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.
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.
We study the effects of quenched disorder on the two-dimensional d-wave superconductors (SCs) at zero temperature by Monte Carlo simulations. The model is defined on the three-dimensional (3D) lattice and the SC pair field is put on each spatial link as motivated in the resonating-valence-bond theory of the high-Tc SCs. For the nonrandom case, the model exhibits a second-order phase transition to a SC state as density of charge carriers is increased. It belongs to the universality class different from that of the 3D XY model. Quenched disorders (impurities) are introduced both in the hopping amplitude and the plaquette term of pair fields. Then the second-order transition disappears at a critical concentration of quenched disorder, ${p}_{c}\ensuremath{\simeq}15%$. Implication of the results to cold atomic systems in optical lattices is also discussed.
We have studied disorder effects on the coefficients of Ginzburg-Landau expansion for attractive Hubbard model within the generalized DMFT+Σ approximation for the wide region of the values of attractive potential U—from the weak-coupling limit, where superconductivity is described by BCS model, towards the strong coupling, where superconducting transition is related to Bose-Einstein condensation (BEC) of compact Cooper pairs. For the case of semi-elliptic initial density of states disorder influence on the coefficients A and B before the square and the fourth power of the order parameter is universal for at all values of electronic correlations and is related only to the widening of the initial conduction band (density of states) by disorder. Similar universal behavior is valid for superconducting critical temperature Tc (the generalized Anderson theorem) and specific heat discontinuity at the transition. This universality is absent for the coefficient C before the gradient term, which in accordance with the standard theory of “dirty” superconductors is strongly suppressed by disorder in the weak-coupling region, but can slightly grow in BCS–BEC crossover region, becoming almost independent of disorder in the strong coupling region. This leads to rather weak disorder dependence of the penetration depth and coherence length, as well as the slope of the upper critical magnetic field at Tc, in BCS–BEC crossover and strong coupling regions.
I study the effect of Coulomb interaction on superconducting order in a d-wave lattice superconductor at T=0 by considering the superconducting saddle point in the two-dimensional $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ model with a repulsion U. The theory of low-energy superconducting phase fluctuations around this saddle point is derived in terms of the effective hard-core bosons (representing the density of spin-up electrons and the phase of the order parameter), interacting with the fluctuating density of spin-down electrons. Whereas the saddle-point value of the superconducting gap is found to continuously increase towards half filling, the phase stiffness at T=0 has a maximum, and then decreases with further underdoping. Right at half filling the phase stiffness vanishes for large U. This argues that the pseudogap phenomenon of the type observed in cuprates is in principle possible without a development of any competing order, purely as a result of growing correlations in the superconducting state. Implications for the finite temperature superconducting transition and the effects of static disorder are discussed qualitatively.
Zero-temperature or quantum phase transitions in itinerant electronic systems both with and without quenched disordered are discussed. Phase transitions considered include, the ferromagnetic transition, the antiferromagnetic transition, the superconductor-metal transition, and various metal-insulator transitions. Emphasis is placed on how to determine the universal properties that characterize these quantum phase transitions. For the first three of the phase transitions listed above, one of the main physical ideas established is that in zero-temperature systems there are soft or slow modes that exist in addition to the soft order parameter fluctuations, and that these modes can couple to the critical modes. These extra soft modes are shown to have a profound effect on the quantum critical properties. For quantum phase transitions involving zero wavenumber order parameters, i.e., the ferromagnetic and superconductor-metal transitions, these extra modes effectively lead to long-ranged effective interactions between order parameter fluctuations, which in turn lead to exactly soluble critical behaviors. For the antiferromagnetic case, we argue that while in low enough dimensions disorder fluctuation effects tend to destroy long-range order, quantum fluctuations counteract this effect and in some parameter regions manage to re-establish antiferromagnetic long-range order. For the metal-insulator transition, some recent new ideas are reviewed. In particular, it is pointed out that for interacting disordered electrons, one expects that in high dimensions the metal-insulator transition is related to the phase transition that occurs in random-field magnets in high dimensions. If the analogy also holds in three dimensions this suggests that the metal-insulator transition might have glassy characteristics.
In this thesis a systematic, functional matrix field theory is developed to describe both clean and disordered s-wave and d-wave superconductors and the quantum phase transitions associated with them. The thesis can be divided into three parts. The first part includes chapters 1 to 3. In chapter one a general physical introduction is given. In chapters two and three the theory is developed and used to compute the equation of state as well as the number-density susceptibility, spin-density susceptibility, the sound attenuation coefficient, and the electrical conductivity in both clean and disordered s-wave superconductors. The second part includes chapter four. In this chapter we use the theory to describe the disorder-induced metal - superconductor quantum phase transition. The key physical idea here is that in addition to the superconducting order-parameter fluctuations, there are also additional soft fermionic fluctuations that are important at the transition. We develop a local field theory for the coupled fields describing superconducting and soft fermionic fluctuations. Using simple renormalization group and scaling ideas, we exactly determine the critical behavior at this quantum phase transition. Our theory justifies previous approaches. The third part includes chapter five. In this chapter we study the analogous quantum phase transition in disordered d-wave superconductors. This theory should be related to high Tc superconductors. Surprisingly, we show that in both the underdoped and overdoped regions, the coupling of superconducting fluctuations to the soft disordered fermionic fluctuations is much weaker than that in the s-wave case. The net result is that the disordered quantum phase transition in this case is a strong coupling, or described by an infinite disordered fixed point, transition and cannot be described by the perturbative RG description that works so well in the s-wave case. The transition appears to be related to the one that occurs in disordered quantum antiferromagnets.
The phase diagram of a system of interacting bosons (Cooper pairs) hoping on a one-dimensional (1D) lattice with onsite phase dissipation describing the Josephson tunneling to a nearby diffusive normal-metal electrode is studied. Starting from the system at commensurate lattice filling, it is shown by a combination of analytical techniques that the phase diagram contains two quantum phases: A dissipative Bose-Einstein condensate (D-BEC) or superconductor with long-range phase coherence, and a dissipative Mott insulator (D-Mott) or "metal" with exponentially decaying phase correlations in space and local imaginary-time correlations decaying as the local pairing correlations of the electrode. The D-Mott/metal phase can be described as a 1D array of dissipative boson puddles, weakly coupled by Josephson tunneling. The puddle size roughly corresponds to the length scale beyond which phase slips suppress phase coherence. The dissipative time-dependent Ginsburg-Landau theory phenomenologically used by Sachdev, Werner, and Troyer [Phys. Rev. Lett. {\bf 92} 237003 (2004)] for the superconductor-metal transition in quasi-1D wires is derived from this microscopic puddle picture. Thus, the criticality of the D-Mott/D-BEC transition is shown to belong to the Wilson-Fisher universality class with dynamical exponent z≈2. At small doping, the D-Mott/metal phase remains stable due to its finite compressibility, which is computed to leading order in a perturbation expansion of the dissipation strength and the inter-puddle Josephson coupling. At larger doping, using a mapping to a pseudospin chain combined with bosonization, the D-BEC/superconductor phase is the ground state for non-vanishing but arbitrarily small dissipation. Similarities and differences with deconfinement transition of an array 1D bosonic Mott insulators in anisotropic optical lattices are also discussed.