Strongly Interacting Electron Systems

Transition metal oxides form crystals that have phases with exotic properties such as high temperature superconductivity, ferromagnetism, ferroelectricity, and charge and orbital ordering. Often these phases are in competition with each other leading to complicated phase diagrams, for example YBa2Cu3O7, which is a high temperature superconductor, and LaMnO3, which exhibits a “colossal magneto resistance” at a magnetic field induced metal-to-insulator transition. The important operative effect in all these materials is the strong interaction energies between the d-state electrons on the transition metal ions. As electrons hop on or off the transition metal ion the Coulomb energy of the ion changes by an amount large compared with the electron kinetic energy. This can inhibit the hopping leading to an insulator as observed by S. N. Mott in 1949. Conversely the electrons can cleverly use various other degrees of freedom to get around this large energy barrier and, in the process, produce metals, superconductors and the other exotic phases. These degrees of freedom include spin, orbital state, and ion positions (including vibrational motions). Even in conventional metals like copper or aluminum the electron interaction energies are not particularly small. In fact they are comparable with their kinetic energy, as measured by their Fermi energy. However, in 1941 Lev Landau observed that the Pauli principle so restricts the scattering processes that the electrons behave very nearly like non-interacting Fermions, i.e., they become a Landau Fermi liquid. But in the transition metal compounds the interactions are so strong in some cases that this Landau picture breaks down. The resulting exotic phases are interesting both because of the strong interaction physics and because many of the resulting complex behaviors have potential for important applications. One of these potentials is related to the new subject of spintronics and has lead to the term “orbitronics.” The intriguing and yet defiant question in this field is how the transformation from a Fermi liquid to a Mott insulator occurs in these systems. The motion (or transport) of the charges in response to electric and magnetic fields provides important clues to the central mystery of these materials and bears directly the curious metal-insulator transition as well as on important applications of the materials. Prof. Drew’s group has developed novel techniques to observe charge transport in these materials in high magnetic fields. These techniques involve measurements at infrared wavelengths where the optical frequency is greater than the scattering rates of the charge carriers so that their intrinsic response becomes apparent. They also probe the characteristic frequencies of the system such as the carrier scattering rates, the plasma frequency 2 2 4 p ne m ω π ∗ = (which, together with the carrier scattering