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High-temperature superconductivity in the iron-based materials emerges from, or sometimes coexists with, their metallic or insulating parent compound states. This is surprising since these undoped states display dramatically different…
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…
Many-body states described by a Schr\"{o}dinger equation include states of overlapping waves of non-vanishing interaction energies. These peculiar states formed in many-body transitions remain in asymptotic regions, and lead a new component…
We propose a scenario for superconductivity at strong electron-electron attractive interaction, in the case when the increase of the interaction strength promotes the nucleation of the local Cooper pairs and forms a state with a spatially…
The correlations in the ground state of interacting electrons in a two-dimensional quantum dot in a high magnetic field are known to undergo a qualitative change from liquid-like to crystal-like as the total angular momentum becomes large.…
We solve the problem of fermionic pairing mediated by a massless boson in the limit of large coupling constant. At weak coupling, the transition temperature is exponentially small and superconductivity is robust against phase fluctuation.…
Complex phase diagrams are generic feature of quantum materials that display high temperature superconductivity. In addition to d-wave superconductivity (or other unconventional states), these phase diagrams typically include various forms…
One view of the cuprate high-transition temperature (high-Tc) superconductors is that they are conventional superconductors where the pairing occurs between weakly interacting quasiparticles, which stand in one-to-one correspondence with…
The behaviour of electrons in solids is remarkably well described by Landau's Fermi-liquid theory, which says that even though electrons in a metal interact they can still be treated as well-defined fermions, called ``quasiparticles''. At…
Correlated electron states are at the root of many important phenomena including unconventional superconductivity (USC), where electron-pairing arises from repulsive interactions. Computing the properties of correlated electrons, such as…
We discuss the possibility that the electron may be fractionalized in some quantum phases of matter in two or higher dimensions. We review the theory of such phases, and show that their effective theory is a $Z_2$ gauge theory. These phases…
A field theory is proposed where the regular fermionic matter and the dark fermionic matter can be different states of the same "primordial" fermion fields. In regime of the fermion densities typical for normal particle physics, the…
We calculate the damping of excitations due to four-fermionic interaction in the case of two-dimensional superconductor with nodes in the spectrum. At zero temperature and low frequencies it reveals gapless $\omega^3$ behavior at the nodal…
A model of a strongly correlated electron liquid based on the fermion condensation (FC) is applied to the consideration of high temperature superconductors in its superconducting and normal states. Within our model the appearance of FC…
We investigate the possibility of the emergence of ultra-complex conductivity diagrams in the nearly free electron approximation for metals with cubic symmetry. Estimates show that the emergence of such diagrams requires the Fermi level to…
Based on experimental results and our previous theoretical work, a microscopic theory of high temperature superconductivity is conjectured. In this conjecture, superconducting and antiferromagnetic long-range orders are driven by interlayer…
A general quasi-phenomenological theory that describes phases and phase transitions of ferromagnetic superconductors with spin-triplet electron Cooper pairing is presented. The theory is based on extended Ginzburg-Landau expansion in powers…
In the present article we discuss theoretically the emergence of superconductivity in field cooled $FeCr_2S_4$. The chromium electrons form a triplet $t_{2g}$ states and due to antiferromagnetic exchange with the iron spins have Zeeman…
The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to…
The normal state behaviour of the density of states of the electrons described by the BOSON - FERMION model for Bose-Einstein condensation driven superconductivity is characterized by the appearence of a pseudogap which developes into a…