Mottness collapse and statistical quantum criticality

We forward here the case that the anomalous electron states found in cuprate superconductors and related systems are rooted in a deeply non-classical fermion sign structure. The collapse of Mottness as advocated by Phillips and supported by recent DCA results on the Hubbard model is setting the necessary microscopic conditions. The crucial insight is due to Weng who demonstrated that in the presence of Mottness the fundamental workings of quantum statistics changes and we will elaborate on the effects of this Weng statistics with an emphasis on characterizing these further using numerical methods. The pseudogap physics of the underdoped regime appears as a consequence of the altered statistics and the profound question is how to connect this by a continuous quantum phase transition to the overdoped regime ruled by normal Fermi-Dirac statistics. Proof of principle follows from Ceperley's constrained path integral formalism where states can be explicitly constructed showing a merger of Fermi-Dirac sign structure and scale invariance of the quantum dynamics.Comment: 27 pages, 4 figures, submitted to theme issue of Phil. Trans. R. Soc.

Effect of inter-edge Coulomb interactions on transport through a point contact in a \nu = 5/2 quantum Hall state

We study transport across a point contact separating two line junctions in a \nu = 5/2 quantum Hall system. We analyze the effect of inter-edge Coulomb interactions between the chiral bosonic edge modes of the half-filled Landau level (assuming a Pfaffian wave function for the half-filled state) and of the two fully filled Landau levels. In the presence of inter-edge Coulomb interactions between all the six edges participating in the line junction, the stable fixed point corresponds to a point contact which is neither fully opaque nor fully transparent. Remarkably, this fixed point represents a situation where the half-filled level is fully transmitting, while the two filled levels are completely backscattered; hence the fixed point Hall conductance is given by G_H = {1/2} e^2/h. We predict the non-universal temperature power laws by which the system approaches the stable fixed point from the two unstable fixed points corresponding to the fully connected case (G_H = {5/2} e^2/h) and the fully disconnected case (G_H = 0).Comment: 6 pages, 3 figures; made several changes -- this is the published versio

Long tunneling contact as a probe of fractional quantum Hall neutral edge modes

We study the tunneling current between edge states of quantum Hall liquids across a single long contact region, and predict a resonance at a bias voltage set by the scale of the edge velocity. For typical devices and edge velocities associated with charged modes, this resonance occurs outside the physically accessible bias domain. However, for edge states that are expected to support neutral modes, such as the $\nu={2/3}$, and $\nu={5/2}$ Pfaffian and anti-Pfaffian states, the neutral velocity can be orders of magnitude smaller than the charged mode and if so the resonance would be accessible. Therefore, such long tunneling contacts can resolve the presence of neutral edge modes in certain quantum Hall liquids.Comment: 5+ pages, 2 figures; v2 expanded versio

Inequivalent classes of interference experiments with non-abelian anyons

We present a theoretical analysis of inequivalent classes of interference experiments with non-abelian anyons using an idealized Mach-Zender type interferometer. Because of the non-abelian nature of the braid group action one has to distinguish the different possibilities in which the experiment can be repeated, which lead to different interference patterns. We show that each setup will, after repeated measurement, lead to a situation where the two-particle (or multi-particle) state gets locked into an eigenstate of some well defined operator. Also the probability to end up in such an eigenstate is calculated. Some representative examples are worked out in detail

Observing the origin of superconductivity in quantum critical metals

Despite intense efforts during the last 25 years, the physics of unconventional superconductors, including the cuprates with a very high transition temperature, is still a controversial subject. It is believed that superconductivity in many of these strongly correlated metallic systems originates in the physics of quantum phase transitions, but quite diverse perspectives have emerged on the fundamentals of the electron-pairing physics, ranging from Hertz style critical spin fluctuation glue to the holographic superconductivity of string theory. Here we demonstrate that the gross energy scaling differences that are behind these various pairing mechanisms are directly encoded in the frequency and temperature dependence of the dynamical pair susceptibility. This quantity can be measured directly via the second order Josephson effect and it should be possible employing modern experimental techniques to build a `pairing telescope' that gives a direct view on the origin of quantum critical superconductivity.Comment: 19 pages, 9 figures; minor changes in the experimental part; added a new appendix section calculating the pair susceptibility of marginal Fermi liqui

Edge tunneling and transport in non-abelian fractional quantum Hall systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 115-121).Several aspects of tunneling at the edge of a fractional quantum Hall (FQH) state are studied. Most examples are given for the non- abelian filling fraction ? = 5 2 Moore-Read Pfaffian state. For tunneling between opposite edges of an abelian fractional quantum Hall state at a quantum point contact, the perturbative calculation of tunneling current, conductance, and current noise, as a function of finite bias and temperature, is reviewed. We extend this formalism to include non-abelian FQH states as well. The crucial ingredient is conformal block decomposition. We argue the validity of perturbation theory to arbitrary order. A double point contact interferometer is considered for the v = 5/2 FQH state, for which a vanishing interference pattern in the tunneling current was predicted when a non-abelian quasiparticle is trapped inside the interferometer. We confirm this result in a dynamical edge calculation. We show how interference can be restored through a higher order tunneling process, which exchanges a charge neutral quasiparticle between the central island and one of the edges. On the edge of the v = 5/2 Pfaffian and anti-Pfaffian FQH states interactions can cause a transition to another phase. The relevant operator that condenses in this process consists of tunneling of electrons between the different edge branches. Under the phase transition a pair of counter propagating Majorana modes acquires a gap. The transition is an edge only phase transition, as the bulk state is unchanged. Such a transition can change the observed quasiparticle charge and exponent as measured in transport. The Majora-gapping transition shows similarities to a transition due to edge reconstruction. A setup is proposed that can probe slow edge velocities that may be present in certain abelian and non-abelian FQH state. At a long tunneling contact the coherent interference of tunneling quasiparticles causes a resonance in the tunneling current. From a high-precision observation of such a resonance not only the slow edge velocity can be determined, but also quasiparticle charge as well as neutral and charged tunneling exponents. Temperature is found to set an effective decoherence length scale.by Bas Jorn Overbosch.Ph.D