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The discovery of high-temperature superconductivity in Fe-based compounds [1,2] has triggered numerous investigations on the interplay between superconductivity and magnetism [3] and, more recently, on the enhancement of transition…
In several families of iron-based superconducting materials, a d-wave pairing instability may compete with the leading s-wave instability. Here we show that when both states have comparable free energies, superconducting and nematic degrees…
In one dimension the coupling of electrons to phonons leads to a transition from a metallic to a Peierls distorted insulated state if the coupling exceeds a critical value. On the other hand, in two dimensions the electron-phonon…
Motivated by the recent scanning tunneling microscopy (STM) and neutron scattering experiments, we investigate various charge density wave orders coexisting with superconductivity in the cuprate superconductors. The explicit expressions of…
We introduce and study an XY-type model of thermal and quantum phase fluctuations in a two-dimensional correlated lattice d-wave superconductor based on the QED3 effective theory of high temperature superconductors. General features of and…
An indispensable ingredient for pair density wave (PDW) superconductivity is the presence of an attractive pairing interaction at finite momentum. Here, we show how this condition can be met with straightforward electron-density…
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…
The nature of unconventional superconductivity is intimately linked to the microscopic nature of the pairing interactions. In this work, motivated by cubic heavy fermion compounds with embedded multipolar moments, we theoretically…
We present a calculation of a 'modulated' superconducting state in iron-selenide superconductors. The zero-momentum $d-$wave pairing breaks the translational symmetry of the conventional BaFe$_2$Se$_2$-like crystal of $I4/mmm$ space group.…
Pair spin-orbit interaction can emerge in strongly-interacting systems characterized by a large spin-orbit coupling. Here we study the role of this interaction in stabilizing ordered and unconventional superconducting phases. We find that,…
We review the physics of pair density wave (PDW) superconductors. We begin with a macroscopic description that emphasizes order induced by PDW states, such as charge density wave, and discuss related vestigial states that emerge as a…
In contrast to bulk FeSe, which exhibits nematic order and low temperature superconductivity, atomic layers of FeSe reverse the situation, having high temperature superconductivity appearing alongside a suppression of nematic order. To…
The most profound effect of disorder on electronic systems is the localization of the electrons transforming an otherwise metallic system into an insulator. If the metal is also a superconductor then, at low temperatures, disorder can…
Some of the iron pnictides show coexisting superconductivity and spin-density-wave order. We study the superconducting pairing instability in the spin-density-wave phase. Assuming that the pairing interaction is due to spin fluctuations, we…
A very fundamental and unconventional characteristic of superconductivity in iron-based materials is that it occurs in the vicinity of {\it two} other instabilities. Apart from a tendency towards magnetic order, these Fe-based systems have…
I present a simple analytical model describing the normal state of a superconductor with a pseudogap in the density of states, such as in underdoped cuprates. In nearly two-dimensional systems, where the superconducting transition…
By analyzing simple models of fermions in lattice potentials we argue that the zero-temperature pairing instability of any ideal band-insulator occurs at a finite momentum. The resulting supersolid state is known as "pair density wave". The…
Bulk FeSe is a special iron-based material in which superconductivity emerges inside a well-developed nematic phase. We present a microscopic model for this nematic superconducting state, which takes into account the mixing between $s-$wave…
Order-disorder transitions take place in many physical systems, but observing them in detail in real materials is difficult. In two- or quasi-two-dimensional systems, the transition has been studied by computer simulations and…
The interplay between magnetism and superconductivity is one of the dominant themes in the study of unconventional superconductors, such as high-Tc cuprates, iron pnictides and heavy fermions. In such systems, the same d- or f-electrons…