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

Abstract

In recent experiments on thin 4 He films absorbed to rough surfaces Luhman and Hallock (Ref. 1) attempted to observe KT features of the superfluid-normal transition of this strongly disordered 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 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).

Bose-Einstein coherence in two-dimensional superfluidH4e

“…[1][2][3][4][5][6][7][8] The most accessible example of low dimensional Bose systems in nature is 4 He films adsorbed on porous materials or on flat surfaces. 2,4,[8][9][10][11][12] Other topical examples are Cooper pairs of electrons in thin-film superconductors, 13 Josephson junction arrays, 14 sodium atoms in optical and magnetic traps, 5,15 and spin polarized atomic hydrogen. 16 The order parameter used to characterize coherence properties of Bose systems is the one-body density matrix ͑OBDM͒; the Fourier transform of the atomic momentum distribution n͑k͒.…”

Oscillating paramagnetic Meissner effect and Berezinskii-Kosterlitz-Thouless transition in underdoped Bi2Sr2CaCu2O8+δ

“…The interception \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $1/{\mathrm{\Lambda }}( {{T}_{{\mathrm{BKT}}}} ) = \frac{{4\pi {\mu }_0}}{{{\mathrm{\Phi }}_0^2}}k{T}_{{\mathrm{BKT}}}$\end{document} , where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\mu }_0$\end{document} is the vacuum permeability, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} ${{\mathrm{\Phi }}}_0$\end{document} the flux quantum and k the Boltzmann constant, corresponds to the BKT temperature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} ${T}_{{\mathrm{BKT}}}$\end{document} in the thermodynamic limit. For a finite-sized domain in our case, the universal jump in the phase stiffness is smoothed out by finite-size effects [ 55 ] and the interception temperature merely provides an energy scale for the BKT crossover.…”