Normal modes and specific heat of a lattice of undamped pancake vortices in thin superconducting mulitlayers

Journal Article · Tue Nov 01 04:00:00 EST 1994 · Physical Review, B: Condensed Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.50.13695· OSTI ID:6903793

Fetter, A L ^[1]

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1. Department of Physics, Stanford University, Stanford, California 94305 (United States)

Recent high-field ([ital B][le]8 T) experiments on single crystals of Bi[sub 2]Sr[sub 2]CaCu[sub 2]O[sub [ital x]] (BSCCO-2:2:1:2) have found a significant anisotropy in the specific heat, with an excess contribution for perpendicular field (along the [ital c] axis) relative to that for parallel or zero field. One possible explanation for these observations is the undamped vibrational modes of the lattice of pancake vortices, which occur only for the perpendicular orientation. The London model of thin superconducting layers provides a simple theoretical picture that allows a direct evaluation of the elastic energy for small deformations of the vortex lattice. For typical temperatures, the resulting vortex contribution [ital C][sub [ital v]] to the heat capacity has a Debye form for two-dimensional phonons, with a Debye temperature [Theta][sub [ital v]]=1/2[h bar][omega][sub [ital c]]/[ital k][sub [ital B]], where [omega][sub [ital c]] is the electron cyclotron frequency (for [ital B]=10 T and free electrons, [Theta][sub [ital v]][approx]6.7 K). For [ital T][gt][Theta][sub [ital v]], the resulting [ital C][sub [ital v]] approaches [ital k][sub [ital B]] per pancake vortex, as appropriate for vortex dynamics and in qualitative agreement with the experimental observations; for [ital T][lt][Theta][sub [ital v]], the theory predicts that [ital C][sub [ital v]][proportional to][ital T][sup 2], but this particular power law remains to be verified experimentally. If an inertial mass [ital m][sub [ital c]] is ascribed to each pancake vortex, an additional set of (Newtonian) normal modes yields a further (Einstein) heat capacity, with [Theta][sub [ital E]][proportional to][ital m][sub [ital c]][sup [minus]1]. The presence (absence) of such a contribution to [ital C][sub [ital v]] could help determine (bound) the value of the currently controversial quantity [ital m][sub [ital c]].

• OSTI ID: 6903793
• Journal Information: Physical Review, B: Condensed Matter; (United States), Journal Name: Physical Review, B: Condensed Matter; (United States) Vol. 50:18; ISSN PRBMDO; ISSN 0163-1829
• Country of Publication: United States
• Language: English

Related Subjects

665411* -- Basic Superconductivity Studies-- (1992-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ELASTICITY
ENERGY LEVELS
EQUATIONS
EXCITED STATES
FILMS
LONDON EQUATION
MAGNETIC FLUX
MECHANICAL PROPERTIES
NORMAL-MODE ANALYSIS
PHYSICAL PROPERTIES
SPECIFIC HEAT
SUPERCONDUCTING FILMS
TENSILE PROPERTIES
THERMODYNAMIC PROPERTIES
VIBRATIONAL STATES