Itinerant and localized magnetism on the triangular lattice: sodium rich phases of Nax_xCoO2_2

We study the interplay between correlation, itinerant ferromagnetism and local moment formation on the electron doped triangular lattice of sodium cobaltates Na$_x$CoO$_2$. We find that strong correlation renormalizes the Stoner criterion and stabilizes the paramagnetic state for $x<x_c\simeq0.67$. For $x>x_c$, ferromagnetic (FM) order emerges. The enhanced Na dopant potential fluctuations play a crucial role in the sodium rich phases and lead to an inhomogeneous FM state, exhibiting nonmagnetic Co$^{3+}$ patches, antiferromagnetic (AF) correlated regions, and FM clusters with AF domains. Hole doping the band insulator at x=1 leads to the formation of local moments near the Na vacancies and AF correlated magnetic clusters. We explain recent observations by neutron, $\mu$SR, and NMR experiments on the evolution of the magnetic properties in the sodium rich phases.Comment: revtex4 file, 5 pages, 3 figures, published versio

Pseudogap, competing order and coexistence of staggered flux and d-wave pairing in high-temperature superconductors

We study the t-J-V model of a doped Mott insulator in connection to high-T_c superconductors. The nearest neighbor Coulomb interaction (V) is treated quantum mechanically on equal footing as the antiferromagnetic exchange interaction (J). Motivated by the SU(2) symmetry at half-filling, we construct a large-N theory which allows a systematic study of the interplay between staggered flux order and superconductivity upon doping. We solve the model in the large-N limit and obtain the ground state properties and the phase diagram as a function of doping. We discuss the competition and the coexistence of the staggered flux and the d-wave superconductivity in the underdoped regime and the disappearance of superconductivity in the overdoped regimeComment: 5 pages, 3 figures, published versio

Chern Fermi pocket, topological pair density wave, and charge-4e and charge-6e superconductivity in kagome superconductors

The recent discovery of novel charge density wave (CDW) and pair density wave (PDW) in kagom\'e lattice superconductors $A$V$_3$Sb$_5$ ($A=$ K, Rb, Cs) hints at unexpected time-reversal symmetry breaking correlated and topological states whose physical origin and broader implications are not understood. Here, we make conceptual advances toward a mechanism behind the striking observations and new predictions for novel macroscopic phase coherent quantum states. We show that the metallic CDW state with circulating loop currents is a doped orbital Chern insulator near van Hove filling. The emergent Chern Fermi pockets (CFPs) carry concentrated Berry curvature and orbital magnetic moment. We find that the pairing of electrons on the CFPs leads to a superconducting state with an emergent vortex-antivortex lattice and the formation of a complex triple-\textbf{Q} PDW. A plethora of correlated and topological states emerge, including a never-before-encountered chiral topological PDW superconductor, a loop-current pseudogap phase, and vestigial charge-4$e$ and charge-6$e$ superconductivity in staged melting of the vortex-antivortex lattice and hexatic liquid crystal. Our findings reveal previously unknown nature of the superconducting state of a current-carrying Chern metal, with broad implications for correlated and topological materials.Comment: 11 pages, 8 figures

Inhomogeneous states with checkerboard order in the t-J Model

We study inhomogeneous states in the t-J model using an unrestricted Gutzwiller approximation. We find that $pa\times pa$ checkerboard order, where $p$ is a doping dependent number, emerges from Fermi surface instabilities of both the staggered flux phase and the Fermi liquid state with realistic band parameters. In both cases, the checkerboard order develops at wave vectors $(\pm 2\pi/pa,0)$, $(0,\pm2\pi/pa)$ that are tied to the peaks of the wave-vector dependent susceptibility, and is of the Lomer-Rice-Scott type. The properties of such periodic, inhomogeneous states are discussed in connection to the checkerboard patterns observed by STM in underdoped cuprates.Comment: Published Versio