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Electron pairing at low temperatures leads to superconductivity. A fundamental question is whether more complex states - characterized by order in four-electron composite objects, termed electron quadrupling or composite order - can exist…
Striped high-$T_{\rm c}$ superconductors such as La$_{2-y-x}$Nd$_{y}$Sr$_x$CuO$_4$ and La$_{2-x}$Ba$_{x}$CuO$_4$ near $x=1/8$ show a fascinating competition between spin and charge order and superconductivity. A theory for these systems…
Electronic charge order is a symmetry breaking state in high-$T_\mathrm{c}$ cuprate superconductors. In scanning tunneling microscopy, the detected charge-order-induced modulation is an electronic response of the charge order. For an…
Superconductivity, magnetic order, and quadrupolar order have been investigated in the filled skutterudite system Pr$_{1-x}$Nd$_{x}$Os$_4$Sb$_{12}$ as a function of composition $x$ in magnetic fields up to 9 tesla and at temperatures…
Trilayer nickelates, which exhibit a high degree of orbital polarization combined with an electron count (d8.67) corresponding to overdoped cuprates, have been identified as a promising candidate platform for achieving high-Tc…
The phenomena of superconductivity and charge density waves are observed in close vicinity in many strongly correlated materials. Increasing evidence from experiments and numerical simulations suggests both phenomena can also occur in an…
A higher angular momentum ($\ell =2$) $d$-density wave, a mixed triplet and a singlet, interestingly, admits skyrmionic textures. The Skyrmions carry charge $2e$ and can condense into a spin-singlet s-wave superconducting state. In…
Superstructure reflections due to the ordering of holes into stripes in La_(1.45)Nd_(0.4)Sr_(0.15)CuO_4 have been studied with high energy x-ray diffraction. These reflections have been observed clearly for the first time in a sample which…
Condensation of bosons in Bose-Einstein condensates or Cooper pairs in superconductors refers to a macroscopic occupation of a few single- or two-particle states. A condensate is called "fragmented" if not a single, but multiple states are…
Copper-oxide high TC superconductors possess a number of exotic orders co-existing with or proximal to superconductivity, whose quantum fluctuations may account for the unusual behaviors of the normal state, even affecting…
In two-dimensional superconductors with a Rashba-type spin-orbit coupling, it is known that an in-plane magnetic field can induce a helical superconducting (SC) state with a phase modulation $e^{i {\bf q}\cdot {\bf r}}$. Here, we…
Upon doping, Mott insulators often exhibit symmetry breaking where charge carriers and their spins organize into patterns known as stripes. For high-Tc superconducting cuprates, stripes are widely suspected to exist in a fluctuating form.…
Entanglement of charge orderings and other electronic orders such as superconductivity is in the core of challenging physics issues of complex materials including high temperature superconductivity. Here, we report on the observation of a…
In this paper we show, using scanning tunneling spectroscopy (STS), the existence of static striped density of electronic states in nearly optimally doped $\rm Bi_2Sr_2CaCu_2O_{8+\delta}$ in zero field. The observed modulation is strongest…
Superconductors are a striking example of a quantum phenomenon in which electrons move coherently over macroscopic distances without scattering. The high-temperature superconducting oxides(cuprates) are the most studied class of…
Spin- and charge- stripe order has been extensively studied in the superconducting cuprates, among which underdoped ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ (LSCO) is an archetype with static spin stripes at low…
The discovery of multiple charge-density-wave (CDW) orders in superconducting cuprates and Kagome CsV3Sb5 has offered a unique milieu for studying the interplay of CDW and superconductivity and altered our perspective on their nature. Here,…
The experimentally measured phase diagram of cuprate superconductors in the temperature-applied magnetic field plane illuminates key issues in understanding the physics of these materials. At low temperature, the superconducting state gives…
In those cases where charge stripe order has been observed in cuprates, the crystal structure is such that the average rotational symmetry of the CuO2 planes is reduced from four-fold to two-fold. As a result, one could argue that the…
Switching on interchain coupling in a system of one-dimensional strongly interacting chains often leads to an ordered state. Quite generally, there is a competition between an insulating charge-density-wave and a superconducting state. In…