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In this paper, we present a comprehensive study of Casimir effect in setups involving high-T_c superconductors with different oxygen content, in the presence of an external magnetic field. Nearby an upper critical value, $H_{c2}$, the field induces the formation of an Abrikosov vortex lattice. The field-induced redistribution of the superconducting surface charge gives rise to a periodic Casimir interaction with nearby objects. We focused our analysis on a setup defined by a scanning gold nano-sphere and a planar substrate made of made of YBa₂Cu₃O${}_{6+y}$. However, the derived results may be straightforwardly applied to any cuprate superconductor.

This study investigates the vertex corrections of the optical conductivity in high-$T_c$ superconductors for hole-spin wave scattering in the superconducting state. The Feynman diagram technique is used to determine the mathematical expressions of the ladder diagrams in the calculation of the current–current correlation function. The sum of these vertex terms leads to a self-consistent form of the vertex function. By evaluating the frequency summation through contour integration, a general expression for the current–current correlation function is obtained, which allows us to determine the zeroth-order term and the first-order correction of the optical conductivity explicitly. Our findings for the dc conductivity in a clean superconductor indicate that the zeroth-order term is zero, a result attributed to the conservation of momentum and energy. Meanwhile, the first-vertex correction reveals the Drude behavior in the superconducting state at zero frequency.

To further understand the argument about the superconductivity in PrBa₂Cu₃O_y, We try to change YBa₂Cu₃O_y to PrBa₂Cu₃O_y gradually, studying the detailed change during the change, and hope to find some clue to the argument. The single-phase samples of Y_1-xPr_xBa₂Cu₃O_y (x = 0, 0.1, 0.2, 0.3, 0.5, 0.6, 0.8, 1.0, respectively) were synthesized and characterized by DC magnetization measurement and X-ray diffraction. The structure of the samples was refined by Rietveld method. After careful analysis, it is found that as the x increasing, Ba moves toward the Cu-O(1) plane, the bond length between Y-Ba, Y-Cu(2), and Ba-O(1), and Cu(1)-0(4) increase simultaneously. It demonstrates that as the Pr content increases, the distance between the active block and the carrier reservoir block becomes farer and farer, and the area of the carrier reservoir block increases. It is suggested that the doping of Pr to Y in YBa₂Cu₃O_y changes some local structure and result in the suppression and vanishing of the superconductivity.

The change in thermodynamic quantities (e.g., entropy, specific heat etc.) by the application of magnetic field in the case of the high-T_c superconductor YBCO system is examined phenomenological by the Ginzburg–Landau theory of anisotropic type-II superconductors. An expression for the change in the entropy (ΔS) and change in specific heat (ΔC) in a magnetic field for any general orientation of an applied magnetic field B_a with respect to the crystallographic c-axis is obtained. The observed large reduction of specific heat anomaly just below the superconducting transition and the observed variation of entropy with magnetic field are explained quantitatively.

The electron doped rare earth copper oxide superconductors R_2-xCe_xCuO₄ exhibit anomalous heavy fermion behavior at low temperature with large Sommerfeld specific heat coefficient which is different from the conventional heavy fermion systems. The system is described by a model Hamiltonian consisting of staggered magnetic field in the two sub-lattices of the copper sites in presence of hybridization between the localized 4f electrons of Nd atom and the conduction electrons as well as the f-electron kinetic energy term. The Hamiltonian is solved by Zubarev's Green's function technique and the sub-lattice magnetization is calculated and solved self-consistently. The entropy and specific heat are calculated from the free energy of the system. The temperature dependent entropy and specific heat are numerically evaluated by successive differentiations of sub-lattice magnetization and temperature dependent entropy. It is observed that when the position of the f-level of Nd atom is of the order of hybridization strength, the sub-lattice magnetization is destroyed drastically at lower temperatures. As a result, the specific heat exhibits a large enhancement at low temperatures suggesting the enhancement of the electron density of states and the effective mass of the itinerant electrons exhibiting the heavy fermion character. Similarly, the specific heat shows anomalously sharp jump near the Néel temperature.

An update of a previous review on the many effects and novel consequences of the midgap states predicted to exist in d-wave superconductors is given. Four works done by the author and his collaborators are reviewed with a bit more details, but many works done by other researchers since the previous review are also included. These predictions, if not proven later to require modifications due to additional considerations, can help settle unequivocally the d-wave nature of pairing in high-T_c superconductors.

We have studied the effect of superconducting fluctuations on the electrical conductivity of granular samples of YbBa₂Cu₃O_{7 -δ} superconductors. Two different polycrystalline samples were prepared for this study. Special attention is taken above T_c, where Gaussian and critical regimes are observed. Far from T_c, we can observe the regime dominated by Gaussian fluctuations, with exponent approximately , which is the predicted one for homogeneous 3D fluctuations. Inside the critical region, we have observed two power-law regimes: one of them is consistent with predictions for the 3D-XY universality class, with exponent . Below T_c, in the approach to the zero resistance state, our results show a power-law behavior with critical exponents s₁ = 2.6 ± 0.2 and s₂ = 4.2 ± 0.3. We have previously shown that this corresponds to a phase transition from a paracoherent to a coherent state of the granular array.

High pressure electrical resistivity studies were carried out on the high temperature superconductor Nd_1-xCa_xBa₂Cu₃O_7-δ for various calcium concentrations x=0.00, 0.03, 0.06 and 0.10 obtained by the solid-state reaction method. The electrical resistivity study was performed using the four-probe technique with a Bridgman opposed anvil device. All four samples show an initial drastic fall in electrical resistivity up to a pressure of around 3 GPa that remains almost constant up to 8 GPa.

We report the far-infrared (far-IR) observation of the Goldstone mode at ~ 72 cm^-1 (~ 9 meV) predicted to exist in the superconducting phase of the transition temperature (T_c) at 45 K in the La₂CuO₄-based superconductors. Our observation furthers the experimental support for the two-component picture where the localized charge texture, formed at a specific planar hole density (P_pl), is tied to the high temperature super-conductivity (HTS) at T_c = 15 K, 30 K, and 45 K in a hierarchical fashion at the so-called "magic" doping level at P_pl = 1/16, 2/16, and 3/16 respectively.

We have proposed a model Hamiltonian describing the interlayer tunneling in d-wave bilayer cuprate superconductors. The Hamiltonian is solved for the quasi-particle energy bands and the superconducting (SC) order parameter by using Zubarev’s technique of double time Green’s functions. The effects of interlayer tunneling and the strength of non-magnetic potential are studied for SC order parameter, density of states (DOS), electronic specific heat and quasi-particle energy bands, and the results are compared with others.

Some times ago, in the framework of the Boltzmann kinetic equation in the so-called $\tau$-approximation, it was shown that perpendicular resistivity in quasi-two-dimensional (Q2D) conductors can be impurity independent in a broad range of high parallel magnetic fields [A. G. Lebed and N. N. Bagmet, Phys. Rev. B 55 (1997) R8654]. In this paper, we demonstrate that this result is much more general than the Boltzmann kinetic equation in the $\tau$-approximation and is valid in a pure Q2D metal at low frequencies of the electric field. The above-mentioned statement open possibilities to test the above discussed phenomenon in a number of Q2D organic, high-T_c, and some other Q2D superconductors in their metallic phases and gives a method to extract some important information about their Q2D Fermi surfaces.

Angle-resolved photoemission spectroscopy is a powerful technique that can directly probe the electronic structure of materials. By utilizing the synchrotron radiation, which can provide high-intense monochromatic photon beam with tunable polarization and photon energy, ARPES can resolve detailed electronic structure with ultra-high energy and momentum resolutions, detect three-dimensional momentum space, and probe electrons with different orbital characters selectively, etc. In this chapter, we will briefly review the recent progress obtained by ARPES using the synchrotron radiation. The focused materials will cover the iron-based high-T_C superconductors, the charge-density-wave materials, and Mott-insulators.