J. Phys. Soc. Jpn. 91, 014603 (2022) [20 Pages]
FULL PAPERS

4D-XY Superfluid Transition and Dissipation in 4He Confined in Nanoporous Media

+ Affiliations
1Department of Physics, Keio University, Yokohama 223-8522, Japan2Cryogenic Research Center, The University of Tokyo, Bunkyo, Tokyo 113-0032, Japan

4He confined in nanoporous Gelsil glass is a unique, strongly correlated Bose system exhibiting quantum phase transition (QPT) by controlling pressure. Previous studies revealed that the QPT occurs with four-dimensional (4D) XY criticality, which appears in the zero-temperature limit of the superfluid density. However, the PT phase diagram also suggested that the 4D XY nature appears at finite temperatures. Here, we have determined the critical exponent of the superfluid density ρs of 4He in two Gelsil samples that have pore diameter to be about 3 nm, using a newly developed mechanical resonator technique. The critical exponent ζ in the powerlaw fitting ρs ∝ |1 − T/Tc|ζ, where Tc is the superfluid transition temperature, was found to be 1.0 ± 0.1 for all pressures realized in this experiment, 0.1 < P < 2.4 MPa. This value of ζ gives decisive evidence that the finite-temperature superfluid transition belongs to the 4D XY universality class. The emergence of the 4D XY criticality is explained by the existence of many nanoscale superfluid droplets, the so-called localized Bose–Einstein condensates (LBECs), above Tc. Due to the large energy cost for 4He atoms to move between the LBECs, the phase of the LBEC order parameters fluctuates not only in spatial (3D) but imaginary time (+1D) dimensions, resulting in the 4D XY criticality by a temperature near Tc. Since the finite size of the system in the imaginary time dimension Lτ is larger than the pore size, the 4D XY critical phenomenon is observed. In the very vicinity of Tc at which the correlation length exceeds Lτ, there may be a crossover from 4D to 3D XY criticality. Below Tc, macroscopic superfluidity grows in the nanopores of Gelsil by the alignment of the phases of the LBEC order parameters. An excess dissipation peak observed below Tc is well explained by this phase-matching process.

©2022 The Physical Society of Japan

References

  • 1 S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. Shahar, Rev. Mod. Phys. 69, 315 (1997). 10.1103/RevModPhys.69.315 CrossrefGoogle Scholar
  • 2 S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, U.K., 2011). CrossrefGoogle Scholar
  • 3 P. Gegenwart, Q. Si, and F. Steglich, Nat. Phys. 4, 186 (2008). 10.1038/nphys892 CrossrefGoogle Scholar
  • 4 B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, and J. Zaanen, Nature 518, 179 (2015). 10.1038/nature14165 CrossrefGoogle Scholar
  • 5 D. M. Broun, W. A. Huttema, P. J. Turner, S. Özcan, B. Morgan, R. Liang, W. N. Hardy, and D. A. Bonn, Phys. Rev. Lett. 99, 237003 (2007). 10.1103/PhysRevLett.99.237003 CrossrefGoogle Scholar
  • 6 M. Franz and A. P. Iyengar, Phys. Rev. Lett. 96, 047007 (2006). 10.1103/PhysRevLett.96.047007 CrossrefGoogle Scholar
  • 7 K. Yamamoto, H. Nakashima, Y. Shibayama, and K. Shirahama, Phys. Rev. Lett. 93, 075302 (2004). 10.1103/PhysRevLett.93.075302 CrossrefGoogle Scholar
  • 8 K. Yamamoto, Y. Shiabayama, and K. Shirahama, Phys. Rev. Lett. 100, 195301 (2008). 10.1103/PhysRevLett.100.195301 CrossrefGoogle Scholar
  • 9 K. Yamamoto, Y. Shiabayama, and K. Shirahama, J. Phys. Soc. Jpn. 77, 013601 (2008). 10.1143/JPSJ.77.013601 LinkGoogle Scholar
  • 10 K. Shirahama, J. Low Temp. Phys. 146, 485 (2007). 10.1007/s10909-006-9277-6 CrossrefGoogle Scholar
  • 11 K. Shirahama, K. Yamamoto, and Y. Shibayama, Low Temp. Phys. 34, 273 (2008). 10.1063/1.2908885 CrossrefGoogle Scholar
  • 12 K. Shirahama, K. Yamamoto, and Y. Shibayama, J. Phys. Soc. Jpn. 77, 111011 (2008). 10.1143/JPSJ.77.111011 LinkGoogle Scholar
  • 13 Th. Eggel, M. Oshikawa, and K. Shirahama, Phys. Rev. B 84, 020515(R) (2011). 10.1103/PhysRevB.84.020515 CrossrefGoogle Scholar
  • 14 Th. Eggel, Ph.D. Thesis, University of Tokyo (2011). Google Scholar
  • 15 D. S. Greywall and G. Ahlers, Phys. Rev. A 7, 2145 (1973); 10.1103/PhysRevA.7.2145 Crossref;, Google ScholarG. Ahlers, Rev. Mod. Phys. 52, 489 (1980). 10.1103/RevModPhys.52.489 CrossrefGoogle Scholar
  • 16 M. Barmatz, I. Hahn, J. A. Lipa, and R. V. Duncan, Rev. Mod. Phys. 79, 1 (2007). 10.1103/RevModPhys.79.1 CrossrefGoogle Scholar
  • 17 M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B 40, 546 (1989). 10.1103/PhysRevB.40.546 CrossrefGoogle Scholar
  • 18 O. Avenel and E. Varoqaux, Phys. Rev. Lett. 55, 2704 (1985). 10.1103/PhysRevLett.55.2704 CrossrefGoogle Scholar
  • 19 X. Rojas and J. P. Davis, Phys. Rev. B 91, 024503 (2015). 10.1103/PhysRevB.91.024503 CrossrefGoogle Scholar
  • 20 T. Tani, Y. Nago, S. Murakawa, and K. Shirahama, J. Phys. Soc. Jpn. 90, 033601 (2021). 10.7566/JPSJ.90.033601 LinkGoogle Scholar
  • 21 E. P. Barrett, L. G. Joyner, and P. P. Halenda, J. Am. Chem. Soc. 73, 373 (1951). 10.1021/ja01145a126 CrossrefGoogle Scholar
  • 22 R. Blaauwgeers, M. Blazkova, M. Clivecko, V. B. Eltsov, R. de Graaf, J. Hosio, M. Krusius, D. Schmoranzer, W. Schoepe, L. Skrbek, P. Skyba, R. E. Solntsev, and D. E. Zmeev, J. Low Temp. Phys. 146, 537 (2007). 10.1007/s10909-006-9279-4 CrossrefGoogle Scholar
  • 23 L. S. Goldner, N. Mulders, and G. Ahlers, J. Low Temp. Phys. 93, 131 (1993). 10.1007/BF00682285 CrossrefGoogle Scholar
  • 24 M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 63, 214503 (2001). 10.1103/PhysRevB.63.214503 CrossrefGoogle Scholar
  • 25 C. W. Kiewiet, H. E. Hall, and J. D. Reppy, Phys. Rev. Lett. 35, 1286 (1975). 10.1103/PhysRevLett.35.1286 CrossrefGoogle Scholar
  • 26 J. Yoon and M. H. W. Chan, Phys. Rev. Lett. 78, 4801 (1997). 10.1103/PhysRevLett.78.4801 CrossrefGoogle Scholar
  • 27 A. B. Harris, J. Phys. C 7, 1671 (1974). 10.1088/0022-3719/7/9/009 CrossrefGoogle Scholar
  • 28 J. A. Lipa, J. A. Nissen, D. A. Stricker, D. R. Swanson, and T. C. P. Chui, Phys. Rev. B 68, 174518 (2003). 10.1103/PhysRevB.68.174518 CrossrefGoogle Scholar
  • 29 M. Chan, N. Mulders, and J. Reppy, Phys. Today 49 [8], 30 (1996). 10.1063/1.881509 CrossrefGoogle Scholar
  • 30 M. H. W. Chan, K. I. Blum, S. Q. Murphy, G. K. S. Wong, and J. D. Reppy, Phys. Rev. Lett. 61, 1950 (1988). 10.1103/PhysRevLett.61.1950 CrossrefGoogle Scholar
  • 31 G. K. S. Wong, P. A. Crowell, H. A. Cho, and J. D. Reppy, Phys. Rev. B 48, 3858 (1993); 10.1103/PhysRevB.48.3858 Crossref;, Google ScholarG. K. S. Wong, Ph.D. Thesis, Cornell University (1990). Google Scholar
  • 32 J. Yoon, D. Sergatskov, J. Ma, N. Mulders, and M. H. W. Chan, Phys. Rev. Lett. 80, 1461 (1998). 10.1103/PhysRevLett.80.1461 CrossrefGoogle Scholar
  • 33 N. Mulders, R. Mehrotra, L. S. Goldner, and G. Ahlers, Phys. Rev. Lett. 67, 695 (1991). 10.1103/PhysRevLett.67.695 CrossrefGoogle Scholar
  • 34 H. Nishimori and G. Ortiz, Elements of Phase Transitions and Critical Phenomena (Oxford University Press, Oxford, U.K., 2010). CrossrefGoogle Scholar
  • 35 R. J. Donnelly and C. F. Barenghi, J. Phys. Chem. Ref. Data 27, 1217 (1998). 10.1063/1.556028 CrossrefGoogle Scholar
  • 36 G. Zassenhaus, Ph.D. Thesis, Cornell University (1999). Google Scholar
  • 37 D. F. Brewer, J. Low Temp. Phys. 3, 205 (1970). 10.1007/BF00628144 CrossrefGoogle Scholar
  • 38 E. G. Syskakis, F. Pobell, and H. Ullmaier, Phys. Rev. Lett. 55, 2964 (1985). 10.1103/PhysRevLett.55.2964 CrossrefGoogle Scholar
  • 39 F. M. Gasparini, M. O. Kimball, K. P. Mooney, and M. Diaz-Avila, Rev. Mod. Phys. 80, 1195 (2008). 10.1103/RevModPhys.80.1195 CrossrefGoogle Scholar
  • 40 B. D. Josephson, Phys. Lett. 21, 608 (1966). 10.1016/0031-9163(66)90088-6 CrossrefGoogle Scholar
  • 41 M. E. Fisher, M. N. Barber, and D. Jasnow, Phys. Rev. A 8, 1111 (1973). 10.1103/PhysRevA.8.1111 CrossrefGoogle Scholar
  • 42 G. Zassenhaus and J. D. Reppy, Phys. Rev. Lett. 83, 4800 (1999). 10.1103/PhysRevLett.83.4800 CrossrefGoogle Scholar
  • 43 T. Makiuchi, M. Tagai, Y. Nago, D. Takahashi, and K. Shirahama, Phys. Rev. B 98, 235104 (2018). 10.1103/PhysRevB.98.235104 CrossrefGoogle Scholar
  • 44 G. Y. Gor, D. W. Siderius, C. J. Raumussen, W. P. Krekelberg, V. K. Shen, and N. Bernstein, J. Chem. Phys. 143, 194506 (2015). 10.1063/1.4935430 CrossrefGoogle Scholar
  • 45 A. Weinrib and B. I. Halperin, Phys. Rev. B 27, 413 (1983). 10.1103/PhysRevB.27.413 CrossrefGoogle Scholar
  • 46 See, for example, M. N. Barber, in Phase Transitions and Critical Phenomena, ed. C. Domb and J. L. Lebowitz (Academic, New York, 1983) Vol. 8; Google ScholarK. Binder, Ferroelectrics 73, 43 (1987). 10.1080/00150198708227908 CrossrefGoogle Scholar
  • 47 B. D. Josephson, Phys. Lett. 1, 251 (1962). 10.1016/0031-9163(62)91369-0 CrossrefGoogle Scholar
  • 48 P. W. Anderson, Rev. Mod. Phys. 38, 298 (1966). 10.1103/RevModPhys.38.298 CrossrefGoogle Scholar
  • 49 R. E. Packard, Rev. Mod. Phys. 70, 641 (1998). 10.1103/RevModPhys.70.641 CrossrefGoogle Scholar
  • 50 T. Kobayashi, J. Taniguchi, A. Saito, S. Fukazawa, M. Suzuki, and K. Shirahama, J. Phys. Soc. Jpn. 79, 084601 (2010). 10.1143/JPSJ.79.084601 LinkGoogle Scholar
  • 51 K. Yamamoto, Y. Shibayama, and K. Shirahama, J. Phys. Soc. Jpn. 77, 013601 (2007). 10.1143/JPSJ.77.013601 LinkGoogle Scholar
  • 52 D. Stauffer, M. Ferer, and M. Wortis, Phys. Rev. Lett. 29, 345 (1972). 10.1103/PhysRevLett.29.345 CrossrefGoogle Scholar
  • 53 P. C. Hohenberg, A. Aharony, B. I. Halperin, and E. D. Siggia, Phys. Rev. B 13, 2986 (1976). 10.1103/PhysRevB.13.2986 CrossrefGoogle Scholar
  • 54 O. A. Prośniak, M. Łącki, and B. Damski, Sci. Rep. 9, 8687 (2019). 10.1038/s41598-019-44825-9 CrossrefGoogle Scholar
  • 55 O. Plantevin, H. R. Glyde, B. Fåk, J. Bossy, F. Albergamo, N. Mulders, and H. Schober, Phys. Rev. B 65, 224505 (2002). 10.1103/PhysRevB.65.224505 CrossrefGoogle Scholar
  • 56 See, for example, Low Temperature Physics, ed. Ch. Enss and S. Hunklinger (Springer, New York, 2005). Google Scholar
  • 57 R. D. Maurer and M. A. Herlin, Phys. Rev. 81, 444 (1951). 10.1103/PhysRev.81.444 CrossrefGoogle Scholar
  • 58 J. S. Brooks and R. J. Donnelly, J. Phys. Chem. Ref. Data 6, 51 (1977). 10.1063/1.555549 CrossrefGoogle Scholar