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The phase diagram of the cuprate superconductors has posed a formidable scientific challenge for more than three decades. This challenge is perhaps best exemplified by the need to understand the normal-state charge transport as the system…

High temperature superconductivity in cuprates arises from doping a parent Mott insulator by electrons or holes. A central issue is how the Mott gap evolves and the low-energy states emerge with doping. Here we report angle-resolved…

Within the kinetic energy driven superconducting mechanism, the interplay between the single particle coherence and superconducting instability in doped cuprates is studied. The superconducting transition temperature increases with…

The extreme variability of observables across the phase diagram of the cuprate high temperature superconductors has remained a profound mystery, with no convincing explanation of the superconducting dome. While much attention has been paid…

The cuprate high-temperature superconductors are among the most intensively studied materials, yet essential questions regarding their principal phases and the transitions between them remain unanswered. Generally thought of as doped…

Strongly correlated materials often undergo a Mott metal-insulator transition, which is tipically first-order, as a function of control parameters like pressure. Upon doping, rich phase diagrams with competing instabilities are found. Yet,…

High-temperature superconductivity in the copper-oxide ceramics remains an unsolved problem because we do not know what the propagating degrees of freedom are in the normal state. As a result, we do not know what are the weakly interacting…

The experimentally measured phase diagram of cuprate superconductors in the temperature-applied magnetic field plane illuminates key issues in understanding the physics of these materials. At low temperature, the superconducting state gives…

An understanding of the anomalous charge dynamics in the high-Tc cuprates is obtained based on a model study of doped Mott insulators. The high-temperature optical conductivity is found to generally have a two-component structure: a Drude…

An intricate interplay between superconductivity, pseudogap and Mott transition, either bandwidth driven or doping driven, occurs in materials. Layered organic conductors and cuprates offer two prime examples. We provide a unified…

Understanding the interplay between charge order (CO) and other phenomena (e.g. pseudogap, antiferromagnetism, and superconductivity) is one of the central questions in the cuprate high-temperature superconductors. The discovery that…

Identification of the electronic state that appears upon doping a Mott insulator is important to understand the physics of cuprate high-temperature superconductors. Recent scanning tunneling microscopy of cuprates provides evidence that a…

A central question in the high temperature cuprate superconductors is the fate of the parent Mott insulator upon charge doping. Here we use scanning tunneling microscopy to investigate the local electronic structure of lightly doped cuprate…

Copper oxide high temperature superconductors universally exhibit multiple forms of electronically ordered phases that break the native translational symmetry of the CuO2 planes. The interplay between these orders and the superconducting…

In the last few years charge density waves (CDWs) have been ubiquitously observed in high-temperature superconducting cuprates and are now the most investigated among the competing orders in the still hot debate on these systems. A wealth…

The copper-oxide based high temperature superconductors have complex phase diagrams with multiple ordered phases. It even appears that the highest superconducting transition temperatures for certain cuprates are found in samples which…

For doped two-dimensional Mott insulators in their normal state, the challenge is to understand the evolution from a conventional metal at high doping to a strongly correlated metal near the Mott insulator at zero doping. To this end, we…

The standard theory of metals, Fermi liquid theory, hinges on the key assumption that although the electrons interact, the low-energy excitation spectrum stands in a one-to-one correspondence with that of a non-interacting system. In the…

While the phase diagrams of the one- and multi-orbital Hubbard model have been well studied, the physics of real Mott insulators is often much richer, material dependent, and poorly understood. In the prototype Mott insulator…

Charge density waves are a common occurrence in all families of high critical temperature superconducting cuprates. Although consistently observed in the underdoped region of the phase diagram and at relatively low temperatures, it is still…