Quantum liquid crystals

Abstract

The phenomenon of high temperature (high-Tc) superconductivity, although discovered 20 years ago, still remains mysterious. In conventional superconductors, the supercurrent is carried by a gas of weakly interacting pairs of electrons (Cooper pairs). Experiments suggest that the electron in high-Tc superconductors are at the verge of solidifying into a stripe-crystal, invalidating the conventional `gaseous' picture. Inspired by this problem, the work in this thesis offers an opposite paradigm for high-Tc superconductivity, based on the notion of the `almost ordered' superconductor. Formulating the problem in the field theoretical language of quantum elasticity and utilizing the duality transformation, quantum phases of matter are constructed which are as close as possible to a solid, which can be considered as quantum version of liquid crystals. We find that these ``dual shear superconductors'' are also genuine electromagnetic superconductors with properties which are however subtly different from conventional superconductors and invoke rather unconventional experiments: quantum-liquid crystalline orders, oscillations of magnetic screening currents, overscreening of Coulomb force, and especially a new collective mode found in the dynamical electromagnetic response.