Interplay of Broken Symmetries and Quantum Criticality in Correlated Electronic Systems

This thesis delves into a study of phases of strongly correlated quantum matter confined to two spatial dimensions. The thesis can broadly be divided into three parts. In the first part, comprising of chapters 2 and 3, we investigate some interesting aspects of symmetry breaking and quantum criticality in the superconducting phase of the iron-based superconductors. In particular, motivated by tunneling microscopy measurements on FeSe, in chapter 2 we study the effect of spontaneously broken rotational symmetry on the structure of the superconducting vortex. In chapter 3, we study the critical singularities associated with the superfluid-density at a wide class of symmetry-breaking and topological phase transitions in a clean superconductor. Inspired by experiments on BaFe$_2$(As$_{1-x}$P$_x$)$_2$, we also analyze the effect of quenched disorder on the superfluid-density in the vicinity of magnetic quantum critical points. The second part of this thesis, consisting of chapters 4 and 5, is devoted to a study of the pseudogap phase in the underdoped cuprates. In chapter 4 we study the effect of thermal fluctuations of various competing order parameters, including preformed superconductivity and short-ranged charge-density wave, on the electronic excitations. In chapter 5 we analyze the feedback of pairing fluctuations on the landscape of various competing charge-density wave order parameters within the framework of fermi-liquid theory. In the final part of the thesis, consisting of chapters 6 and 7, we propose an alternative picture for describing the pseudogap metal. In chapter 6, we study a quantum-disordered phase of matter---the fractionalized fermi-liquid (FL*)---where the electrons are coupled to the fractionalized excitations of a strongly fluctuating antiferromagnet and propose it to be a candidate state for the pseudogap. We investigate instabilities of the FL* to density-wave order and compare with experiments. In chapter 7, we describe a framework for describing a novel quantum phase transition without any broken-symmetries---a Higgs transition---that describes a transition from a conventional fermi-liquid to a parent phase of the FL* state via an intermediate non-fermi liquid. We discuss its possible connection to the optimal doping critical point in the cuprates.Physic