Doping a Mott Insulator: Physics of High Temperature Superconductivity

This article reviews the effort to understand the physics of high temperature superconductors from the point of view of doping a Mott insulator. The basic electronic structure of the cuprates is reviewed, emphasizing the physics of strong correlation and establishing the model of a doped Mott insulator as a starting point. A variety of experiments are discussed, focusing on the region of the phase diagram close to the Mott insulator (the underdoped region) where the behavior is most anomalous. We introduce Anderson's idea of the resonating valence bond (RVB) and argue that it gives a qualitative account of the data. The importance of phase fluctuation is discussed, leading to a theory of the transition temperature which is driven by phase fluctuation and thermal excitation of quasiparticles. We then describe the numerical method of projected wavefunction which turns out to be a very useful technique to implement the strong correlation constraint, and leads to a number of predictions which are in agreement with experiments. The remainder of the paper deals with an analytic treatment of the t-J model, with the goal of putting the RVB idea on a more formal footing. The slave-boson is introduced to enforce the constraint of no double occupation. The implementation of the local constraint leads naturally to gauge theories. We give a rather thorough discussion of the role of gauge theory in describing the spin liquid phase of the undoped Mott insulator. We next describe the extension of the SU(2) formulation to nonzero doping. We show that inclusion of gauge fluctuation provides a reasonable description of the pseudogap phase.Comment: 69 pages, 36 fgiures. Submitted to Rev. Mod. Phy

Spin-triplet p-wave pairing in a 3-orbital model for iron pnictide superconductors

We examine the possibility that the superconductivity in the newly discovered FeAs materials may be caused by the Coulomb interaction between d-electrons of the iron atoms. We find that when the Hund's rule ferromagnetic interaction is strong enough, the leading pairing instability is in spin-triplet p-wave channel in the weak coupling limit. The resulting superconducting gap has nodal lines on the 3D Fermi surfaces. The k dependent hybridization of several orbitals around a Fermi pocket is the key for the appearance of the spin-triplet p-wave pairing.Comment: 6 pages, 4 figure

Spontaneous spin ordering of Dirac spin liquid in a magnetic field

The Dirac spin liquid was proposed to be the ground state of the spin-1/2 Kagome antiferromagnets. In a magnetic field $B$, we show that the state with Fermi pocket is unstable to the Landau level (LL) state. The LL state breaks the spin rotation around the axis of the magnetic field. We find that the LL state has an in-plane 120$^{\circ}$ $q=0$ magnetization $M$ which scales with the external field $M\sim B^{\alpha}$, where $\alpha$ is an intrinsic calculable universal number of the Dirac spin liquid. We discuss the related experimental implications which can be used to detect the possible Dirac spin liquid phase in Herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$.Comment: rewritten for clarit

Spinon Fermi surface in a cluster Mott insulator model on a triangular lattice and possible application to 1T-TaS2_2

1T-TaS$_2$ is a cluster Mott insulator on the triangular lattice with 13 Ta atoms forming a star of David cluster as the unit cell. We derive a two dimensional XXZ spin-1/2 model with four-spin ring exchange term to describe the effective low energy physics of a monolayer 1T-TaS$_2$, where the effective spin-1/2 degrees of freedom arises from the Kramers degenerate spin-orbital states on each star of David. A large scale density matrix renormalization group simulation is further performed on this effective model and we find a gapless spin liquid phase with spinon Fermi surface at moderate to large strength region of four-spin ring exchange term. All peaks in the static spin structure factor are found to be located on the "$2k_F$" surface of half-filled spinon on the triangular lattice. Experiments to detect the spinon Fermi surface phase in 1T-TaS$_2$ are discussed.Comment: 5+11 pages, 4+13 figure

Doped Kagome System as Exotic Superconductor

A Chern--Simons theory for the doped spin-1/2 kagom\'e system is constructed, from which it is shown that the system is an exotic superconductor that breaks time-reversal symmetry. It is also shown that the system carries minimal vortices of flux $hc/4e$ (as opposed to the usual $hc/2e$ in conventional superconductors) and contains fractional quasiparticles (including fermionic quasiparticles with \emph{semionic} mutual statistics and spin-1/2 quasiparticles with \emph{bosonic} self-statistics) in addition to the usual spin-1/2 fermionic Bougoliubov quasiparticle. Two Chern--Simons theories--one with an auxiliary gauge field kept and one with the auxiliary field and a redundant matter field directly eliminated--are presented and shown to be consistent with each other.Comment: 13 pages, 7 figures and 1 table; Extensive revision and expansion, including a new section on classifying the quasiparticles and a new section on an alternative Chern--Simons Lagrangia

Theory of Quasi-Particles in the Underdoped High Tc Superconducting State

The microscopic theory of superconducting (SC) state in the SU(2) slave-boson model is developed. We show how the pseudogap and Fermi surface (FS) segments in the normal state develop into a d-wave gap in the superconducting state. Even though the superfluid density is of order x (the doping concentration), the physical properties of the low lying quasiparticles are found to resemble those in BCS theory. Thus the microscopic theory lay the foundation for our earlier phenomenological discussion of the unusual SC properties in the underdoped cuprates.Comment: 4 pages in RevTeX, 1 figure in eps, revised versio

Staggered-vorticity correlations in a lightly doped t-J model: a variational approach

We report staggered vorticity correlations of current in the d-wave variational wave function for the lightly-doped t-J model. Such correlations are explained from the SU(2) symmetry relating d-wave and staggered-flux mean-field phases. The correlation functions computed by the variational Monte Carlo method suggest that pairs are formed of holes circulating in opposite directions.Comment: ReVTeX, 4 pages, 3 figure