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How to detect quasiparticle entropy current with lots of phonons around

In superconductors, electrons form Cooper pairs, which are collectively called the condensate.  The condensate displays all the spectacular electronic properties that one associates with superconductivity, such as flux expulsion (Meissner effect).  At finite temperature, however, a small fraction of the pairs is 'broken' to form quasiparticles (entropy must be finite!).  The quasiparticle is a quantum superposition of a pure-particle state and a pure-hole state.  For many purposes, however, we may simply regard it as an 'electron' drifting inside the condensate.  There is enormous interest in the properties of quasiparticles because they are the fundamental, low-energy excitations of the condensate.  Moreover, in the cuprates, the quasiparticles have a linear E(k) vs. k dispersion.  This Dirac-like dispersion adds to their interest.  However, they are difficult to 'see' experimentally.  A powerful approach is to investigate the heat (or entropy) current of the quasiparticles.  The condensate is indifferent to a thermal gradient (since it carries zero entropy), whereas quasiparticles drift down the gradient to produce an electronic heat current.  A drawback to overcome is that the thermal gradient also produces a phonon current (lattice vibrations), which may be much larger than the electronic heat current.

So, here's the problem.  How do you see the quasiparticle entropy current against the large background of the phonons?  Let's consider piercing the condensate with an array of vortices (quantized flux lines) by applying a magnetic field.  Each vortex core is surrounded by a tight supercurrent loop whose sense of circulation is fixed by the applied field direction.  The vortex strongly scatters quasiparticles (figure).  Because of the superfluid circulation around the vortex, the quasiparticles suffer a left-right scattering asymmetry.  More of them end up, say, to the left of the core compared with the right (viewed from the incident direction).  This unbalance leads to a transverse temperature gradient that translates into a large thermal Hall conductivity kxy.  Phonons, which are electrically neutral, do not suffer this asymmetric scattering.  Thus, by monitoring kxy, we measure a 'Hall' heat current entirely from the quasiparticles.  With this technique (and some simple assumptions) we can objectively back out the quasiparticle lifetime and density, and learn a lot about their behavior in an intense field.
 

Figure 1   Traces of the thermal Hall conductivity kxy versus field H at selected temperatures above 35 K in a BZO-grown crystal of optimally-doped superconductor YBa2Cu3O7 with Tc = 92 K.  At each temperature, kxy rises steeply in weak fields, reaches a broad maximum and then decreases slowly.  The rate of the initial increase is proportional to the square of the zero-field mean-free-path l. The inset compares the thermal conductivity ka in this crystal (solid circles) with that in a non-BZO grown crystal (open circles).  Both are detwinned.  These curves were taken by Yuexing Zhang at Princeton.  The BZO crystal was grown at the Univ. British Columbia (Liang, Bonn, and Hardy).  From Ref. 2 below.

The traces in Figure 1 represent the thermal Hall conductivity kxy versus field H at various temperatures.  kxy is the qp heat current deflected to the left by the vortices (it changes sign when H is reversed in direction).  At high temperatures (85 K) it is simply proportional to B, the vortex density.  At lower temperatures, however, kxy goes through a broad maximum.  A striking feature here is the very rapid increase in the initial slope dkxy/dB, which grows a thousand-fold between 90 K and 30 K.  This reflects a very steep increase in the zero-field mean-free-path of the quasiparticles.
 

 

 

 

 

 

 


 

Figure 2   The zero-field mean-free-path l extracted from the initial slope of kxy displayed in Fig. 1. Values of the weak-field Hall angle q/B (proportional to l) is shown on the right scale.  The open and closed circles show two alternate ways of calculating l.  The expanded scale shows the remarkably steep increase in l just below Tc.  From Ref. 2 below.


As shown in Fig. 2, l is not strongly T dependent above Tc, but accelerates rapidly in the superconducting state.  Between Tc and 20 K, l increases 200 fold from about 80 Angstroms to nearly 1 micron.  The steep increase in quasiparticle lifetime below Tc is one of the characteristics of the cuprates, and is not at all understood.
 

References
1. K. Krishana, J. M. Harris, and N. P. Ong, “Quasi-particle mean-free-path in YBa2Cu3O7 measured by the thermal Hall conductivity.”, Phys. Rev. Lett. 75, 3529 (1995).
2. Y. Zhang, N.P. Ong, P. W. Anderson, D. A. Bonn, R. X. Liang, and W. N. Hardy, “Giant enhancement of the thermal Hall conductivity in high-purity YBa2Cu3O7.”, Phys. Rev. Lett. 86, 890 (2001).