The zero temperature d - wave superconductor phase transition theory given in the case of T=0 for two - dimensional superconductors (I. Herbut, PRL {\bf 85}, 1532 (2000)) is generalized for finite temperatures. The Gaussian behavior of the system is associated with a non - Fermi behavior of the normal state observed in the resistivity of cuprate superconductors.
The zero temperature d - wave superconductor phase transition theory given in the case of T=0 for two - dimensional superconductors (I. Herbut, PRL {\bf 85}, 1532 (2000)) is generalized for finite temperatures. The Gaussian behavior of the system is associated with a non - Fermi behavior of the normal state observed in the resistivity of cuprate superconductors.
Using the scaling theory of quantum critical phenomena we explore the occurrence of universal critical behavior at the insulator-to-superconductor and superconductor-to-normal state transitions at zero temperature.Experimentally, these phase transitions are driven by doping and correspond to critical end points of the phase transition łine in the temperature-hole concentration plane.Provided that the order parameter is a complex scalar in two dimensions, and that the London relation between superfluid number density and magnetic penetration depth holds, the scaling theory predicts universal behavior close to the insulator-to-superconductor transition.In particular, transition temperature and zero temperature penetration depth are universally related and the sheet resistance adopts a universal value.These predictions agree remarkably well with available experimental data and provide useful constraints for a microscopic theory.
The Ginzburg-Landau-Wilson theory that describes the disordered-metal- d-wave-superconductor phase transition at zero temperature is derived at weak coupling. The theory represents an interacting dissipative system of bosonic Cooper pairs in an effective random potential. I show that there exists a wide crossover regime in the theory controlled by a line of Gaussian fixed points, each of which in two dimensions is characterized by a different universal value of the dc critical conductivity. Relation to experiments on overdoped and underdoped cuprates is discussed.
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 seven distinct cases (including cases with nematic order) and analyze fluctuations by the renormalization group. We find that only two, the transitions to d(x(2)-y(2))+is and d(x(2)-y(2))+id(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.
Superconductor-insulator transitions, especially in thin films, can provide the simplest examples of the continuous quantum phase transition paradigm. Quantum phase transitions differ from thermal phase transitions in that they occur at zero temperature when the ground state of a system is changed in response to a variation of an external parameter of the Hamiltonian. In the example of the superconductor-insulator transition, this control parameter could be the parallel or perpendicular magnetic field, disorder, or charge density. Quantum phase transitions are studied through measurements at nonzero temperature of physical behaviors influenced by the quantum fluctuations associated with the transition. This review will focus on experimental aspects of superconductor-insulator transition in disordered films that are effectively two-dimensional. In particular, the evidence for quantum critical behavior in the various types of transitions will be presented. The various theoretical scenarios for the transitions will also be discussed along with the extent to which they are supported by experiment. Open questions relating to the nature of the very puzzling insulating regime and whether there are many different types of superconductor-insulator transitions will be presented. Although this research area is more than 20 years old, rather central issues are not resolved.
Quantum critical behaviors induced by a putative quantum phase transition are vigilantly investigated, which separates a d-wave superconducting state and d-wave superconducting+X state below the superconducting dome of the d−wave superconductors with tuning the non-thermal doping variable. Within the framework of renormalization group approach, we start with a phenomenological effective theory originated from the Landau-Ginzburg-Wilson theory and practice one-loop calculations to construct a set of coupled flows of all interaction parameters. After extracting related physical information from these coupled evolutions, we address that both fermion velocities and critical temperatures exhibit critical behaviors, which are robust enough against the initial conditions due to strong quantum fluctuations. At first, the evolution of Yukawa coupling between X-state order parameter and nodal fermions in tandem with quantum fluctuations heavily renormalize fermion velocities and generally drive them into certain finite anisotropic fixed point at the lowest-energy limit, whose concrete value relies upon the very quantum phase transition. In addition, these unique properties of fermion velocities largely reshape the fate of superfluid density, giving rise to either an enhancement or a dip of critical temperature. Moreover, we find that fermion-fermion interactions bring non-ignorable quantitative corrections to quantum critical behaviors despite they are subordinate to quantum fluctuations of order parameters.
Introduction The quantum phase transitions considered so far in this book are mostly continuous, second order. They are associated with the divergence of a correlation length and of a characteristic time that renders the quantum critical point scale invariant. However, there are many important phase transitions at which the order parameter goes abruptly to zero and, more important, at which the characteristics of length and critical time do not diverge. In general there is also a latent heat , or work required, to transform one phase into another. In this and the next chapter we study these discontinuous quantum phase transitions. We proceed by considering initially some important cases of what is known as fluctuation induced quantum phase transitions to next treat a more general case of a first-order quantum phase transition. We will show through the study of these problems that the concepts of critical exponents and scaling remain useful, even though these systems do not exhibit scale invariance at their critical point. In Chapter 15 we present the scaling theory of first-order quantum phase transitions and use its results to treat some general problems. One of the most interesting cases of fluctuation-induced transitions occurs in superconductors due to the coupling of the charged carriers to the electromagnetic field. We consider initially a wider class of systems with macroscopic wave functions, the superfluids, of which superconductors are the charged version. We adopt a macroscopic approach to this problem and describe the superfluid by a complex order parameter φ , such that | φ | 2 is proportional to the density of condensed particles. The zero temperature phase diagram is expressed in terms of a control parameter, m 2 , such that, at m 2 = 0, the system presents a quantum phase transition from a superfluid state, for m 2 < 0, φ ≠ 0, to a normal state for m 2 > 0 where φ = 0. In the case of the superconductor with particles of charge q = 2 e , we will include the coupling of these particles to the electromagnetic field and study its effect in the phase diagram of these systems. We show that in the neutral superfluid, the zero temperature transition to the normal state is continuous and occurs at a quantum critical point.