Abstract:
We give a straightforward generalization of the Ginzburg-Landau theory for superconductors where the scalar phase field is replaced by an antisymmetric Kalb-Ramond field. We predict that at very low temperatures, where quantum phase effects are expected to play a significant role, the presence of vortices destroys superconductivity.

Abstract:
If phase coherence determines the superconducting transition temperature Tc in the cuprate oxides, it is of great interest to understand the role that dynamics of the phase fluctuation plays in bringing about depletion of the superconducting condensate. We will show that a phase correlation function can be calculated that allows us to describe depletion of superconducting condensate as a result of the quantum fluctuation. In two dimension, dynamic phase fluctuation or pair fluctuation gives rise to a condensate depletion linear with temperature as T$\to O$ in superconductors with nodes at the fermi surface.

Abstract:
I study the effect of quantum and thermal phase fluctuations on the in-plane and c-axis superfluid stiffness of layered d-wave superconductors. First, I show that quantum phase fluctuations in the superconductor can be damped in the presence of external screening of Coulomb interactions, and suggest an experiment to test the importance of these fluctuations, by placing a metal in close proximity to the superconductor to induce such screening. Second, I show that a combination of quantum phase fluctuations and the linear temperature dependence of the in-plane superfluid stiffness leads to a linear temperature dependence of the c-axis penetration depth, below a temperature scale determined by the magnitude of in-plane dissipation.

Abstract:
We consider the possibility of quantum phase transitions in the ground state of triplet superconductors where particle density is the tunning parameter. For definiteness, we focus on the case of one band quasi-one-dimensional triplet superconductors but many of our conclusions regarding the nature of the transition are quite general. Within the functional integral formulation, we calculate the electronic compressibility and superfluid density tensor as a function of the particle density for various triplet order parameter symmetries and find that these quantities are non-analytic when a critical value of the particle density is reached.

Abstract:
I begin with a proposed global phase diagram of the cuprate superconductors as a function of carrier concentration, magnetic field, and temperature, and highlight its connection to numerous recent experiments. The phase diagram is then used as a point of departure for a pedagogical review of various quantum phases and phase transitions of insulators, superconductors, and metals. The bond operator method is used to describe the transition of dimerized antiferromagnetic insulators between magnetically ordered states and spin-gap states. The Schwinger boson method is applied to frustrated square lattice antiferromagnets: phase diagrams containing collinear and spirally ordered magnetic states, Z_2 spin liquids, and valence bond solids are presented, and described by an effective gauge theory of spinons. Insights from these theories of insulators are then applied to a variety of symmetry breaking transitions in d-wave superconductors. The latter systems also contain fermionic quasiparticles with a massless Dirac spectrum, and their influence on the order parameter fluctuations and quantum criticality is carefully discussed. I conclude with an introduction to strong coupling problems associated with symmetry breaking transitions in two-dimensional metals, where the order parameter fluctuations couple to a gapless line of fermionic excitations along the Fermi surface.

Abstract:
Motivated by the strong, low temperature damping of nodal quasiparticles observed in some cuprate superconductors, we study quantum phase transitions in d_{x^2-y^2} superconductors with a spin-singlet, zero momentum, fermion bilinear order parameter. We present a complete, group-theoretic classification of such transitions into 7 distinct cases (including cases with nematic order) and analyze fluctuations by the renormalization group. We find that only 2, the transitions to d_{x^2-y^2}+is and d_{x^2-y^2} + i d_{xy} pairing, possess stable fixed points with universal damping of nodal quasiparticles; the latter leaves the gapped quasiparticles along (1,0), (0,1) essentially undamped.

Abstract:
In this paper we shall introduce a lattice model of unconventional superconductors (SC) like d-wave SC in order to study quantum phase transition at vanishing temperature ($T$). Finite-$T$ counterpart of the present model was proposed previously with which SC phase transition at finite $T$ was investigated. The present model is a noncompact U(1) lattice-gauge-Higgs model in which the Higgs boson, the Cooper-pair field, is put on lattice links in order to describe d-wave SC. We first derive the model from a microscopic Hamiltonian in the path-integral formalism and then study its phase structure by means of the Monte Carlo simulations. We calculate the specific heat, monopole densities and the magnetic penetration depth (the gauge-boson mass). We verified that the model exhibits a second-order phase transition from normal to SC phases. Behavior of the magnetic penetration depth is compared with that obtained in the previous analytical calculation using XY model in four dimensions. Besides the normal to SC phase transition, we also found that another second-order phase transition takes place within the SC phase in the present model. We discuss physical meaning of that phase transition.

Abstract:
It is now widely accepted that the cuprate superconductors are characterized by the same long-range order as that present in the Bardeen-Cooper-Schrieffer (BCS) theory: that associated with the condensation of Cooper pairs. We argue that many physical properties of the cuprates require interplay with additional order parameters associated with a proximate Mott insulator. We review a classification of Mott insulators in two dimensions, and contend that the experimental evidence so far shows that the class appropriate to the cuprates has collinear spin correlations, bond order, and confinement of neutral, spin S=1/2 excitations. Proximity to second-order quantum phase transitions associated with these orders, and with the pairing order of BCS, has led to systematic predictions for many physical properties. We use this context to review the results of recent neutron scattering, fluxoid detection, nuclear magnetic resonance, and scanning tunnelling microscopy experiments.

Abstract:
In previous work on quantum phase transition in granular superconductors, where mean-field theory was used, an assumption was made that the order parameter as a function of the mean field is a convex up function. Though this is not always the case in phase transitions, this assumption must be verified, what is done in this article.

Abstract:
The effect of a quantum phase transition associated with the appearance of the fermion condensate in an electron liquid on the properties of superconductors is considered. It is shown that the electron system in both superconducting and normal states exhibits characteristic features of a quantum protectorate after the point of this fermion-condensation quantum phase transition. The single-particle spectrum of a superconductor can be represented by two straight lines corresponding to two effective masses $M^*_{FC}$ and $M^*_{L}$. The $M^*_{FC}$ mass characterizes the spectrum up to the binding energy $E_0$ and $M^*_L$ determines the spectrum at higher binding energies. Both effective masses are retained in the normal state. These results are used to explain the lineshape of single-particle excitations and other properties of high-$T_c$ superconductors and are in a good agreement with recent experimental data.