Developing a theoretical framework for conducting electronic fluids qualitatively distinct from those described by Landaus Fermi-liquid theory is of central importance to many outstanding problems in condensed matter physics. One such problem is that
, above the transition temperature and near optimal doping, high-transition-temperature copper-oxide superconductors exhibit `strange metal behaviour that is inconsistent with being a traditional Landau Fermi liquid. Indeed, a microscopic theory of a strange-metal quantum phase could shed new light on the interesting low-temperature behaviour in the pseudogap regime and on the d-wave superconductor itself. Here we present a theory for a specific example of a strange metal---the d-wave metal. Using variational wavefunctions, gauge theoretic arguments, and ultimately large-scale density matrix renormalization group calculations, we show that this remarkable quantum phase is the ground state of a reasonable microscopic Hamiltonian---the usual t-J model with electron kinetic energy $t$ and two-spin exchange $J$ supplemented with a frustrated electron `ring-exchange term, which we here examine extensively on the square lattice two-leg ladder. These findings constitute an explicit theoretical example of a genuine non-Fermi-liquid metal existing as the ground state of a realistic model.
We formulate a model for magnetic and superconducting ordering at LaAlO3/SrTiO3 interfaces containing both localized magnetic moments and itinerant electrons. Though these both originate in Ti 3d orbitals, the former may be due to electrons more tigh
tly-bound to the interface while the latter are extended over several layers. Only the latter contribute significantly to metallic conduction and superconductivity. In our model, the interplay between the two types of electrons, which is argued to be ferromagnetic, combined with strong spin-orbit coupling of the itinerant electrons, leads to magnetic ordering. Furthermore, we propose a model for interfacial superconductivity, consisting of random superconducting grains in the bulk STO driven, via coupling to the interface conduction band, towards long-ranged or quasi-long-ranged order. Most interestingly, the magnetic order and strong spin orbit coupling can lead in this manner to unconventional interfacial superconductivity, yielding a possible realization of Majorana physics.
Motivated by the recent experimental observation of a Mott insulating state for the layered Iridate Na2IrO3, we discuss possible ordering states of the effective Iridium moments in the presence of strong spin-orbit coupling and a magnetic field. For
a field pointing in the [111] direction - perpendicular to the hexagonal lattice formed by the Iridium moments - we find that a combination of Heisenberg and Kitaev exchange interactions gives rise to a rich phase diagram with both symmetry breaking magnetically ordered phases as well as a topologically ordered phase that is stable over a small range of coupling parameters. Our numerical simulations further indicate two exotic multicritical points at the boundaries between these ordered phases.
