rev. Lett. 94, 216401--1-4 (2005).

In this work, we discover a new set of optical sum rules that are valid for inelastic light scattering, and which relate to the potential energy (rather than the kinetic energy as in the optical sum rule). These sum rules are shown to hold for SmB₆ and should hold for a wide range of strongly correlated materials. The sum rules do suffer from some difficulty with being able to separate the low-energy band from higher bands, but appear for both the Falicov-Kimball model and the Hubbard model.

Last modified September 12, 2004.

Jim Freericks, Professor of Physics