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The role of charge order in the phase diagram of high temperature cuprate superconductors has been recently re-emphasized by the experimental discovery of an incipient bi-directional charge density wave (CDW) phase in a class of underdoped…

We consider a simple model of a quasi-one-dimensional conductor in which two order parameters (OP) may coexist, i.e., the superconducting OP $\Delta$ and the OP $W$ that characterizes the amplitude of a charge-density wave (CDW). In the…

Coexisting orders are key features of strongly correlated materials and underlie many intriguing phenomena from unconventional superconductivity to topological orders. Here, we report the coexistence of two interacting charge-density-wave…

We derive the polarizability of an electron system in (i) the superconducting phase, with d-wave symmetry, (ii) the pseudogap regime, within the precursor pairing scenario, and (iii) the d-density-wave (dDW) state, characterized by a d-wave…

The entanglement of charge density wave (CDW), superconductivity, and topologically nontrivial electronic structure has recently been discovered in the kagome metal $A$V$_3$Sb$_5$ ($A$ = K, Rb, Cs) family. With high-resolution…

It is now well established that superconducting cuprates support a charge density wave state in the so-called underdoped region of their phase diagram. We investigate the possibility of charge order in the square-lattice Hubbard model, both…

The charge-density-wave (CDW) instability in the underdoped, pseudogap part of the cuprate phase diagram has been a major recent research focus, yet measurements of dynamic, energy-resolved CDW correlations are still in their infancy. We…

Charge density waves (CDWs) appear in numerous condensed matter platforms, ranging from high-Tc superconductors to quantum Hall systems. Despite such ubiquity, there has been a lack of direct experimental study on boundary states that can…

We discuss the problem of competition between a superconducting (SC) ordered state with a charge density wave (CDW) state in stripe phases of high $T_c$ superconductors. We consider an effective model for each stripe motivated by studies of…

We study two effective models developed for description of superconductors with short-coherence length: (i) the extended Hubbard model with on-site attraction and intersite repulsion, (ii) the model of hard-core charged bosons on a lattice.…

Nonmagnetic kagome metals and superconductors AV3Sb5 (A = K, Rb, Cs) host unconventional charge density wave (CDW) and superconducting (SC) phases accompanied by multiple electronic symmetry breaking. Due to the centrosymmetric crystal…

We shall review our recent works on d-wave density wave (dDW) and gossamer superconductivity (i.e. d-wave superconductivity in the presence of dDW) in high-T$_{c}$ cuprates and CeCoIn$_{5}$. a) We show that both the giant Nernst effect and…

Although charge density wave (CDW) correlations appear to be a ubiquitous feature of the superconducting cuprates, their disparate properties suggest a crucial role for coupling or pinning of the CDW to lattice deformations and disorder.…

BaNi$_{2}$As$_{2}$ is a non-magnetic analogue of BaFe$_{2}$As$_{2}$, the parent compound of a prototype pnictide high-temperature superconductor, displaying superconductivity already at ambient pressure. Recent diffraction studies…

Two-dimensional (2D) materials have become a fertile playground for the exploration and manipulation of novel collective electronic states. Recent experiments have unveiled a variety of robust 2D orders in highly-crystalline materials…

We show that twisted interfaces between superconductors can serve as a phase-sensitive platform for the detection and characterization of pair density waves (PDW). In the presence of an in-plane magnetic field, the critical Josephson…

The nature of superconductivity in BiS$_2$-based superconductors has been controversial while ab-initio calculations proposed this system in close proximity to a charge-density-wave (CDW) phase. Using high-energy high-flux X-ray…

We study the physical property of pair density wave (PDW) and fluctuating PDW, and use it to build an effective theory of the strongly interacting pseudogap phase in cuprate high temperature superconductors. In Chapter2, we study how…

Superconductivity appears in the cuprates when a spin order is destroyed, while the role of charge is less known. Recently, charge density wave (CDW) was found below the superconducting dome in YBa$_2$Cu$_3$O$_y$ when a high magnetic field…

In the presence of multiple bands, well-known electronic instabilities may acquire new complexity. While multiband superconductivity is the subject of extensive studies, the possibility of multiband charge density waves (CDWs) has been…