Theory of Underdoped Cuprates

We develop a slave-boson theory for the t-J model at finite doping which respects an SU(2) symmetry -- a symmetry previously known to be important at half filling. The mean field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contains d-wave superconductor, spin gap, strange metal, and Fermi liquid phases. The spin gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The electron spectral function shows small Fermi pockets at low doping which continuously evolve into the large Fermi surface at high doping concentrations.Comment: 4 pages, latex(revtex,epsf), 3 figure

Anomalous Hall Effect and Skyrmion Number in Real- and Momentum-space

We study the anomalous Hall effect (AHE) for the double exchange model with the exchange coupling $|J_H|$ being smaller than the bandwidth $|t|$ for the purpose of clarifying the following unresolved and confusing issues: (i) the effect of the underlying lattice structure, (ii) the relation between AHE and the skyrmion number, (iii) the duality between real and momentum spaces, and (iv) the role of the disorder scatterings; which is more essential, $\sigma_H$ (Hall conductivity) or $\rho_H$ (Hall resistivity)? Starting from a generic expression for $\sigma_H$, we resolve all these issues and classify the regimes in the parameter space of $J_H \tau$ ($\tau$: elastic-scattering time), and $\lambda_{s}$ (length scale of spin texture). There are two distinct mechanisms of AHE; one is characterized by the real-space skyrmion-number, and the other by momentum-space skyrmion-density at the Fermi level, which work in different regimes of the parameter space.Comment: 4 pages, 1 figure, REVTe

Quantum Orders and Symmetric Spin Liquids

A concept -- quantum order -- is introduced to describe a new kind of orders that generally appear in quantum states at zero temperature. Quantum orders that characterize universality classes of quantum states (described by {\em complex} ground state wave-functions) is much richer then classical orders that characterize universality classes of finite temperature classical states (described by {\em positive} probability distribution functions). The Landau's theory for orders and phase transitions does not apply to quantum orders since they cannot be described by broken symmetries and the associated order parameters. We find projective representations of symmetry groups (which will be called projective symmetry groups) can be used to characterize quantum orders. With the help of quantum orders and the projective symmetry groups, we construct hundreds of symmetric spin liquids, which have SU(2), U(1) or $Z_2$ gauge structures at low energies. Remarkably, some of the stable quantum phases support gapless excitations even without any spontaneous symmetry breaking. We propose that it is the quantum orders (instead of symmetries) that protect the gapless excitations and make algebraic spin liquids and Fermi spin liquids stable. Since high $T_c$ superconductors are likely to be described by a gapless spin liquid, the quantum orders and their projective symmetry group descriptions lay the foundation for spin liquid approach to high $T_c$ superconductors.Comment: 58 pages, RevTeX4 home page: http://dao.mit.edu/~we

Competitions of magnetism and superconductivity in FeAs-based materials

Using the numerical unrestricted Hartree-Fock approach, we study the ground state of a two-orbital model describing newly discovered FeAs-based superconductors. We observe the competition of a $(0, \pi)$ mode spin-density wave and the superconductivity as the doping concentration changes. There might be a small region in the electron-doping side where the magnetism and superconductivity coexist. The superconducting pairing is found to be spin singlet, orbital even, and mixed s$_{xy}$ + d$_{x^{2}-y^{2}}$ wave (even parity).Comment: 5 pages, 3 figure

Fermionic Chern-Simons theory for the Fractional Quantum Hall Effect in Bilayers

We generalize the fermion Chern-Simons theory for the Fractional Hall Effect (FQHE) which we developed before, to the case of bilayer systems. We study the complete dynamic response of these systems and predict the experimentally accessible optical properties. In general, for the so called $(m, m, n)$ states, we find that the spectrum of collective excitations has a gap, and the wave function has the Jastrow-Slater form, with the exponents determined by the coefficients $m$, and $n$. We also find that the $(m,m,m)$ states, {\it i.~e.~}, those states whose filling fraction is $1\over m$, have a gapless mode which may be related with the spontaneous appearance of the interlayer coherence. Our results also indicate that the gapless mode makes a contribution to the wave function of the $(m,m,m)$ states analogous to the phonon contribution to the wave function of superfluid $\rm{He}_4$. We calculate the Hall conductance, and the charge and statistics of the quasiparticles. We also present an $SU(2)$ generalization of this theory relevant to spin unpolarized or partially polarized single layers.Comment: 55 pages, Urbana Prepin

Mean-Field Description of Phase String Effect in the t−Jt-J Model

A mean-field treatment of the phase string effect in the $t-J$ model is presented. Such a theory is able to unite the antiferromagnetic (AF) phase at half-filling and metallic phase at finite doping within a single theoretical framework. We find that the low-temperature occurrence of the AF long range ordering (AFLRO) at half-filling and superconducting condensation in metallic phase are all due to Bose condensations of spinons and holons, respectively, on the top of a spin background described by bosonic resonating-valence-bond (RVB) pairing. The fact that both spinon and holon here are bosonic objects, as the result of the phase string effect, represents a crucial difference from the conventional slave-boson and slave-fermion approaches. This theory also allows an underdoped metallic regime where the Bose condensation of spinons can still exist. Even though the AFLRO is gone here, such a regime corresponds to a microscopic charge inhomogeneity with short-ranged spin ordering. We discuss some characteristic experimental consequences for those different metallic regimes. A perspective on broader issues based on the phase string theory is also discussed.Comment: 18 pages, five figure

Fermi Surface Evolution, Pseudo Gap and Stagger Gauge Field Fluctuation in Underdoped Cuprates

In the context of t-J model we show that in underdoped regime,beside the usual long wave length gauge field fluctuation, an additional low energy fluctuation, staggered gauge field fluctuation plays a crucial role in the evolution of Fermi surface(FS) as well as the line shape of spectral function for the cuprates. By including the staggered gauge field fluctuation we calculate the spectral function of the electrons by RPA(random phase approximation). The line shape of the spectral function near $(\pi,0)$ is very broad in underdoped case and is quite sharp in overdoped case. For the spectral function near $(0.5\pi,0.5\pi)$, the quasiparticle peaks are always very sharp in both underdoped and overdoped case. The temperature dependence of the spectral function is also discussed in our present calculation. These results fit well with the recent ARPES experiments. We also calculate the FS crossover from a small four segment like FS to a large continuous FS. The reason of such kind of FS crossover is ascribed to the staggered gauge field fluctuation which is strong in underdoped regime and becomes much weaker in overdoped regime. The pseudo gap extracted from the ARPES data can be also interpreted by the calculation.Comment: 4 pages,6 eps figures include

An SU(2) Formulation of the t-J model: Application to Underdoped Cuprates

We develop a slave-boson theory for the t-J model at finite doping which respect a SU(2) symmetry -- a symmetry previously known to be important at half filling. The mean field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contains d-wave superconductor, spin gap, strange metal, and Fermi liquid phases. The spin gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The physical electron spectral function shows small Fermi segments at low doping which continuously evolve into the large Fermi surface at high doping concentrations. The close relation between the SU(2) and the U(1) slave-boson theory is discussed. The low energy effective theory for the low lying fluctuations is derived, and new lying modes (which were over looked in the U(1) theory) are identified.Comment: 28 pages, 8 figures, RevTe

Low Energy Effective Action of Lightly Doped Two-Leg t-J Ladders

We propose a low energy effective theory of lightly doped two-leg t-J ladders with the help of slave fermion technique. The continuum limit of this model consists of two kinds of Dirac fermions which are coupled to the O(3) non-linear sigma model in terms of the gauge coupling with opposite sign of "charges". In addition to the gauge interaction, there is another kind of attractive force between these Dirac fermions, which arises from the short-ranged antiferromagnetic order. We show that the latter is essential to determine the low energy properties of lightly doped two-leg t-J ladders. The effective Hamiltonian we obtain is a bosonic Gaussian model and the boson field basically describes the particle density fluctuation. We also find two types of gapped spin excitations. Finally, we discuss the possible instabilities: charge density wave (CDW) and singlet superconductivity (SC). We find that the SC instability dominates in our approximation. Our results indicate that lightly doped ladders fall into the universality class of Luther-Emery model.Comment: 16 pages, Revtex, no figure

On the Electromagnetic Response of Charged Bosons Coupled to a Chern-Simons Gauge Field: A Path Integral Approach

We analyze the electromagnetic response of a system of charged bosons coupled to a Chern-Simons gauge field. Path integral techniques are used to obtain an effective action for the particle density of the system dressed with quantum fluctuations of the CS gauge field. From the action thus obtained we compute the U(1) current of the theory for an arbitrary electromagnetic external field. For the particular case of a homogeneous external magnetic field, we show that the quantization of the transverse conductivity is exact, even in the presence of an arbitrary impurity distribution. The relevance of edge states in this context is analyzed. The propagator of density fluctuations is computed, and an effective action for the matter density in the presence of a vortex excitation is suggested.Comment: LaTex file, 27 pages, no figure