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Recently, robust $d$-wave superconductive (SC) order has been unveiled in the ground state of the 2D $t$-$t'$-$J$ model -- with both nearest-neighbor ($t$) and next-nearest-neighbor ($t'$) hoppings -- by density matrix renormalization group…
We study the spin fluctuations of pure and Zn-substituted high temperature superconductors (HTS) using the muon spin relaxation (muSR) technique. Superconductivity is found to coexist with low frequency spin fluctuations over a large region…
In this paper the phase diagram of high $T_{c}$ cuprates is {\it qualitatively} studied in the context of competing orders: antiferromagnetism, d-wave superconductivity and $d$-density wave. {\it Local} correlation functions are estimated…
One of the central issues in the recent study of cuprate superconductors is the interplay of charge order with superconductivity. Here the interplay of charge order with superconductivity in cuprate superconductors is studied based on the…
We propose a phenomenological Ginzburg-Landau-like theory of cuprate superconductivity. The free energy is expressed as a functional F of the spin-singlet pair amplitude psi_ij=psi_m=Delta_m exp(i phi_m); i and j are nearest-neighbor sites…
The density-of-states at the Fermi energy, $N(E_F)$, is low in doped superconducting semiconductors and high-$T_C$ cuprates. This contrasts with the common view that superconductivity requires a large electron-boson coupling $\lambda$ and…
In the recent studies of the unconventional physics in cuprate superconductors, one of the central issues is the interplay between charge order and superconductivity. Here the mechanism of the charge-order formation in the electron-doped…
We have discovered a new example of quantum spin liquid which is a superconducting (SC) phase in 2D electron system close to electronic topological transition. As a quantum spin liquid in low dimensional localized spin systems it is…
Significant progress towards a theory of high-temperature superconductivity in cuprates has been achieved via the study of effective one- and three-band Hubbard models. Nevertheless, material-specific predictions, while essential for…
We study the square-lattice extended Hubbard model with on-site $U$ and nearest-neighbor $V$ interactions by exact diagonalization. We show that non-equilibrium quench dynamics can help determine the equilibrium phase transition boundaries,…
Several recent experiments have challenged the premise that cuprate high-temperature superconductors approach conventional Landau-BCS behavior in the high-doping limit. We argue, based on an analysis of their superconducting spectra, that…
One of the key issues in unraveling the mystery of high Tc superconductivity in the cuprates is to understand the normal state outside the superconducting dome. Here we perform scanning tunneling microscopy and spectroscopy measurements on…
When superconducting (SC) and charge-density wave (CDW) orders compete, novel low temperature behaviors can result. From an analysis of the Landau-Ginzberg-Wilson theory of competing orders, we demonstrate the generic occurrence of a…
We first argue that the collective behaviour of the Cooper pairs created by thermal fluctuations well above the superconducting transition temperature, Tc, is dominated by the uncertainty principle which, in particular, leads to a…
We argue based on theoretical considerations and analysis of experimental data that quasiparticle excitations near the nodes determine the low temperature properties in the superconducting state of cuprates. Quantum effects of phase…
Unconventional superconductivity typically occurs in materials in which a small change of a parameter such as bandwidth or doping leads to antiferromagnetic or Mott insulating phases. As such competing phases are approached, the properties…
The interpretation of how superconductivity disappears in cuprates at large hole doping has been controversial. To address this issue, we present an experimental study of single-crystal and thin film samples of La$_{2-x}$Sr$_x$CuO$_4$…
Unlike the hole-doped cuprates, both nodal and nodeless superconductivity (SC) are observed in the electron-doped cuprates. To understand these two types of SC states, we propose a unified theory by considering the two-dimensional t-J model…
We present a comparative study of Nernst effect and resistivity in underdoped samples of Bi$_2$Sr$_2$CuO$_{6+\delta}$ and La$_{2-x}$Sr$_{x}$CuO$_4$. The Nernst effect presents a peak in a region of the H-T diagram where resistivity shows a…
In high-Tc cuprate superconductors, violation of time-reversal symmetry (${\cal T}$) has been observed experimentally. In order to explain this phenomenon, we consider a flux phase in the t-J model. The flux phase has a free energy higher…