[Paper Review] Roton-like mode in solid He-4

E. Blackburn, S. K. Sinha+4 more|ArXiv.org|Feb 25, 2008

Quantum, superfluid, helium dynamics24 references3 citations

TL;DR

This study identifies a roton-like mode in solid 4He using inelastic neutron scattering, revealing delocalized vacancy excitations with a longitudinal effective mass within 15% of superfluid 4He rotons. The mode exhibits dispersive behavior, intersects with acoustic phonons, and provides direct evidence for coherent non-phonon excitations in the solid, suggesting persistent roton-like character despite lattice ordering.

ABSTRACT

Recent theoretical and experimental work on solid He-4 has focused on vacancies, or other lattice defects and whether these can form a Bose-Einstein condensate within the solid. The earliest suggestion that this could happen was based on the conjecture that the ground state of the solid at T = 0 K would include vacancies. Although no direct evidence for zero point vacancies has been presented, a variety of experimental observations have been interpreted as being due to thermally activated vacancies. Here we directly probe the excitation spectrum of hcp solid He-4 using inelastic neutron scattering. We identify a branch of delocalized excitations, with both longitudinal and transverse dispersion that coexist with acoustic phonons. While the energy gap is larger and the characteristic wavevector is shifted to coincide with the position of the (100) Bragg peak, the longitudinal effective mass of this mode is within 15% of that for rotons in superfluid He-4. The dispersion relation intersects the longitudinal acoustic phonon half way to the zone boundary, and this distinguishes the mode from a conventional optic phonon. Our results provide direct evidence for coherent delocalized non-phonon excitations in solid helium, which we identify as delocalized vacancy modes.

Motivation & Objective

• To directly probe the excitation spectrum of hcp solid 4He using high-resolution inelastic neutron scattering.
• To investigate the nature of non-phonon excitations observed in previous indirect measurements.
• To determine whether delocalized vacancies or other defects form coherent, dispersive modes in solid 4He.
• To assess the contribution of these modes to the specific heat and their potential link to supersolid behavior.
• To compare the dispersion and effective mass of these modes with those of rotons in superfluid 4He.

Proposed method

• Inelastic neutron scattering was performed using the NG4 disk chopper time-of-flight spectrometer at the NIST Center for Neutron Research.
• Measurements were conducted on low-density single-crystalline 4He samples at temperatures down to 55 mK using incident neutron wavelengths of 3.7 Å and 5.2 Å.
• Energy transfers were determined from neutron time-of-flight, with a resolution of ~0.2 meV FWHM.
• Acoustic velocity and attenuation were monitored via quartz transducers to assess crystal quality and monitor growth.
• Data were analyzed using Gaussian fitting and the DAVE software package for reduction and analysis.
• The dispersion relation of the new excitation was extracted and fitted to a quadratic form to extract effective mass and energy gap.

Experimental results

Research questions

• RQ1 Do delocalized vacancy modes exist as coherent, dispersive excitations in solid 4He?
• RQ2 How does the dispersion and effective mass of these modes compare to rotons in superfluid 4He?
• RQ3 Can these modes be distinguished from conventional optic phonons based on symmetry and dispersion?
• RQ4 What is the contribution of these modes to the specific heat of solid 4He?
• RQ5 Do these modes persist across the putative supersolid transition, and what does their presence imply for the supersolid phase?

Key findings

• A gapped, dispersive excitation was observed with a longitudinal effective mass of 0.107 ± 0.003 mHe in crystal 1 and 0.114 ± 0.005 mHe in crystal 2, within 15% of the roton effective mass in superfluid 4He.
• The energy gap for the vacancy mode is 0.951 ± 0.004 meV in crystal 1 and 1.002 ± 0.003 meV in crystal 2, with a minimum at wavevector 1.964 ± 0.006 Å⁻¹.
• The dispersion relation intersects the longitudinal acoustic phonon mode halfway to the zone boundary, distinguishing it from conventional optic phonons.
• The linewidth of the mode is constrained to less than 21 μeV, indicating a lower limit on its lifetime of 0.2 ns.
• A broad feature consistent with the transverse optical phonon branch was observed, which had not been resolved in prior experiments.
• No significant change in the density of states between 0.15 meV and 5.5 meV was observed upon cooling through the putative supersolid transition, but the new collective modes remain a key feature of the solid state.