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This is an informal paper that contains a list of ``things we know'' and ``things we do not know'' in manganites. It is adapted from the conclusions chapter of a recent book by the author, {\it Nanoscale Phase Separation and Colossal…
A recent vast experimental and theoretical effort in manganites has shown that the colossal magnetoresistance effect can be understood based on the competition of charge-ordered and ferromagnetic phases. The general aspects of the…
The study of the manganese oxides, widely known as manganites, that exhibit the ``Colossal'' Magnetoresistance (CMR) effect is among the main areas of research within the area of Strongly Correlated Electrons. After considerable theoretical…
In this review, the present status of theories for manganites is discussed. The complex phase diagrams of these materials, with a variety of spin-charge-orbital ordering tendencies, is addressed using mean-field and Monte Carlo simulation…
In many quantum materials, strong electron correlations lead to the emergence of new states of matter. In particular, the study in the last decades of the complex phase diagram of high temperature superconducting cuprates highlighted…
Search for a new quantum state of matter emerging in a crystal is one of recent trends in condensed matter physics. For magnetic materials, geometrical frustration and high magnetic field are two key ingredients to realize it: a…
Hyperuniform states of matter are correlated systems that are characterized by an anomalous suppression of long-wavelength (i.e., large-length-scale) density fluctuations compared to those found in garden-variety disordered systems, such as…
Low-temperature properties of a crystal containing superconducting inclusions of two different materials have been studied. In the approximation that the size of inclusions is much smaller than the coherence length/penetration depth of the…
This paper reviews the new highly interdisciplinary research field studying the behavior of condensed matter systems exposed to radiation. The paper highlights several relevant examples of recent advances in the field and provides a roadmap…
The influence of quenched disorder on the competition between ordered states separated by a first-order transition is investigated. A phase diagram with features resembling quantum-critical behavior is observed, even using classical models.…
Soft condensed matter physics is the study of materials, such as fluids, liquid crystals, polymers, colloids, and emulsions, that are ``soft" to the touch. This article will review some properties, such as the dominance of entropy, that are…
In condensed matter systems, the atoms, electrons or spins can sometimes arrange themselves in ways that result in unexpected properties but that cannot be detected by conventional experimental probes. Several historical and contemporary…
The properties of phase-separated systems, e.g. manganites, close to a I order phase transition between charge-ordered insulator and ferromagnetic metal, are usually described by the percolation picture. We argue that the correlated…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
Ideas from quantum field theory and topology have proved remarkably fertile in suggesting new phenomena in the quantum physics of condensed matter. Here I'll supply some broad, unifying context, both conceptual and historical, for the…
The topic of the review is the application of new ideas of unconventional quantum states to the physics of condensed matter, in particular of solid state, in the context of modern field theory. A comparison is made with classical papers on…
Materials with interesting physical properties are often designed based on our understanding of the target physical effects. The physical properties can be either explicitly observed ("apparent") or concealed by the perceived symmetry…
We argue that the superconducting state found in high-$T_c$ cuprates is inhomogeneous with a corresponding inhomogeneous superfluid density. We introduce two classes of microscopic models which capture the magnetic and superconducting…
Significant advances in numerical techniques have enabled recent breakthroughs in the study of various properties of the Hubbard model - a seemingly simple, yet complex model of correlated electrons that has been a focus of study for more…
Superconductivity in the simple elements is of both technological relevance and fundamental scientific interest in the investigation of superconductivity phenomena. Recent advances in the instrumentation of physics under pressure have…