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The simultaneous interplay of strong electron-electron correlations, topological zero-energy states, and disorder is yet an unexplored territory but of immense interest due to their inevitable presence in many materials. Copper oxide…
A profound problem in modern condensed matter physics is discovering and understanding the nature of the fluctuations and their coupling to fermions in cuprates which lead to high temperature superconductivity and the invariably associated…
The cuprates seem to exhibit statistics, dimensionality and phase transitions in novel ways. The nature of excitations [i.e. quasiparticle or collective], spin-charge separation, stripes [static and dynamics], inhomogeneities, psuedogap,…
The challenge of understanding high-temperature superconductivity has led to a plethora of ideas, but 30 years after its discovery in cuprates, very few have achieved convincing experimental validation. While Hubbard and t-J models were…
We propose a finite temperature Landau theory that describes competing orders and interlayer tunneling in cuprate superconductors as an important extension to a corresponding theory at zero temperature [Nature {\bf 428}, 53 (2004)], where…
Following the discovery of superconductivity in the cuprates and the seminal work by Anderson, the theoretical efforts to understand high-temperature superconductivity have been focusing to a large extent on a simple model: the one-band…
The 2019 discovery of high temperature superconductivity in layered nickelate films, Nd$_{1-x}$SrNiO$_2$, has galvanized a community that has been studying nickelates for more than 30 years both as cuprate analogs and in their own right. On…
Cuprates currently hold the record for the highest temperature superconductivity at ambient pressure, but the microscopic understanding of these materials remains elusive. Here we utilize nuclear magnetic resonance (NMR) data of planar…
The electronic structure of the high-Tc cuprates is studied in terms of "large-U" and "small-U" orbitals. A striped structure and three types of quasiparticles are obtained, polaron-like "stripons" carrying charge, "svivons" carrying spin,…
Cuprate high temperature superconductors consist of two quasi-two-dimensional (2D) substructures: CuO2 superconducting layers and charge reservoir layers. The superconductivity is realized by charge transfer from the charge reservoir layers…
The concept of interface superconductivity was introduced over 50 years ago. Some of the greatest physicists of that time wondered whether a quasi-two-dimensional (2D) superconductor can actually exist, what are the peculiarities of 2D…
Although there is no complete theory of high temperature superconductivity, the importance of CuO$_2$ planes in cuprate superconductors is confirmed from both theory and experiments. Strong Coulomb repulsion between electrons on the CuO$_2$…
Single- and multi-band Hubbard models have been found to describe many of the complex phenomena that are observed in the cuprate and iron-based high-temperature superconductors. Simulations of these models therefore provide an ideal…
The nature of the effective interaction responsible for pairing in the high-temperature superconducting cuprates remains unsettled. This question has been studied extensively using the simplified single-band Hubbard model, which does not…
Numerous contemporary investigations in condensed matter physics are devoted to high temperature (high-$T_c$ ) cuprate superconductors. Despite its unique effulgence among research subjects, the enigma of the high-$T_c$ mechanism still…
Cuprate superconductors have long been known to exhibit an energy gap that persists high above the superconducting transition temperature ($T_c$). Debate has continued now for decades as to whether it is a precursor superconducting gap or a…
A comprehensive angle resolved photoemission spectroscopy study of the band structure in single layer cuprates is presented with the aim of uncovering universal trends across different materials. Five different hole- and electron-doped…
Potential application fields for cuprate high-temperature superconductors (HTS) and the status of respective projects are reviewed. The availability of a reliable and inexpensive cooling technique will be essential for a future broad…
A possible pairing mechanism for high temperature superconductivity in the cuprates is discussed.
Phase fluctuations of the superconducting order parameter play a larger role in the cuprates than in conventional BCS superconductors because of the low superfluid density of a doped insulator. In this paper, we analyze an XY model of…