Related papers: Four Last Conjectures
High temperature superconductivity in cuprate superconductors is generally considered to be generated from doping the Mott insulators. The fundamental nature of the doped parent compounds as well as the microscopic origin of electron…
Band theory and BCS theory are arguably the most successful theories of condensed matter physics. Yet, in a number of materials, in particular the high-temperature superconductors and the layered organic superconductors, they fail. In these…
The origin of strange metallic phase is shown to exist due to these two conditions---(i) the electrons are strongly interacting such that there are no band and Mott-Hubbard gaps, and (ii) the electronic energy levels are crossed in such a…
I survey theoretical advances in our understanding of the quantum phases and phase transitions of Mott insulators, and of allied conducting systems obtained by doping charge carriers. A number of new experimental examples of Mott insulators…
Starting with a minimal model for the CuO$_2$ planes with the on-site Hilbert space reduced to a charge triplet of the three effective valence centers [CuO$_4$]$^{7-,6-,5-}$ (nominally Cu$^{1+,2+,3+}$) with different conventional spin,…
The phase diagrams of quasi two-dimensional organic superconductors display a plethora of fundamental phenomena associated with strong electron correlations, such as unconventional superconductivity, metal-insulator transitions, frustrated…
The last 15 years have witnessed important progresses in our understanding of the mechanism of superconductivity in the high-$T_{c}$ cuprates. There is now strong evidence that the strange metal behavior is induced by the quantum critical…
The evolution of Ca$_{2-x}$Na$_{x}$CuO$_{2}$Cl$_{2}$ from Mott insulator to superconductor was studied using angle-resolved photoemission spectroscopy. By measuring both the excitations near the Fermi energy as well as non-bonding states,…
We develop a slave-boson theory for the t-J model at finite doping which respects an SU(2) symmetry -- a symmetry previously known to be important at half filling. The mean field phase diagram is found to be consistent with the phases…
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…
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…
Recent development in the physics of high-temperature cuprate superconductivity is reviewed, with special emphasis on the phenomena of unconventional and non-universal low-energy excitations of hole- and electron-type cuprate…
In conventional metal superconductors such as aluminum, the large number of weakly bounded Cooper pairs become phase coherent as soon as they start to form. The cuprate high critical temperature ($T_c$) superconductors, in contrast, belong…
The observations of quantum oscillations in overdoped cuprate superconductors were in agreement with a charge density contained in a cylindrical Fermi surface but the frequencies of lightly doped compounds were much smaller than expected.…
There are two seemingly unrelated puzzles about the cuprate superconductors. The first puzzle concerns the strong non-BCS behavior around $x_{c}$, the end point of the superconducting dome on the overdoped side, where the cuparte is…
The intrinsic instability of underdoped copper oxides towards inhomogeneous states is one of the central puzzles of the physics of correlated materials. The influence of the Mott physics on the doping-temperature phase diagram of copper…
The phase diagram of the cuprate superconductors continues to pose formidable scientific challenges. While these materials are typically viewed as doped Mott insulators, it is well known that they are Fermi liquids at high hole-dopant…
The strange metal phase of optimally and overdoped cuprates exhibits a number of anomalous transport properties: unsaturating linear T resistivity, distinct relaxation times for Hall angle and resistivity, temperature dependent anisotropic…
We propose that an extension of the exciton concept to doped Mott insulators offers a fruitful insight into challenging issues of the copper oxide superconductors. In our extension, new fermionic excitations called cofermions emerge in…
We examine a two-dimensional Fermi liquid with a Fermi surface which touches the Umklapp surface first at the 4 points $(\pm \pi/2, \pm \pi/2)$ as the electron density is increased. Umklapp processes at the 4 patches near $(\pm \pi/2,…