6 Kosterlitz Thouless transition in 4 He thin films

Transcription

1 6 Kosterlitz Thouless transition in 4 He thin films J.M. Kosterlitz and D.J. Thouless, Phys. 5, L124 (1972); ibid. 6, 1181 (1973) Topological phase transitions associated with: 1. dislocation-pair unbinding in 2D solids 2. vortex-pair unbinding in 2D superfluids or 2D XY spins David J. Thouless J. Michael Kosterlitz + torsional oscillator exp. dissipation peak KT theory was first experimentally verified by observation of 2D superfluid transition in 4 He thin films adsorbed on Mylar sheet. D.J. Bishop and J.D. Reppy, PRL 40, 1727 (1978) universal jump ρ s ( T KT ) = 2k B m2 T π 2 KT T KT jump in superfluid density Δρ s John D. Reppy

2 Experiments on 2D superfluid and superconducting KT transitions Torsional oscillator experiment on 4 He thin films adsorbed on Mylar sheet I-V characteristics in superconducting Josephson network H.S.J. van der Zant et al., PRB 50, 340 (1994) Nb x Si 1-x (x = 0.7, 0.42) D.J. Bishop and J.D. Reppy, PRB 22, 5171 (1980) J.D. Reppy, Physica B 126, 335 (1984) 1 μm V I a jump in a = 1 3 superfluid density

3 Specific heat anomalies of superfluid KT-transition in 4 He thin films T peak ( )T KT Theoretical calculation for 2D XY model AN.. Berker and D.R. Nelson, PRB 19, 2488(1979) T KT Specific heat anomaly at T = T KT is immeasurably small. On the other hand, around T = ( )T KT, there is a broad specific-heat peak due to dissociation of vortex pairs (proliferation of free vortices). Experimental observations for 2D superfluid transition in 4 He thin films adsorbed on porous media L.M. Steele, C. Yeager, and D. Finotello, PRL 71, 3673 (1993) (C) (ρ s ) 2D SF transition μmol/m 2 Broad specific C-peak was observed at T = ( )T c, where T c is the superfluid transition temperature determined by TO exp. (C) (C) (ρ s ) 3D SF transition

4 Various topological defects in 2D crystal dislocations (bound disclination pair) disclinations K.J. Strandburg, RMP 60, 161 (1988) 5 extra crystalline planes 3 Burgers vector 5-1 disclination (5-fold) 7 +1 disclination (7-fold) Vacancy string terminated by two dislocations W. Lechner et al., PRE 88, (R) (2013) R vacancy

5 Melting transition of 2D solids KTHNY model (Kosterlitz-Thouless-Halperin-Nelson-Young) B.I. Halperin and D.R. Nelson, PRL 41, 121 (1978), D.R. Nelson and B.I. Halperin, PRB 19, 2457 (1979), A.P. Young, PRB 19, 1855 (1979) T m 2D solids melt via two successive continuous phase transitions with an intermediate hexatic phase. T i temperature solid translational quasi-lo bond-orientational LO hexatic phase bond-orientational quasi-lo isotropic liquid b 1 + b 2 = 0 dissociation of dislocation pairs Burgers vector dissociation of disclination pairs 5-fold 7-fold dislocation pairs free dislocation (bound disclination pair) free disclinations

6 Hexatic phase in classical 2D solids Hexatic phase is widely accepted experimentally and theoretically in classical systems. adsorbed atoms on substrate, liquid crystals, charged or magnetic colloidal particles, etc. Colloidal particles of sub-μm size with superparamagnetic interaction ( χ eff B) 2 ( πn) 32 Γ = μ 0 4πk B T correlation functions P. Keim, R. Lenke, and G. Maret, PRL 82, 2721 (1999) Transition nature is still somewhat controversial. 10,000 36, ,400 10, ,000 90, Continuous transitions (?) M. Li, W.L. Johnson and W.A. Goddard III, PRB 46, (1996) F.L. Somer, Jr., G.S. Canright, and T. Kaplan, PRE 58, 5748 (1998) K. Wierschem and E. Manousakis, PRB 83, (2011) 2. 1st-order transition (?) K. Chen, T. Kaplan and M. Mostoller, PRL 74, (1995) M.R. Sadr-Lahijany, P. Ray and H.E. Stanley, PRL 79, 3206 (1997) D. Asenjo et al., PRB 83, (2011) structure factor P. Keim, G. Maret, and H.H. von Grünberg, PRB 75, (2007) Γ = 61.0 Γ = 59.6 Γ = 52.4 number of particles in simulation solid hexatic liquid

7 Order-disorder transitions in 2D commensurate phases of He stabilized by strong adsorption potential corrugation of graphite 4 He/gr or 3 He/gr 4 He/Kr/gr A A B C B A A B B A (1 1)[1/2] phase 3-states Potts model α C = AT ( T c ) T c α = 1/3 I-sing type logarithmic divergence α exp = 0.33 ± 0.01 Grafoil scaled to A = 30.5 m 2 (T T c ) / T c S. Nakamura et al., JLTP 171, 717 (2013) M.J. Tejwani, O. Ferreira and O.E. Vilches, PRL 44, 152 (1980)

8 Anomalous quantum phase in the 2nd layer of He on graphite S. Nakamura et al., PRB ZYX Grafoil 4 He C/Nk B He 0.2 C1: 1st layer commensurate phase S. Nakamura et al., to appear ZYX Grafoil T (K) A A B C C/Nk B He 3 He F2 (uniform fluid) L2 + C2 L2 G2 + L2 (uniform liquid) (gas+liquid) C2 C2 + IC2 IC2 (IC solid) T (K)

9 Quantum liquid crystal state in He-C2 phase Possibility-1: quantum hexatic phase, when periodic potential is less important Possibility-2: Commensurate phase with zero-point defectons (ZPDs), when periodic potential is important drawn by S. Nakamura based on MC calculation by K. Wierschem and E. Manousakis, PRB 83, (2011) Not a crystal but a liquid with finite spatial order ZPDs (free dislocation, vacancy chains,...) Not a solid with finite shear modulus but a crystal with fluidity at T = 0

10 4 He-C2 phase seems to be a supersolid Finite superfluid densities (ρ s ) have been observed in TO experiments by three different groups at densities nearby the C2 phase. (1) P.A. Crowell and J.D. Reppy, PRB 53, 2701 (1996) (2) Y. Shibayama et al., J. Phys.: 150, (2009) (3) J. Nyéki et al., Nature Phys. 13, 455 (2017) 6) Ref. [3] F2 (uniform fluid) L2 + C2 C2 IC2 (IC solid) G2 + L2 (gas+liquid) L2 (uniform liquid) C2 + IC2

11 Δ v Possible supersolidity in hcp solid 4 He ZPV scenario for supersolidity A.F. Andreev and I.M. Lifshitz, Sov. Phys. JETP 29, 1107 (1969) 0 E ZPV W v D(E) Δ v : vacancy creation energy W v : vacancy band width ( zt) z : number of nearest neighbors t : hopping integral Alexander F. Andreev Bose-Einstein condensation of ZPVs Ilya M. Lifshitz Torsional oscillator exp. on hcp 4 He E. Kim and M.H.W. Chan, Nature 427, 225 (2004);; Science 305, 1941 (2004) D.Y. Kim and M.H.W. Chan, PRL 109, (2012) torsional oscillator 1D S.F. network along screw dislocation cores? M. Boninsegni et al., PRL 99, (2007) winding-circle map by PIMC calculation DC super flow meas. Y. Vekhov et al., PRL 113, (2014)