arXiv subjects

Eduardo Fradkin

Publications and source records attributed to Eduardo Fradkin.

At least 163 records · Page 9Linked to original sources

arXiv2002

Competing Order in the Mixed State of High Temperature Superconductors

We examine the low temperature behavior of the mixed state of a layered superconductor in the vicinity of a quantum critical point separating a pure superconducting phase from a phase in which a competing order coexists with superconductivity. At zero temperature, we find that there is an avoided critical point in the sense that the phase boundary in the limit $B\to 0$ does not connect to the B=0 critical point. Consequently, there exists a quasi-1D regime of the phase diagram, in which the competing order is largely confined to 1D ``halos'' about each vortex core, and in which interactions between neighboring vortices, although relevant at low temperature, are relatively weak.

cond-mat.supr-con↗

arXiv2001

Quantum Theory of a Nematic Fermi Fluid

We develop a microscopic theory of the electronic nematic phase proximate to an isotropic Fermi liquid in both two and three dimensions. Explicit expressions are obtained for the small amplitude collective excitations in the ordered state; remarkably, the nematic Goldstone mode (the directorwave) is overdamped except along special directions dictated by symmetry. At the quantum critical point we find a dynamical exponent of $z=3$, implying stability of the gaussian fixed point. The leading perturbative effect of the overdamped Goldstone modes leads to a breakdown of Fermi liquid theory in the nematic phase and to strongly angle dependent electronic self energies around the Fermi surface. Other metallic liquid crystal phases, {\it e. g.} a quantum hexatic, behave analogously.

cond-mat.str-el↗

arXiv2001

Effective field theory for the bulk and edge states of quantum Hall states in unpolarized single layer and bilayer systems

We present an effective theory for the bulk Fractional Quantum Hall states in spin-polarized bilayer and spin-1/2 single layer two-dimensional electron gases (2DEG) in high magnetic fields consistent with the requirement of global gauge invariance on systems with periodic boundary conditions. We derive the theory for the edge states that follows naturally from this bulk theory. We find that the minimal effective theory contains two propagating edge modes that carry charge and energy, and two non-propagating topological modes responsible for the statistics of the excitations. We give a detailed description of the effective theory for the spin-singlet states, the symmetric bilayer states and for the $(m,m,m)$ states. We calculate explicitly, for a number of cases of interest, the operators that create the elementary excitations, their bound states, and the electron. We also discuss the scaling behavior of the tunneling conductances in different situations: internal tunneling, tunneling between identical edges and tunneling into a FQH state from a Fermi liquid.

cond-mat.mes-hall↗

arXiv2001

Short-ranged RVB physics, quantum dimer models and Ising gauge theories

Quantum dimer models are believed to capture the essential physics of antiferromagnetic phases dominated by short-ranged valence bond configurations. We show that these models arise as particular limits of Ising (Z_2) gauge theories, but that in these limits the system develops a larger local U(1) invariance that has different consequences on different lattices. Conversely, we note that the standard Z_2 gauge theory is a generalised quantum dimer model, in which the particular relaxation of the hardcore constraint for the dimers breaks the U(1) down to Z_2. These mappings indicate that at least one realization of the Senthil-Fisher proposal for fractionalization is exactly the short ranged resonating valence bond (RVB) scenario of Anderson and of Kivelson, Rokhsar and Sethna. They also suggest that other realizations will require the identification of a local low energy, Ising link variable {\it and} a natural constraint. We also discuss the notion of topological order in Z_2 gauge theories and its connection to earlier ideas in RVB theory. We note that this notion is not central to the experiment proposed by Senthil and Fisher to detect vortices in the conjectured Z_2 gauge field.

cond-mat.supr-con↗

arXiv2000

Antiferromagnetic spin ladders effectively coupled by one-dimensional electron liquids

We study a model of the stripe state in strongly correlated systems consisting of an array of antiferromagnetic spin ladders, each with $n_{leg}$ legs, coupled to each other through the spin-exchange interaction to charged stripes in between each pair of ladders. The charged stripes are assumed to be Luttinger liquids in a spin-gap regime (Luther-Emery). An effective interaction for a pair of neighboring ladders is calculated by integrating out the gapped spin degree of freedom in the charged stripe. The low energy effective theory of each ladder is the usual nonlinear $σ$-model with additional cross couplings of neighboring ladders. These interactions are found to favor either in-phase or anti-phase short range spin orderings depending on whether the charge stripe is site-centered or bond-centered as well as on its filling factor and other physical parameters of the charged stripe.

cond-mat.str-el↗

arXiv2000

Effective Chern-Simons Theories of Pfaffian and Parafermionic Quantum Hall States, and Orbifold Conformal Field Theories

We present a pure Chern-Simons formulation of families of interesting Conformal Field Theories describing edge states of non-Abelian Quantum Hall states. These theories contain two Abelian Chern-Simons fields describing the electromagnetically charged and neutral sectors of these models, respectively. The charged sector is the usual Abelian Chern-Simons theory that successfully describes Laughlin-type incompressible fluids. The neutral sector is a 2+1-dimensional theory analogous to the 1+1-dimensional orbifold conformal field theories. It is based on the gauge group O(2) which contains a ${\bf Z}_2$ disconnected group manifold, which is the salient feature of this theory. At level q, the Abelian theory of the neutral sector gives rise to a ${\bf Z}_{2q}$ symmetry, which is further reduced by imposing the ${\bf Z}_2$ symmetry of charge-conjugation invariance. The remaining ${\bf Z}_q$ symmetry of the neutral sector is the origin of the non-Abelian statistics of the (fermionic) q-Pfaffian states.

cond-mat.mes-hall↗

arXiv2000

Quantum Theory of the Smectic Metal State in Stripe Phases

We present a theory of the electron smectic fixed point of the stripe phases of doped layered Mott insulators. We show that in the presence of a spin gap three phases generally arise: (a) a smectic superconductor, (b) an insulating stripe crystal and (c) a smectic metal. The latter phase is a stable two-dimensional anisotropic non-Fermi liquid. In the abscence of a spin gap there is also a more conventional Fermi-liquid-like phase. The smectic superconductor and smectic metal phases may have already been seen in Nd-doped LSCO.

cond-mat.str-el↗

arXiv1999

Nematic phase of the two-dimensional electron gas in a magnetic field

The two dimensional electron gas (2DEG) in moderate magnetic fields in ultra-clean AlAs-GaAs heterojunctions exhibits transport anomalies suggestive of a compressible, anisotropic metallic state. Using scaling arguments and Monte Carlo simulations, we develop an order parameter theory of an electron nematic phase. The observed temperature dependence of the resistivity anisotropy behaves like the orientational order parameter if the transition to the nematic state occurs at a finite temperature, $T_c \sim 65 mK$, and is slightly rounded by a small background microscopic anisotropy. We propose a light scattering experiment to measure the critical susceptibility.

cond-mat.mes-hall↗

arXiv1999

Exploring the fractional quantum Hall effect with electron tunneling

In this talk I present a summary of recent work on tunnel junctions of a fractional quantum Hall fluid and an electron reservoir, a Fermi liquid. I consider first the case of a single point contact. This is a an exactly solvable problem from which much can be learned. I also discuss in some detail how these solvable junction problems can be used to understand many aspects of the recent electron tunneling experiments into edge states. I also give a detailed picture of the unusual behavior of these junctions in their strong coupling regime. A pedagogical introduction to the theories of edge states is also included.

cond-mat.mes-hall↗

arXiv1998

Landau-Ginzburg Theories for Non-Abelian Quantum Hall States

We construct Landau-Ginzburg effective field theories for fractional quantum Hall states -- such as the Pfaffian state -- which exhibit non-Abelian statistics. These theories rely on a Meissner construction which increases the level of a non-Abelian Chern-Simons theory while simultaneously projecting out the unwanted degrees of freedom of a concomitant enveloping Abelian theory. We describe this construction in the context of a system of bosons at Landau level filling factor $ν=1$, where the non-Abelian symmetry is a dynamically-generated SU(2) continuous extension of the discrete particle-hole symmetry of the lowest Landau level. We show how the physics of quasiparticles and their non-Abelian statistics arises in this Landau-Ginzburg theory. We describe its relation to edge theories -- where a coset construction plays the role of the Meissner projection -- and discuss extensions to other states.

cond-mat.mes-hall↗

arXiv1998

Universal structure of the edge states of the fractional quantum Hall states

We present an effective theory for the bulk fractional quantum Hall states on the Jain sequences on closed surfaces and show that it has a universal form whose structure does not change from fraction to fraction. The structure of this effective theory follows from the condition of global consistency of the flux attachment transformation on closed surfaces. We derive the theory of the edge states on a disk that follows naturally from this globally consistent theory on a torus. We find that, for a fully polarized two-dimensional electron gas, the edge states for all the Jain filling fractions $ν=p/(2np+1)$ have only one propagating edge field that carries both energy and charge, and two non-propagating edge fields of topological origin that are responsible for the statistics of the excitations. Explicit results are derived for the electron and quasiparticle operators and for their propagators at the edge. We show that these operators create states with the correct charge and statistics. It is found that the tunneling density of states for all the Jain states scales with frequency as $|ω|^{(1-ν)/ν}$.

cond-mat.mes-hall↗

arXiv1998

Liquid Crystal Phases of Quantum Hall Systems

Mean-field calculations for the two dimensional electron gas (2DEG) in a large magnetic field with a partially filled Landau level with index $N\geq 2$ consistently yield ``stripe-ordered'' charge-density wave ground-states, for much the same reason that frustrated phase separation leads to stripe ordered states in doped Mott insulators. We have studied the effects of quantum and thermal fluctuations about such a state and show that they can lead to a set of electronic liquid crystalline states, particularly a stripe-nematic phase which is stable at $T>0$. Recent measurements of the longitudinal resistivity of a set of quantum Hall devices have revealed that these systems spontaneously develop, at low temepratures, a very large anisotropy. We interpret these experiments as evidence for a stripe nematic phase, and propose a general phase diagram for this system.

cond-mat.mes-hall↗

arXiv1998

What do noise measurements reveal about fractional charge in FQH liquids?

We present a calculation of noise in the tunneling current through junctions between two two-dimensional electron gases (2DEG) in inequivalent Laughlin fractional quantum Hall (FQH) states, as a function of voltage and temperature. We discuss the interpretation of measurements of suppressed shot noise levels of tunneling currents through a quantum point contact (QPC) in terms of tunneling of fractionally charged states. We show that although this interpretation is always possible, for junctions between different FQH states the fractionally charged states involved in the tunneling process are not the Laughlin quasiparticles of the isolated FQH states that make up the junction, and should be regarded instead as solitons of the coupled system. The charge of the soliton is, in units of the electron charge, the harmonic average of the filling fractions of the individual Laughlin states, which also coincides with the saturation value of the differential conductance of the QPC. For the especially interesting case of a QPC between states at filling fractions $ν=1$ and $ν={1/3}$, we calculate the noise in the tunneling current exactly for all voltages and temperatures and investigate the crossovers. These results can be tested by noise experiments on $(1,{1/3})$ QPCs. We present a generalization of these results for QPC's of arbitrary Laughlin fractions in their weak and strong coupling regimes. We also introduce generalized Wilson ratios for the noise in the shot and thermal limits. These ratios are universal scaling functions of $V/T$ that can be measured experimentally in a general QPC geometry.

cond-mat.mes-hall↗

arXiv1998

Andreev reflection in the fractional quantum Hall effect

We study the reflection of electrons and quasiparticles on point-contact interfaces between fractional quantum Hall (FQH) states and normal metals (leads), as well as interfaces between two FQH states with mismatched filling fractions. We classify the processes taking place at the interface in the strong coupling limit. In this regime a set of quasiparticles can decay into quasiholes on the FQH side and charge excitations on the other side of the junction. This process is analogous to an Andreev reflection in normal-metal/superconductor (N-S) interfaces.

cond-mat.mes-hall↗

arXiv1997

Exact calculation of multifractal exponents of the critical wave function of Dirac fermions in a random magnetic field

The multifractal scaling exponents are calculated for the critical wave function of a two-dimensional Dirac fermion in the presence of a random magnetic field. It is shown that the problem of calculating the multifractal spectrum maps into the thermodynamics of a static particle in a random potential. The multifractal exponents are simply given in terms of thermodynamic functions, such as free energy and entropy, which are argued to be self-averaging in the thermodynamic limit. These thermodynamic functions are shown to coincide exactly with those of a Generalized Random Energy Model, in agreement with previous results obtained using Gaussian field theories in an ultrametric space.

cond-mat.mes-hall↗

arXiv1997

Overscreening of magnetic impurities in $d_{x^2-y^2}$ wave superconductors

We consider the screening of a magnetic impurity in a $d_{x^2-y^2}$ wave superconductor. The properties of the $d_{x^2-y^2}$ state lead to an unusual behavior in the impurity magnetic susceptibility, the impurity specific heat and in the quasiparticle phase shift which can be used to diagnose the nature of the condensed state. We construct an effective theory for this problem and show that it is equivalent to a multichannel (one per node) non-marginal Kondo problem with linear density of states and coupling constant J. There is a quantum phase transition from an unscreened impurity state to an overscreened Kondo state at a critical value J_c which varies with $Δ_0$, the superconducting gap away from the nodes. In the overscreened phase, the impurity Fermi level $ε_f$ and the amplitude $Δ$ of the ground state singlet vanish at J_c like $Δ_0 \exp(- const. / Δ)$ and J-J_c respectively. We derive the scaling laws for the susceptibility and specific heat in the overscreened phase at low fields and temperatures.

cond-mat.str-el↗

arXiv1997

How to observe distinct universal conductances in tunneling to quantum Hall states: having the right contacts

We show that different universal values can be obtained for the two-terminal conductance of a fractional quantum Hall state. At large voltages, or strong coupling, the conductance of a point-like tunneling junction between an electron gas reservoir and a Laughlin FQH state at filling fraction $ν$ saturates to a universal value $G={\frac{2ν}{ν+1}} {\frac{e^2}{h}}$. We use this result to show that devices with different types of contacts between the reservoir and the FQH state lead to distinct universal values of saturation conductance which are rational multiples of $e^2/h$. The particular fraction $e^2/h$ is obtained for the case of electron tunneling in and out of a FQH liquid by two point contacts. We demonstrate that the problem of tunneling between an electron gas and a fractional quantum Hall state through an impurity is exactly equivalent to the problem of tunneling between a chiral Fermi liquid and a chiral Luttinger liquid. We investigate in detail the case of tunneling to a $ν=1/3$ FQH state which we show to be equivalent to the problem of tunneling between two $g=1/2$ chiral Luttinger liquids. This system provides an experimental realization of this important exactly solvable case. We use the results of the single impurity problem to consider the case of many tunneling centers coupled independently to an electron reservoir, which is relevant to recent experiments by A.~Chang et.~al. We derive an explicit universal expression for the voltage and temperature dependent conductance which exhibits a crossover reminiscent of a Kondo effect. This universal curve fits the experimental data over the full range of probed voltages.

cond-mat↗

arXiv1997

Fermionic Chern-Simons Field Theory for the Fractional Hall Effect

We review the fermionic Chern-Simons field theory for the Fractional Quantum Hall Effect (FQHE). We show that in this field theoretic approach to the problem of interacting electrons moving in a plane in the presence of an external magnetic field, the FQHE states appear naturally as the semiclassical states of the theory. In this framework, the FQHE states are the unique ground states of a system of electrons on a fixed geometry. The excitation spectrum is fully gapped and these states can be viewed as infrared stable fixed points of the system. It is shown that the long distance, low energy properties of the system are described exactly by this theory. It is further shown that, in this limit, the actual ground state wave function has the Laughlin form. We also discuss the application of this theory to the problem of the FQHE in bilayers and in unpolarized single layer systems.

cond-mat.mes-hall↗