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Anomalous thermal diffusivity in underdoped YBa2Cu3O6+x

Research paper by Jiecheng Zhang, Eli M. Levenson-Falk, B. J. Ramshaw, D. A. Bonn, Ruixing Liang, W. N. Hardy, Sean A. Hartnoll, Aharon Kapitulnik

Indexed on: 09 May '17Published on: 08 May '17Published in: PNAS



Abstract

The thermal diffusivity in the <mml:math><mml:mrow><mml:mi>a</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:math>ab plane of underdoped YBCO crystals is measured by means of a local optical technique in the temperature range of 25–300 K. The phase delay between a point heat source and a set of detection points around it allows for high-resolution measurement of the thermal diffusivity and its in-plane anisotropy. Although the magnitude of the diffusivity may suggest that it originates from phonons, its anisotropy is comparable with reported values of the electrical resistivity anisotropy. Furthermore, the anisotropy drops sharply below the charge order transition, again similar to the electrical resistivity anisotropy. Both of these observations suggest that the thermal diffusivity has pronounced electronic as well as phononic character. At the same time, the small electrical and thermal conductivities at high temperatures imply that neither well-defined electron nor phonon quasiparticles are present in this material. We interpret our results through a strongly interacting incoherent electron–phonon “soup” picture characterized by a diffusion constant <mml:math><mml:mrow><mml:mpadded width="+1.7pt"><mml:mi>D</mml:mi></mml:mpadded><mml:mo>∼</mml:mo><mml:mrow><mml:msubsup><mml:mi>v</mml:mi><mml:mi>B</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mi>τ</mml:mi></mml:mrow></mml:mrow></mml:math>D∼vB2τ, where <mml:math><mml:msub><mml:mi>v</mml:mi><mml:mi>B</mml:mi></mml:msub></mml:math>vB is the soup velocity, and scattering of both electrons and phonons saturates a quantum thermal relaxation time <mml:math><mml:mrow><mml:mpadded width="+1.7pt"><mml:mi>τ</mml:mi></mml:mpadded><mml:mo>∼</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">ℏ</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi>B</mml:mi></mml:msub></mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:mrow></mml:math>τ∼ℏ/kBT.