Thermodynamics of an incommensurate quantum crystal

Abstract

We present a simple theory of the thermodynamics of an incommensurate quantum solid. The ground state of the solid is assumed to be an incommensurate crystal, with quantum zero-point vacancies and interstitials and thus a non-integer number of atoms per unit cell. We show that the low temperature variation of the net vacancy concentration should be as $T^4$, and that the first correction to the specific heat due to this varies as $T^7$; these are quite consistent with experiments on solid ${}^4$He. We also make some observations about the recent experimental reports of ``supersolidity'' in solid ${}^4$He that motivate a renewed interest in quantum crystals.

arXiv commentrevised, new title, somewhat expanded

References in corpus (2)

• Ring exchanges and the supersolid phase of 4He
• Bose Einstein Condensation in solid 4He

Cited by in corpus (29)

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• What makes a crystal supersolid ?
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• Two New Vortex Liquids
• On the origin of the decrease in the torsional oscillator period of solid He4
• Intrinsic and dislocation induced elastic behavior of solid helium
• Entropy of solid He4: the possible role of a dislocation glass
• Solid 4He and the Supersolid Phase: from Theoretical Speculation to the Discovery of a New State of Matter? A Review of the Past and Present Status of Research
• Bose Einstein Condensation of incommensurate solid 4He
• Non Classical Rotational Inertia Fraction in a One Dimensional Model of Supersolid
• Ginsburg-Landau theory of supersolid
• Absence of low temperature anomaly in the Debye-Waller factor of solid He-4
• Melting curve of ${}^4$He: no sign of the supersolid transition down to 10 mK
• Minimal Model for Disorder-induced Missing Moment of Inertia in Solid ${}^4$He
• Absence of low temperature anomaly on the melting curve of ${}^4$He
• Mutual Composite Fermion and composite Boson approaches to balanced and imbalanced bilayer quantum Hall system: an electronic analogy of the Helium 4 system
• Zero-point vacancies in quantum solids
• Onset temperature of Bose-Einstein condensation in incommensurate solid 4He
• Zero-point Divacancy Concentration in the Shadow Wave-Function Model for Solid 4He
• Classification of a supersolid: Trial wavefunctions, Symmetry breakings and Excitation spectra
• Density Wave -Supersolid and Mott Insulator-Superfluid transition in presence of an artificial gauge field : a strong coupling perturbation approach
• Superfluidity versus localization in bulk 4He at zero temperature
• Study of solid 4He in two dimensions. The issue of zero-point defects and study of confined crystal
• Mott Insulator - Superfluid Transitions in a Two Band Model at Finite Temperature and Possible Application to Supersolid 4He
• Theory of Supersolids beyond Mean-Field
• Finite Temperature Properties of a Supersolid: a RPA Approach
• Roton softening and supersolidity in Rb spinor condensates
• Hydrodynamic theory of Rotating Ultracold Bose Einstein Condensates in Supersolid Phase