Condensed Matter Theory

Abstract:

The dipolar-octupolar (DO) pyrochlores, R2M2O7 (R=Ce,Sm,Nd), are key players in the search for realizable novel quantum spin liquid (QSL) states as a large parameter space within the DO pyrochlore phase diagram is theorized to host QSL states of both dipolar and octupolar nature. New single crystals and powders of Ce2Sn2O7, synthesized by hydrothermal techniques, present an opportunity for a new characterization of the exchange parameters in Ce2Sn2O7 using the near-neighbor XYZ model Hamiltonian associated with DO pyrochlores. Utilizing quantum numerical linked cluster expansion fits to heat capacity and magnetic susceptibility measurements, and classical Monte Carlo calculations to the diffuse neutron diffraction of the new hydrothermally grown Ce2Sn2O7 samples, we place Ce2Sn2O7's ground state within the ordered dipolar all-in-all-out (AIAO) Néel phase, with quantum Monte Carlo calculations showing a transition to long-range order at temperatures below those accessed experimentally. Indeed, our new neutron diffraction measurements on the hydrothermally grown Ce2Sn2O7 powders show a broad signal at low scattering wave vectors, reminiscent of a dipolar spin ice, in striking contrast from previous powder neutron diffraction on samples grown from solid-state synthesis, which found diffuse scattering at high scattering wave vectors associated with magnetic octupoles and suggested an octupolar quantum spin ice state. We conclude that new hydrothermally grown Ce2Sn2O7 samples host a finite-temperature proximate dipolar spin ice phase, above the expected transition to AIAO Néel order.

Abstract:

We review the network model for the integer quantum Hall effect. The model provides a simplified description of Anderson localization in this context. It represents non-interacting electrons moving in two dimensions under the combined influence of a strong magnetic field and a smooth disordered potential. In this setting, electron eigenstates form disorder-broadened Landau levels and their character varies with energy across the Landau level. States in both the low-energy and the high-energy tails of the Landau level are localized, with a spatial extent characterized by the localization length. At the center of the Landau level there is a transition between phases with different quantized values of the Hall conductance and the localization length is divergent. The network model captures universal features of this transition.