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 [D.R. Luhman, and R.B. Hallock, Phys. Rev. Lett. \textbf{93}, 086106 (2004)] 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).

arXiv comment9 pages, 7 figures, submitted to Phys. Rev. B; abstract, ``introduction'', and ``discussion and conclusions'' sections were modified; new section ``related physical systems'' was added

References in corpus (21)

• Berezinskii-Kosterlitz-Thouless Crossover in a Trapped Atomic Gas
• Quantum Phase Transitions and Vortex Dynamics in Superconducting Networks
• Worm Algorithm for Continuous-space Path Integral Monte Carlo Simulations
• Worm algorithms for classical statistical models
• Critical Point of a Weakly Interacting Two-Dimensional Bose Gas
• The superconductor-insulator transition in 2D dirty boson systems
• Two-Dimensional Weakly Interacting Bose Gas in the Fluctuation Region
• Superfluid--Insulator Transition in Commensurate Disordered Bosonic Systems:Large-Scale Worm-Algorithm Simulations
• Thermal activation of vortex-antivortex pairs in quasi-2D Bose-Einstein condensates
• Correlation between superfluid density and Tc of underdoped YBa2Cu3O6+x near the superconductor-insulator transition
• Analytical and numerical study of hardcore bosons in two dimensions
• Onset of Superfluidity in 4He Films Adsorbed on Disordered Substrates
• Observable Signature of the Berezinskii-Kosterlitz-Thouless Transition in a Planar Lattice of Bose-Einstein Condensates
• Glassy Vortex State in a Two-Dimensional Disordered XY-Model
• Influence of quenched dilution on the quasi-long-range ordered phase of the 2d XY model
• Finite-Size Effects and Dynamical Scaling in Two-Dimensional Josephson Junction Arrays
• Dynamic Impedance of Two-Dimensional Superconducting Films Near the Superconducting Transition
• Dynamic Scaling and Two-Dimensional High-Tc Superconductors
• Renormalization Group Study of the Intrinsic Finite Size Effect in 2D Superconductors
• Anisotropic Kosterlitz-Thouless Transition Induced by Hard-Wall Boundaries
• XY models with disorder and symmetry-breaking fields in two dimensions

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