Elihu Abrahams

Bio: Elihu Abrahams is an academic researcher from Rutgers University. The author has contributed to research in topics: Superconductivity & Quasiparticle. The author has an hindex of 38, co-authored 112 publications receiving 15151 citations. Previous affiliations of Elihu Abrahams include Centre national de la recherche scientifique & University of California, Berkeley.

Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions

Abstract: Arguments are presented that the $T=0$ conductance $G$ of a disordered electronic system depends on its length scale $L$ in a universal manner. Asymptotic forms are obtained for the scaling function $\ensuremath{\beta}(G)=\frac{d\mathrm{ln}G}{d\mathrm{ln}L}$, valid for both $G\ensuremath{\ll}{G}_{c}\ensuremath{\simeq}\frac{{e}^{2}}{\ensuremath{\hbar}}$ and $G\ensuremath{\gg}{G}_{c}$. In three dimensions, ${G}_{c}$ is an unstable fixed point. In two dimensions, there is no true metallic behavior; the conductance crosses over smoothly from logarithmic or slower to exponential decrease with $L$.

Impurity Conduction at Low Concentrations

Abstract: The conductivity of an $n$-type semiconductor has been calculated in the region of low-temperature $T$ and low impurity concentration ${n}_{D}$. The model is that of phonon-induced electron hopping from donor site to donor site where a fraction $K$ of the sites is vacant due to compensation. To first order in the electric field, the solution to the steady-state and current equations is shown to be equivalent to the solution of a linear resistance network. The network resistance is evaluated and the result shows that the $T$ dependence of the resistivity is $\ensuremath{\rho}\ensuremath{\propto}\mathrm{exp}(\frac{{\ensuremath{\epsilon}}_{3}}{\mathrm{kT}})$. For small $K$, ${\ensuremath{\epsilon}}_{3}=(\frac{{e}^{2}}{{\ensuremath{\kappa}}_{0}}){(\frac{4\ensuremath{\pi}{n}_{D}}{3})}^{\frac{1}{3}}(1\ensuremath{-}1.35{K}^{\frac{1}{3}})$, where ${\ensuremath{\kappa}}_{0}$ is the dielectric constant. At higher $K$, ${\ensuremath{\epsilon}}_{3}$ and $\ensuremath{\rho}$ attain a minimum near $K=0.5$. The dependence on ${n}_{D}$ is extracted; the agreement of the latter and of ${\ensuremath{\epsilon}}_{3}$ with experiment is satisfactory. The magnitude of $\ensuremath{\rho}$ is in fair agreement with experiment. The influence of excited donor states on $\ensuremath{\rho}$ is discussed.

Phenomenology of the normal state of Cu-O high-temperature superconductors.

Abstract: The universal anomalies in the normal state of Cu-O high-temperature superconductors follow from a single hypothesis: There exist charge- and spin-density excitations with the absorptive part of the polarizability at low frequencies \ensuremath{\omega} proportional to \ensuremath{\omega}/T, where T is the temperature, and constant otherwise. The behavior in such a situation may be characterized as that of a marginal Fermi liquid. The consequences of this hypothesis are worked out for a variety of physical properties including superconductivity.

Models of hierarchically constrained dynamics for glassy relaxation

Abstract: A class of models for relaxation in strongly interacting glassy materials is suggested. Degrees of freedom are divided into a sequence of levels such that those in level $n+1$ are locked except when some of those in level $n$ find the right combination to release them, this representing the hierarchy of constraints in real systems. The Kohlrausch anomalous relaxation law, $\mathrm{exp}[\ensuremath{-}{(\frac{t}{\ensuremath{\tau}})}^{\ensuremath{\beta}}]$, emerges naturally, and a maximum time scale is found which exhibits a Vogel-Fulcher-type temperature dependence.

New method for a scaling theory of localization

Abstract: We base a scaling theory of localization on an expression for conductivity of a system of random elastic scatterers in terms of its scattering properties at a fixed energy. This expression, proposed by Landauer, is first derived and generalized to a system of indefinite size and number of scattering channels (a "wire"), and then an exact scaling theory for the one-dimensional chain is given. It is shown that the appropriate scaling variable is $f(\ensuremath{\rho})=\mathrm{ln}(1+\ensuremath{\rho})$ where $\ensuremath{\rho}$ is the dimensionless resistance, which has the property of "additive mean," and that scaling leads to a well-behaved probability distribution of this variable and to a very simple scaling law not previously given in the literature.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Two-dimensional gas of massless Dirac fermions in graphene

Abstract: Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrodinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.

Topological insulators and superconductors

Abstract: Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.

Free Radicals in the Physiological Control of Cell Function

Abstract: At high concentrations, free radicals and radical-derived, nonradical reactive species are hazardous for living organisms and damage all major cellular constituents. At moderate concentrations, how...

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

Abstract: We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-range order), and the calculation of thermodynamic properties, one-particle Green's functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article.