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Title: Effect of disorder on the superfluid transition in two-dimensional systems

Abstract

In recent experiments on thin {sup 4}He films absorbed to rough surfaces Luhman and Hallock [Phys. Rev. Lett. 93, 086106 (2004)] attempted to observe Kosterlitz-Thouless (KT) features of the superfluid-normal transition of this strongly disordered two-dimensional (2D) bosonic system. It came as a surprise that while peak of dissipation was measured for a wide range of surface roughness there were no indications of the theoretically expected universal jump of the areal superfluid density for the strongly disordered samples. We test the hypothesis that this unusual behavior is a manifestation of finite-size effects by numerical study of the corresponding 2D bosonic model with strong diagonal disorder. We demonstrate that the discontinuous features of the underlying KT transition are severely smoothed out for finite system sizes (or finite frequency measurements). We resolve the universal discontinuity of the areal superfluid density by fitting our data to the KT renormalization group equations for finite systems. In analogy to our simulations, we suggest that in experiments on strongly disordered 2D bosonic systems the very existence of the KT scenario can and should be revealed only from a proper finite-size scaling of the data (for {sup 4}He films finite-size scaling can be effectively controlled by themore » scaling of finite frequency of measurements). We also show relevance of our conclusions for a wider class of systems, such as superconducting granular films, Josephson junction arrays, and ultracold atomic gases, where similar difficulties appear in experiments designed to verify KT transition (especially in disordered cases)« less

Authors:
 [1]
  1. Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003 (United States)
Publication Date:
OSTI Identifier:
20957805
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 75; Journal Issue: 14; Other Information: DOI: 10.1103/PhysRevB.75.144512; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; BOSONS; DENSITY; EQUATIONS; FILMS; FREQUENCY MEASUREMENT; HELIUM 4; JOSEPHSON JUNCTIONS; NUMERICAL ANALYSIS; RENORMALIZATION; ROUGHNESS; SCALING; SUPERFLUIDITY; SURFACES; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Balabanyan, Karen G. Effect of disorder on the superfluid transition in two-dimensional systems. United States: N. p., 2007. Web. doi:10.1103/PHYSREVB.75.144512.
Balabanyan, Karen G. Effect of disorder on the superfluid transition in two-dimensional systems. United States. doi:10.1103/PHYSREVB.75.144512.
Balabanyan, Karen G. Sun . "Effect of disorder on the superfluid transition in two-dimensional systems". United States. doi:10.1103/PHYSREVB.75.144512.
@article{osti_20957805,
title = {Effect of disorder on the superfluid transition in two-dimensional systems},
author = {Balabanyan, Karen G.},
abstractNote = {In recent experiments on thin {sup 4}He films absorbed to rough surfaces Luhman and Hallock [Phys. Rev. Lett. 93, 086106 (2004)] attempted to observe Kosterlitz-Thouless (KT) features of the superfluid-normal transition of this strongly disordered two-dimensional (2D) bosonic system. It came as a surprise that while peak of dissipation was measured for a wide range of surface roughness there were no indications of the theoretically expected universal jump of the areal superfluid density for the strongly disordered samples. We test the hypothesis that this unusual behavior is a manifestation of finite-size effects by numerical study of the corresponding 2D bosonic model with strong diagonal disorder. We demonstrate that the discontinuous features of the underlying KT transition are severely smoothed out for finite system sizes (or finite frequency measurements). We resolve the universal discontinuity of the areal superfluid density by fitting our data to the KT renormalization group equations for finite systems. In analogy to our simulations, we suggest that in experiments on strongly disordered 2D bosonic systems the very existence of the KT scenario can and should be revealed only from a proper finite-size scaling of the data (for {sup 4}He films finite-size scaling can be effectively controlled by the scaling of finite frequency of measurements). We also show relevance of our conclusions for a wider class of systems, such as superconducting granular films, Josephson junction arrays, and ultracold atomic gases, where similar difficulties appear in experiments designed to verify KT transition (especially in disordered cases)},
doi = {10.1103/PHYSREVB.75.144512},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 14,
volume = 75,
place = {United States},
year = {Sun Apr 01 00:00:00 EDT 2007},
month = {Sun Apr 01 00:00:00 EDT 2007}
}
  • We study the nature of the superfluid-insulator quantum phase transition in a one-dimensional system of lattice bosons with off-diagonal disorder in the limit of a large integer filling factor. Monte Carlo simulations of two strongly disordered models show that the universality class of the transition in question is the same as that of the superfluid-Mott-insulator transition in a pure system. This result can be explained by disorder self-averaging in the superfluid phase and the applicability of the standard quantum hydrodynamic action. We also formulate the necessary conditions which should be satisfied by the stong-randomness universality class, if one exists.
  • We investigate the nature of the superfluid-insulator quantum phase transition driven by disorder for noninteracting ultracold atoms on one-dimensional lattices. We consider two different cases: Anderson-type disorder, with local energies randomly distributed, and pseudodisorder due to a potential incommensurate with the lattice, which is usually called the Aubry-Andre model. A scaling analysis of numerical data for the superfluid fraction for different lattice sizes allows us to determine quantum critical exponents characterizing the disorder-driven superfluid-insulator transition. We also briefly discuss the effect of interactions close to the noninteracting quantum critical point of the Aubry-Andre model.
  • We investigate a Bose-Einstein condensate (BEC) trapped in a two-dimensional optical lattice in the presence of weak disorder within the framework of the Bogoliubov theory. In particular, we analyze the combined effects of disorder and an optical lattice on quantum fluctuations and superfluid density of the BEC system. Accordingly, the analytical expressions of the ground-state energy and quantum depletion of the system are obtained. Our results show that the lattice still induces a characteristic three-dimensional (3D) to one-dimensional crossover in the behavior of quantum fluctuations, despite the presence of weak disorder. Furthermore, we use the linear response theory to calculatemore » the normal fluid density of the condensate induced by disorder. Our results in the 3D regime show that the combined presence of disorder and lattice induce a normal fluid density that asymptotically approaches 4/3 of the corresponding condensate depletion. Conditions for possible experimental realization of our scenario are also proposed.« less
  • A two-dimensional system of atoms in an anisotropic optical lattice is studied theoretically. If the system is finite in one direction, it is shown to exhibit a transition between a two-dimensional superfluid and a one-dimensional Mott insulating chain of superfluid tubes. Monte Carlo simulations are consistent with the expectation that the phase transition is of Kosterlitz-Thouless type. The effect of the transition on experimental time-of-flight images is discussed.
  • The adsorption of bromide on an Ag(001) electrode has been investigated using {ital in situ} x-ray scattering methods. With increasing potential, the bromide undergoes a second order phase transition from a lattice gas to an ordered c(2{times}2) structure. The order parameter is consistent with the 2D Ising model prediction {beta}=1/8 . A comparison of x-ray and electrochemical measurements indicates significant lateral disorder at low coverages which decreases with increasing coverage. {copyright} {ital 1997} {ital The American Physical Society}