Disorder and the Superfluid Transition in LiquidHe4

Abstract

The influence of quenched disorder on the critical behavior of superfluid He is studied by confinement of the helium to the pores of three diflerent porous media: Vycor, xerogel, and aerogel glasses. In each case a well defined power-law behavior for the superfluid density is observed as the transition temperature is approached. In Vycor the superfluid critical exponent is bulklike, whereas strikingly diff'erent critical exponents are seen in the other two media.

Numerical study of phase transitions inside the pores of aerogels

“…In the case of 4 He, it has been observed that the decrease of T c (compared to the pure case) is more and more pronouced when it is diluted in aerogel, xerogel, and vycor, successively [1].…”

“…Number of experiments have been dedicated to study of new features of transitions in helium [1][2][3][4][5] or liquid crystals [6][7][8][9][10] when they are confined within the pores of an aerogel. Theoretical reconstruction of those phenomena has been attempted through various models [11][12][13][14][15][16].…”

Three-dimensional Ising model confined in low-porosity aerogels: A Monte Carlo study

“…In contrast, the long-range correlated ͑LRC͒ regime extends the criterion to systems satisfying condition ͑2͒, even if ␣ Ͻ 0. This generalization explains why critical exponents for the superfluid ͑SF͒ transition of 4 He change when the fluid is confined in very light aerogels 3,4 and do not when confined in, for example, porous gold. 5 Aerogels are fractal for several length scales, 6 while porous gold has exponentially decaying correlations beyond the size of a typical pore.…”

“…5 Aerogels are fractal for several length scales, 6 while porous gold has exponentially decaying correlations beyond the size of a typical pore. 5 Nevertheless, the authors 3,4 argued that the critical behavior of SF 4 He in aerogels yet poses intriguing questions to be solved. For instance, light aerogels are fractal for several length scales, up to a certain value ⌳ that depends on aerogel density.…”

The one-dimensional extended Bose-Hubbard model

“…Progress in this field has been driven by an interplay between theory, 1-10 numerical simulations, [11][12][13][14] and experiments. The latter include studies of liquid 4 He in porous media like vycor or aerogel, 15 Bose-Einstein condensates trapped in optical lattices, 16,17 micro-fabricated Josephson-junction arrays, 18-20 the disorder-driven superconductor-insulator transition in thin films of superconducting materials like bismuth, 21 and flux lines in type-II superconductors pinned by columnar defects aligned with the external magnetic field. 22 Theoretical and numerical studies [2][3][4]7,11,12 have concentrated on the Bose-Hubbard model which exhibits superfluid (SF) and bosonicMott-insulator (MI) phases and, if onsite disorder is included, a Bose-glass (BG) phase too.…”