arXiv subjects

A. M. M. Pruisken

Publications and source records attributed to A. M. M. Pruisken.

32 records · Page 2Linked to original sources

arXiv2002

The $θ$ vacuum reveals itself as the fundamental theory of the quantum Hall effect II. The Coulomb interaction

Within the Grassmannian $U(2N) / U(N) \times U(N)$ non-linear $σ$ model representation of localization one can study the low energy dynamics of both the free and interacting electron gas. We study the cross-over between these two fundamentally different physical problems. We show how the topological arguments for the exact quantization of the Hall conductance are extended to include the Coulomb interaction problem. We discuss dynamical scaling and make contact with the theory of variable range hopping.

cond-mat.mes-hall↗

arXiv2002

Quantum criticality, particle-hole symmetry, and duality of the plateau-insulator transition in the quantum Hall regime

We report new experimental data on the plateau-insulator transition in the quantum Hall regime, taken from a low mobility InGaAs/InP heterostructure. By employing the fundamental symmetries of the quantum transport problem we are able to disentangle the universal quantum critical aspects of the magnetoresistance data (critical indices and scaling functions) and the sample dependent aspects due to macroscopic inhomogeneities. Our new results and methodology indicate that the previously established experimental value for the critical index (kappa = 0.42) resulted from an admixture of both universal and sample dependent behavior. A novel, non-Fermi liquid value is found (kappa = 0.57) along with the leading corrections to scaling. The statement of self-duality under the Chern Simons flux attachment transformation is verified.

cond-mat.mes-hall↗

arXiv2001

Establishing a non-Fermi liquid theory for disordered metals near two dimensions

We consider the finkelstein action describing a system of spin polarized or spinless electrons near two dimensions, in the presence of disorder as well as the Coulomb interactions.We extend the renormalization group analysis of our previous work and evaluate the metal-insulator transition of the electron gas to second order in an (d-2) expansion. We obtain the complete scaling behavior of physical observables like the conductivity and the specific heat with varying frequency, temperature and/or electron density.

cond-mat.mes-hall↗

arXiv2001

Evidence for a Quantum Hall Insulator in an InGaAs/InP Heterostructure

We study the quantum critical behavior of the plateau-insulator (PI) transition in a low mobility InGaAs/InP heterostructure. By reversing the direction of the magnetic field (B) we find an averaged Hall resistance ρ_xy which remains quantized at the plateau value h/e^2 throughout the PI transition. We extract a critical exponent κ'= 0.57 +/- 0.02 for the PI transition which is slightly different from (and possibly more accurate than) the established value 0.42 +/- 0.04 as previously obtained from the plateau-plateau (PP) transitions.

cond-mat.mes-hall↗

arXiv2001

Localization, Coulomb interaction, topological principles and the quantum Hall effect

We report the consequences of a new interaction symmetry that protects the renormalization of the electron gas in low dimensions in general, and in the quantum Hall regime in particular. We introduce a generalized Thouless' criterion for localization to include the effects of the Coulomb interaction and establish the quantization of the Hall conductance as well as the theory of massless edge bosons.

cond-mat.mes-hall↗

arXiv2000

The large N theory exactly reveals the quantum Hall effect and theta-renormalization

We revisit the $θ$ dependence in $CP^{N-1}$ model with large $N$. We study the consequences of a recently discovered new ingredient of the instanton vacuum, i.e. the massless chiral edge excitations. Contrary to the previous believes, our results demonstrate that the large $N$ expansion displays all the fundamental features of the quantum Hall effect. This includes the {\em robust} quantization of the Hall conductance, as well as the appearance of massless bulk excitations at $θ= π$. We conclude that the quantum Hall effect is a generic feature of the instanton vacuum, i.e. for any number of field components and not just for the theory in the replica limit alone.

cond-mat.mes-hall↗

arXiv2000

The problem of Coulomb interactions in the theory of the quantum Hall effect

We summarize the main ingredients of a unifying theory for abelian quantum Hall states. This theory combines the Finkelstein approach to localization and interaction effects with the topological concept of an instanton vacuum as well as Chern-Simons gauge theory. We elaborate on the meaning of a new symmetry ($\cal F$ invariance) for systems with an infinitely ranged interaction potential. We address the renormalization of the theory and present the main results in terms of a scaling diagram of the conductances.

cond-mat.mes-hall↗

arXiv1999

(Mis-)handling gauge invariance in the theory of the quantum Hall effect I: Unifying action and the ν=1/2 state

We propose a unifying theory for both the integral and fractional quantum Hall regimes. This theory reconciles the Finkelstein approach to localization and interaction effects with the topological issues of an instanton vacuum and Chern-Simons gauge theory. We elaborate on the microscopic origins of the effective action and unravel a new symmetry in the problem with Coulomb interactions which we name F-invariance. This symmetry has a broad range of physical consequences which will be the main topic of future analyses. In the second half of this paper we compute the response of the theory to electromagnetic perturbations at a tree level approximation. This is applicable to the theory of ordinary metals as well as the composite fermion approach to the half-integer effect. Fluctuations in the Chern-Simons gauge fields are found to be well behaved only when the theory is F-invariant.

cond-mat.mes-hall↗

arXiv1999

(Mis-)handling gauge invariance in the theory of the quantum Hall effect II: Perturbative results

The concept of F-invariance, which previously arose in our analysis of the integral and half-integral quantum Hall effects, is studied in 2+2εspatial dimensions. We report the results of a detailed renormalization group analysis and establish the renormalizability of the (Finkelstein) action to two loop order. We show that the infrared behavior of the theory can be extracted from gauge invariant (F-invariant) quantities only. For these quantities (conductivity, specific heat) we derive explicit scaling functions. We identify a bosonic quasiparticle density of states which develops a Coulomb gap as one approaches the metal-insulator transition from the metallic side. We discuss the consequences of F-invariance for the strong coupling, insulating regime.

cond-mat.mes-hall↗

arXiv1999

(Mis-)handling gauge invariance in the theory of the quantum Hall effect III: The instanton vacuum and chiral edge physics

The concepts of an instanton vacuum and F-invariance are used to derive a complete effective theory of massless edge excitations in the quantum Hall effect. We establish, for the first time, the fundamental relation between the instanton vacuum approach and the theory of chiral edge bosons. Two longstanding problems of smooth disorder and Coulomb interactions are addressed. We introduce a two dimensional network of chiral edge states and tunneling centers (saddlepoints) as a model for the plateau transitions. We derive a mean field theory including the Coulomb interactions and explain the recent empirical fits to transport at low temperatures. Secondly, we address the problem of electron tunneling into the quantum Hall edge. We express the problem in terms of an effective Luttinger liquid with conductance parameter (g) equal to the filling fraction (ν) of the Landau band. Hence, even in the integral regime our results for tunneling are completely non-Fermi liquid like, in sharp contrast to the predictions of single edge theories.

cond-mat.mes-hall↗

arXiv1998

The fractional quantum Hall effect: Chern-Simons mapping, duality, Luttinger liquids and the instanton vacuum

We derive, from first principles, the complete Luttinger liquid theory of abelian quantum Hall edge states. This theory includes the effects of disorder and Coulomb interactions as well as the coupling to external electromagnetic fields. We introduce a theory of spatially separated (individually conserved) edge modes, find an enlarged dual symmetry and obtain a complete classification of quasiparticle operators and tunneling exponents. The chiral anomaly on the edge and Laughlin's gauge argument are used to obtain unambiguously the Hall conductance. In resolving the problem of counter flowing edge modes, we find that the long range Coulomb interactions play a fundamental role. In order to set up a theory for arbitrary filling fractions $ν$ we use the idea of a two dimensional network of percolating edge modes. We derive an effective, single mode Luttinger liquid theory for tunneling processes into the quantum Hall edge which yields a continuous tunneling exponent $1/ν$. The network approach is also used to re-derive the instanton vacuum or $Q$-theory for the plateau transitions.

cond-mat.mes-hall↗

arXiv1998

Probing the plateau-insulator quantum phase transition in the quantum Hall regime

We report quantum Hall experiments on the plateau-insulator transition in a low mobility In_{.53} Ga_{.47} As/InP heterostructure. The data for the longitudinal resistance ρ_{xx} follow an exponential law and we extract a critical exponent κ= .55 \pm .05 which is slightly different from the established value κ= .42 \pm .04 for the plateau transitions. Upon correction for inhomogeneity effects, which cause the critical conductance σ_{xx}^* to depend marginally on temperature, our data indicate that the plateau-plateau and plateau- insulator transitions are in the same universality class.

cond-mat.mes-hall↗

arXiv1997

The Quantum Hall Effect: Unified Scaling Theory and Quasi-particles at the Edge

We address two fundamental issues in the physics of the quantum Hall effect: a unified description of scaling behavior of conductances in the integral and fractional regimes, and a quasi-particle formulation of the chiral Luttinger Liquids that describe the dynamics of edge excitations in the fractional regime.

cond-mat.mes-hall↗

arXiv1994

Incommensurate Phase on a Disordered Surface: Instability Against the Formation of Overhangs and Finite Loops

The stability of the quenched incommensurate phase in two dimensions against the creation of overhangs and finite loops (OH/FL) in the replica space is investigated for a model of domain walls with $N$ colors. Introducing a chemical potential $ε$ for OH/FL, the probability for the formation of these objects is studied for $ε\to0$. In the pure limit this probability vanishes with $\sqrtε$, whereas the fluctuations of this probability are long-range correlated in the quenched system. This indicates an instability related to the symmetry in replica space. It is accompanied by the creation of a massless boson. The latter leads to a power law decay with exponent $\propto 1/N$ for the product of the correlation functions along the domain walls.

cond-mat↗