Related papers: Universal properties of cuprate superconductors: E…
To provide an understanding of the universal properties emerging from the empirical correlations and phase diagrams of cuprate superconductors, we invoke the scaling theory of finite temperature and quantum critical phenomena. The universal…
We analyze the empirical correlation between the zero temperature penetration depth $\lambda_{c}(0) $ and the corresponding normal state DC conductivity $\sigma_{c}^{DC}$, measured slightly above the transition temperature $T_{c}$, in…
Anisotropy, thermal and quantum fluctuations and their dependence on dopant concentration appear to be present in all cuprate superconductors, interwoven with the microscopic mechanisms responsible for superconductivity. Here we review…
We show that the unusual doping dependence of the isotope effects on transition temperature and zero temperature in - plane penetration depth naturally follows from the doping driven 3D-2D crossover, the 2D quantum superconductor to…
It is shown that the empirical relations between transition temperature, normal state conductivity linearly extrapolated to the value at the transition temperature, zero temperature penetration depths, etc., as observed in a rich variety of…
We outline the universal and finite temperature critical properties of the 3D-XY model, extended to anisotropic extreme type-II superconductors, as well as the universal quantum critical properties in 2D. On this basis we review: (i) the…
Using the scaling theory of quantum critical phenomena we present a detailed analysis of various superconducting properties of La$_{2-x}$Sr$_{x}$CuO$_{4}$, Y$_{0.8}$Ca$_{0.2}$-123, Tl-1212 and Tl-2201. Our results include: the experimental…
We show that in anisotropic superconductors, falling at finite temperature into the 3D-XY- and at zero temperature into the 2D-XY-QSI universality class, the isotope effects on transition temperature, specific heat and magnetic penetration…
We report that four properties of cuprates and their evolution with doping are consequences of simply counting four-site plaquettes arising from doping: (1) the universal Tc phase diagram (superconductivity between \approx0.05 and…
We discuss the temperature-dependent thermoelectric transport properties of semiconductor nanostructures comprising a quantum dot coupled to quantum wires: the thermal dependence of the electrical conductance, thermal conductance, and…
We review the empirical scenario emerging from the measured doping dependence of the transition temperature and the anisotropy parameter $% \gamma $ $=\xi _{ab}/\xi_{c}$, defined as the ratio of the correlation lengths parallel and…
The strongly correlated electron fluids in high temperature cuprate superconductors demonstrate an anomalous linear temperature ($T$) dependent resistivity behavior, which persists to a wide temperature range without exhibiting saturation.…
Dramatic evolution of properties with minute change in the doping level is a hallmark of the complex chemistry which governs cuprate superconductivity as manifested in the celebrated superconducting domes as well as quantum criticality…
We describe the different regimes of finite temperature dynamics in the vicinity of a zero temperature superconductor to insulator quantum phase transition in two dimensions. New results are obtained for a low temperature phase-only…
The three central phenomena of cuprate superconductors are linked by a common doping $p^{\star}$, where the enigmatic pseudogap phase ends, around which the superconducting phase forms a dome, and at which the resistivity exhibits an…
I review a variety of model systems and their quantum critical points, motivated by recent experimental and theoretical developments. These are used to present a general discussion of the non-zero temperature crossovers in the vicinity of a…
A microscopic analysis of the superconducting quantum critical point realized via a pair-breaking quantum phase transition is presented. Finite temperature crossovers are derived for the electrical conductivity, which is a key probe of…
We discuss the occurrence of crossing points in the magnetization - temperature $(m,T$) plane within the framework of critical phenomena. It is shown that in a two-dimensional superconducting slab of thickness $d_{s}$ $m_{z}(\delta)$ versus…
One of the long standing puzzles in strongly correlated materials is the microscopic origin of the quantum critical Planckian strange metal phase with universal linear in temperature scattering rate from which unconventional…
We consider wires near a zero temperature transition between superconducting and metallic states. The critical theory obeys hyperscaling, which leads to a universal frequency, temperature, and length dependence of the conductance; quantum…