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

Chiral Solitons in a Current Coupled Schr\"odinger Equation With Self Interaction

Recently non-topological chiral soliton solutions were obtained in a derivatively coupled non-linear Schr\"odinger model in 1+1 dimensions. We extend the analysis to include a more general self-coupling potential (which includes the previous cases) and find chiral soliton solutions. Interestingly even the magnitude of the velocity is found to be fixed. Energy and U(1) charge associated with this non-topological chiral solitons are also obtained.Comment: 8 pages, no figure, to appear in Phys. Rev.

Field Theoretical Description of Quantum Hall Edge Reconstruction

We propose a generalization of the chiral Luttinger liquid theory to allow for a unified description of quantum Hall edges with or without edge reconstruction. Within this description edge reconstruction is found to be a quantum phase transition in the universality class of one-dimensional dilute Bose gas transition, whose critical behavior can be obtained exactly. At principal filling factors $\nu=1/m$, we show the additional edge modes due to edge reconstruction modifies the point contact tunneling exponent in the low energy limit, by a small and non-universal amount.Comment: 4 pages with 1 ps figure embedde

Non-equilibrium tunneling into general quantum Hall edge states

In this paper we formulate the theory of tunneling into general Abelian fractional quantum Hall edge states. In contrast to the simple Laughlin states, a number of charge transfer processes must be accounted for. Nonetheless, it is possible to identify a unique value corresponding to dissipationless transport as the asymptotic large-$V$ conductance through a tunneling junction, and find fixed points (CFT boundary conditions) corresponding to this value. The symmetries of a given edge tunneling problem determine the appropriate boundary condition, and the boundary condition determines the strong-coupling operator content and current noise.Comment: 6 pages, 3 figures; published versio

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

Edge excitations and Topological orders in rotating Bose gases

The edge excitations and related topological orders of correlated states of a fast rotating Bose gas are studied. Using exact diagonalization of small systems, we compute the energies and number of edge excitations, as well as the boson occupancy near the edge for various states. The chiral Luttinger-liquid theory of Wen is found to be a good description of the edges of the bosonic Laughlin and other states identified as members of the principal Jain sequence for bosons. However, we find that in a harmonic trap the edge of the state identified as the Moore-Read (Pfaffian) state shows a number of anomalies. An experimental way of detecting these correlated states is also discussed.Comment: Results extended to larger systems. Improved presentatio

Anomalous Exponent of the Spin Correlation Function of a Quantum Hall Edge

The charge and spin correlation functions of partially spin-polarized edge electrons of a quantum Hall bar are studied using effective Hamiltonian and bosonization techniques. In the presence of the Coulomb interaction between the edges with opposite chirality we find a different crossover behavior in spin and charge correlation functions. The crossover of the spin correlation function in the Coulomb dominated regime is characterized by an anomalous exponent, which originates from the finite value of the effective interaction for the spin degree of freedom in the long wavelength limit. The anomalous exponent may be determined by measuring nuclear spin relaxation rates in a narrow quantum Hall bar or in a quantum wire in strong magnetic fields.Comment: 4 pages, Revtex file, no figures. To appear in Physical Revews B, Rapid communication

Dynamics of Dissipative Quantum Hall Edges

We examine the influence of the edge electronic density profile and of dissipation on edge magnetoplasmons in the quantum Hall regime, in a semiclassical calculation. The equilibrium electron density on the edge, obtained using a Thomas-Fermi approach, has incompressible stripes produced by energy gaps responsible for the quantum Hall effect. We find that these stripes have an unobservably small effect on the edge magnetoplasmons. But dissipation, included phenomenologically in the local conductivity, proves to produce significant oscillations in the strength and speed of edge magnetoplasmons in the quantum Hall regime.Comment: 23 pages including 10 figure

Periphery deformations and tunneling at correlated quantum-Hall edges

We argue that, at any filling factor, correlated quantum-Hall systems possess a set of chiral boson excitations which are generated by electronically rigid deformations of the system's periphery. We submit that tunneling electrons can be accommodated, at low energies, in these systems only by periphery-deformation excitations. This property would explain the recent observation of a tunneling density of states at the edge which does not exhibit a strong dependence on the occurrence or absence of the quantum Hall effect and has a power-law dependence on energy with exponent (inverse filling factor)-1.Comment: 5 pages, RevTex, final version, to appear in PR