| This thesis is devoted to an investigation of quantum electronic liquid crystal phases of matter. With the recent discovery of electronic phases that are neither isotropic liquids, nor crystalline solids, it is now vital to gain a comprehensive understanding of these intermediate "electronic liquid crystal" phases. Examples of these new phases include the highly anisotropic phases in quantum Hall systems, static stripes in cuprate superconductors and Fermi surface distortions in some heavy fermion and ruthenate systems. Owing to the strong correlations involved, such an investigation requires the use of non-perturbative methods and we choose to utilize the method of bosonization both in its one-dimensional form and its extension to greater than one-dimension. Our focus will be on two electronic liquid crystal phases representing two paradigms: one on the establishment of orientational order (the nematic phase) and the other on translational order (the smectic phase) both of which are intermediately ordered in comparison to a crystal.; Using the method of bosonization, extended from one to two dimensions, we study the quantum nematic phase which arises due to shape (Pomeranchuk) instabilities of the Fermi surface of a Fermi liquid. Using this method, we demonstrate that in this phase and at the phase transition, the system of electrons is a non-Fermi liquid as defined by the existence of fermionic quasiparticles. At finite temperatures, we find that while order parameter correlations become long ranged as the system begins to order, fermionic correlations become correspondingly short ranged, a phenomena that has become known as 'local' quantum criticality.; We also discuss translational ordering via an investigation of the quantum Hall smectic state which exhibits sliding symmetry: the ordered layers slide freely next to one another. We show, through renormalization group calculations, that such a symmetry causes the naive continuum approximation in the direction perpendicular to the stripes to break down. In particular, we show that the correct fixed point has the form of an array of sliding Luttinger liquids making sliding symmetry a dramatic features of this liquid crystalline phase. Similar considerations apply to all theories with sliding symmetries. |
