A Criterion for the Critical Number of Fermions and Chiral Symmetry Breaking in Anisotropic QED(2+1)

By analyzing the strength of a photon-fermion coupling using basic scattering processes we calculate the effect of a velocity anisotropy on the critical number of fermions at which mass is dynamically generated in planar QED. This gives a quantitative criterion which can be used to locate a quantum critical point at which fermions are gapped and confined out of the physical spectrum in a phase diagram of various condensed matter systems. We also discuss the mechanism of relativity restoration within the symmetric, quantum-critical phase of the theory.Comment: To appear in Physical Review

Low-Magnetic Field Critical Behavior in Strongly Type-II Superconductors

A new description is proposed for the low-field critical behavior of type-II superconductors. The starting point is the Ginzburg-Landau theory in presence of an external magnetic field H. A set of fictitious vortex variables and a singular gauge transformation are used to rewrite a finite H Ginzburg-Landau functional in terms of a complex scalar field of zero average vorticity. The continuum limit of the transformed problem takes the form of an H = 0 Ginzburg-Landau functional for a charged field coupled to a fictitious `gauge' potential which arises from long wavelength fluctuations in the background liquid of field-induced vorticity. A possibility of a novel phase transition involving zero vorticity degrees of freedom and formation of a uniform condensate is suggested. A similarity to the superconducting [Higgs] electrodynamics and the nematic-smectic-A transition in liquid crystals is noted. The experimental situation is discussed.Comment: 19 pages RevTeX, one figure available by fax [email requests to [email protected]], to appear in Physical Review B

Density of states of a type-II superconductor in a high magnetic field: Impurity effects

We have calculated the density of states $N(\omega)$ of a dirty but homogeneous superconductor in a high magnetic field. We assume a dilute concentration of scalar impurities and find how $N(\omega)$ behaves as one crosses from the weak scattering to the strong scattering limit. At low energies, $N(\omega)\sim \omega ^2$ for small values of the impurity concentration and scattering strength. When the disorder becomes stronger than some critical value, a finite density of states is created at the Fermi surface. These results are a consequence of the gapless nature of the quasiparticle excitation spectrum in a high magnetic field.Comment: 20 pages in RevTeX, 4 figures, to appear in Phys. Rev. B (July 1, 1997

The effect of a velocity barrier on the ballistic transport of Dirac fermions

We propose a novel way to manipulate the transport properties of massless Dirac fermions by using velocity barriers, defining the region in which the Fermi velocity, $v_{F}$, has a value that differs from the one in the surrounding background. The idea is based on the fact that when waves travel accross different media, there are boundary conditions that must be satisfied, giving rise to Snell's-like laws. We find that the transmission through a velocity barrier is highly anisotropic, and that perfect transmission always occurs at normal incidence. When $v_{F}$ in the barrier is larger that the velocity outside the barrier, we find that a critical transmission angle exists, a Brewster-like angle for massless Dirac electrons.Comment: 4.3 pages, 5 figure

Flux tubes, visons, and vortices in spin-charge separated superconductors

The idea of spin-charge separation in cuprate superconductors has been recently energized by Senthil and Fisher who formulated a Z_2 gauge theory and, within its context, proposed a ``vison detection'' experiment as a test for topological order in a sample with multiply connected geometry. Here we show that the same experiment can be performed to test for the spin-charge separation in U(1) [but not in SU(2)] theory and argue that vortex core spectroscopy can in fact distinguish between the different symmetries of the fictitious gauge field.Comment: 3 pages, 1 ps figure. Invited talk at the 13th International Symposium on Superconductivity in Toky

Comment on "Algebraic Fermi Liquid from Phase Fluctuations: 'Topological' Fermions, Vortex 'Berryons,' and QED 3 Theory of Cuprate Superconductor" [2] (multiple letters)

In a recent Letter[1], Franz and Tesanovic predicted a Luttinger-like behavior in the pseudogap phase of under-doped cuprates

Critical fluctuations in superconductors and the magnetic field penetration depth

The superconducting transition is studied within the one-loop renormalization group in fixed dimension $D=3$ and at the critical point. A tricritical behavior is found, and for $\kappa > \kappa_c$, an attractive charged fixed point, distinct from that of a neutral superfluid. The critical exponents of the continuous transition are evaluated, and it is shown that the anomalous dimension of the gauge field equals unity. This implies the proportionality of the magnetic field penetration depth and the superconducting correlation length below the transition. The penetration depth exponent is nonclassical. We argue that it can not be extracted from the dual theory in a straightforward manner since it is not renormalized by fluctuations of the dual field.Comment: 12 pages, LaTex, two figures available upon reques

Magnetic field induced charge and spin instabilities in cuprate superconductors

A d-wave superconductor, subject to strong phase fluctuations, is known to suffer an antiferromagnetic instability closely related to the chiral symmetry breaking in (2+1)-dimensional quantum electrodynamics (QED3). On the basis of this idea we formulate a "QED3 in a box" theory of local instabilities of a d-wave superconductor in the vicinity of a single pinned vortex undergoing quantum fluctuations around its equilibrium position. As a generic outcome we find an incommensurate 2D spin density wave forming in the neighborhood of a vortex with a concomitant "checkerboard" pattern in the local electronic density of states, in agreement with recent neutron scattering and tunneling spectroscopy measurements.Comment: 4 pages REVTeX + 2 PostScript figures included in text. Version to appear in PRL (minor stylistic changes, references updated). For related work and info visit http://www.physics.ubc.ca/~fran

Chiral symmetry breaking in QED3{\rm QED}_{3} in presence of irrelevant interactions: a renormalization group study

Motivated by recent theoretical approaches to high temperature superconductivity, we study dynamical mass generation in three dimensional quantum electrodynamics ${\rm QED}_{3}$) in presence of irrelevant four-fermion quartic terms. The problem is reformulated in terms of the renormalization group flows of certain four-fermion couplings and charge, and then studied in the limit of large number of fermion flavors $N$. We find that the critical number of fermions $N_c$ below which the mass becomes dynamically generated depends continuously on a weak chiral-symmetry-breaking interaction. One-loop calculation in our gauge-invariant approach yields $N_{c0} = 6$ in pure ${\rm QED}_3$. We also find that chiral-symmetry-preserving mass cannot become dynamically generated in pure ${\rm QED}_{3}$.Comment: 7 pages, 7 figure