arXiv subjects

Chetan Nayak

Publications and source records attributed to Chetan Nayak.

154 records · Page 9Linked to original sources

arXiv1995

Quantum Numbers of Textured Hall Effect Quasiparticles

We propose a class of variational wave functions with slow variation in spin and charge density and simple vortex structure at infinity, which properly generalize both the Laughlin quasiparticles and baby Skyrmions. We argue that the spin of the corresponding quasiparticle has a fractional part related in a universal fashion to the properties of the bulk state, and propose a direct experimental test of this claim. We show that certain spin-singlet quantum Hall states can be understood as arising from primary polarized states by Skyrmion condensation.

cond-mat↗

arXiv1995

Spin Singlet Ordering Suggested by Repulsive Interactions

We consider a correlated wavefunction including particle-hole pairing at half a reciprocal lattice vector for itinerant electrons hopping on a square lattice in two dimensions and subject both to on-site and nearest-neighbor repulsion. We find, within mean field theory, that in a suitable range of parameters there is a tendency toward a novel form of ordering characterized by discrete symmetry breaking and a gap at the magnetic zone boundary, which supports hole-like semiconductor behavior near half filling despite an apparently normal Fermi surface. The effective quasiparticle couplings to phonons includes a significant d-wave piece, which plausibly leads to an especially robust tendency toward superconductivity.

cond-mat↗

arXiv1995

Spin-Singlet to Spin Polarized Phase Transition at $ν=2/3$: Flux-Trading in Action

We analyze the phase transition between spin-singlet and spin-polarized states which occurs at $ν=2/3$. The basic strategy is to use adiabatic flux-trading arguments to relate this transition to the analogous transition at $ν=2$. The transition is found to be similar to a transition in ferromagnets. In our analysis, we find two possible scenarios. In one, the transition is first-order, in agreement with experimental and numerical studies of the $ν=2/3$ transition. In the other, we find a second-order transition to a partially polarized state followed by a second-order transition to a fully polarized state. This picture is in qualitative agreement with experiments on the $ν=4/3$ state, the particle-hole conjugate of $ν=2/3$. We analyze the edge modes which propagate at the boundaries between regions of different phases and show that these do not support gapless excitations. Finally, we consider the possibility of a finite-temperature compressible state with a Fermi surface which would explain the non-zero $ρ_{xx}$ seen in experiments.

cond-mat↗

arXiv1995

Physical Properties of Metals from a Renormalization Group Standpoint

We derive the equilibrium and transport properties of metals using renormalization group equations and finite-size scaling. Particular attention is given to the well-known cases of Fermi and Luttinger liquids. An important subtlety is that the temperature dependence of many transport coefficients is determined by ``dangerous'' irrelevant operators. We also characterize violations of Fermi or Luttinger liquid behavior in terms of indices, analogous to the critical indices describing phase transitions. We briefly consider the normal-state properties of the cuprates from this standpoint.

cond-mat↗

arXiv1995

Quantum Numbers of Hall Effect Skyrmions

By carefully considering a family of wave functions for Skyrmions in simple quantum Hall states, whose members are labelled by a non-negative integer and which properly generalizes the traditional Laughlin quasiparticle, we argue that the spin of this particle has a fractional part related in a universal fashion to the properties of the bulk state, and propose a direct experimental test of this claim. We argue directly also for the fractional charge and fractional quantum statistics of these particles. We show that certain spin-singlet quantum Hall states can be understood as arising from primary polarized states by Skyrmion condensation.

cond-mat↗

arXiv1995

Quantum Hall States of High Symmetry

We identify some hidden symmetries of Chern-Simons theories, such as appear in the effective theory for quantized Hall states. This allows us to determine which filling fractions admit spin-singlet quantum Hall states. Our results shed some light on states already observed at $ν=2/3$, and transitions between them. We identify SU(2), or higher, symmetries of many additional states -- including spin-polarized states. Our symmetries classify low-lying excited states and may be of use in the construction of trial wavefunctions, but are typically not present in the edge theory, where they are lifted by non-universal couplings.

cond-mat↗

arXiv1995

``Space Time Aspects of Quasiparticle Propagation''

Highly correlated states of electrons are thought to produce quasiparticles with very unusual properties. Here we consider how these properties are manifested in space-time propagation. Specifically, we discuss how spin-charge separation is realized in a simple double-layer geometry, how mass renormalization affects time-of-flight in compressible Hall states, and how quantum drifts can reveal the effective charge, mass, and quantum statistics in incompressible Hall states. We also discuss the possibility of observing the effect of fractional statistics directly in scattering. Finally we propose that, as a result of incompressibility and the fundamental charge-flux relation, charged probes induce macroscopic, measurable rotation of Hall fluids.

cond-mat↗

arXiv1994

Renormalization Group Approach to Low Temperature Properties of a Non-Fermi Liquid Metal

We expand upon on an earlier renormalization group analysis of a non-Fermi liquid fixed point that plausibly govers the two dimensional electron liquid in a magnetic field near filling fraction $ν=1/2$. We give a more complete description of our somewhat unorthodox renormalization group transformation by relating both our field-theoretic approach to a direct mode elimination and our anisotropic scaling to the general problem of incorporating curvature of the Fermi surface. We derive physical consequences of the fixed point by showing how they follow from renormalization group equations for finite-size scaling, where the size may be set by the temperature or by the frequency of interest. In order fully to exploit this approach, it is necessary to take into account composite operators, including in some cases dangerous ``irrelevant'' operators. We devote special attention to gauge invariance, both as a formal requirement and in its positive role providing Ward identities constraining the renormalization of composite operators. We emphasize that new considerations arise in describing properties of the physical electrons (as opposed to the quasiparticles.) We propose an experiment which, if feasible, will allow the most characteristic feature of our results, that is

cond-mat↗

arXiv1994

Exclusion Statistics: Low-Temperature Properties, Fluctuations, Duality, Applications

We derive some physical properties of ideal assemblies of identical particles obeying generalized exclusion statistics. We discuss fluctuations, and in this connection point out a fundamental contrast to conventional quantum statistics. We demonstrate a duality relating the distribution of particles at statistics $g$ to the distribution of holes at statistics $1/g$. We suggest applications to Mott insulators.

cond-mat↗

arXiv1994

Non-Fermi Liquid Fixed Point in 2+1 Dimensions

We construct models of excitations about a Fermi surface that display calculable deviations from Fermi liquid behavior in the low-energy limit. They arise as a consequence of coupling to a Chern-Simons gauge field, whose fluctations are controlled through a ${1\over{k^x}}$ interaction. The Fermi liquid fixed point is shown to be unstable in the infrared for $x<1$, and an infrared-stable fixed point is found in a $(1-x)$-expansion, analogous to the $ε$-expansion of critical phenomena. $x=1$ corresponds to Coulomb interactions, and in this case we find a logarithmic approach to zero coupling. We describe the low-energy behavior of metals in the universality class of the new fixed point, and discuss its possible application to the compressible $ν={1\over2}$ quantum Hall state and to the normal state of copper-oxide superconductors.

cond-mat↗