# Transport entropy of vortices in superconductors with paramagnetic impurities

## Abstract

The entropy S/sub D/ transported by a unit segment of a moving vortex line, in a type-II superconductor in the flux-flow regime, is calculated microscopically for gapless superconductors containing arbitrary amounts of paramagnetic and nonmagnetic impurities, assuming low average magnetic induction B approx. = 0, and large Ginzburg-Landau parameter kappa >> 1. The calculation is based on a new prescription for calculating certain heat-current-related transport properties in magnetic conductors, recently derived by the author to resolve a contradiction with either the third law of thermodynamics or Onsager's principle. For high concentrations of magnetic impurities, when the gaplessness condition is satisfied at absolute zero temperature, it is shown in the low-field limit that a requirement from the third law, viz., S/sub D/ ..-->.. 0 as T ..-->.. 0, is exactly satisfied, thereby giving strong support to the underlying new method for calculating S/sub D/ and other related transport properties. Combining the present results with our earlier results on S/sub D/ in the high-field limit B approx. = H/sub c//sub 2/, S/sub D/ is predicted to first rise linearly as B is lowered from H/sub c//sub 2/, and then to bend upward to approach a finite limit as B is further loweredmore »

- Authors:

- Publication Date:

- Research Org.:
- Department of Physics, University of Southern California, Los Angeles, California 90007

- OSTI Identifier:
- 7241580

- Resource Type:
- Journal Article

- Journal Name:
- Phys. Rev., B; (United States)

- Additional Journal Information:
- Journal Volume: 14:11

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; TYPE-II SUPERCONDUCTORS; MAGNETIC FLUX; ENTROPY; IMPURITIES; MAGNETIC FIELDS; PARAMAGNETISM; TRANSPORT THEORY; MAGNETISM; PHYSICAL PROPERTIES; SUPERCONDUCTORS; THERMODYNAMIC PROPERTIES; 656100* - Condensed Matter Physics- Superconductivity

### Citation Formats

```
Hu, C.
```*Transport entropy of vortices in superconductors with paramagnetic impurities*. United States: N. p., 1976.
Web. doi:10.1103/PhysRevB.14.4834.

```
Hu, C.
```*Transport entropy of vortices in superconductors with paramagnetic impurities*. United States. https://doi.org/10.1103/PhysRevB.14.4834

```
Hu, C. Wed .
"Transport entropy of vortices in superconductors with paramagnetic impurities". United States. https://doi.org/10.1103/PhysRevB.14.4834.
```

```
@article{osti_7241580,
```

title = {Transport entropy of vortices in superconductors with paramagnetic impurities},

author = {Hu, C},

abstractNote = {The entropy S/sub D/ transported by a unit segment of a moving vortex line, in a type-II superconductor in the flux-flow regime, is calculated microscopically for gapless superconductors containing arbitrary amounts of paramagnetic and nonmagnetic impurities, assuming low average magnetic induction B approx. = 0, and large Ginzburg-Landau parameter kappa >> 1. The calculation is based on a new prescription for calculating certain heat-current-related transport properties in magnetic conductors, recently derived by the author to resolve a contradiction with either the third law of thermodynamics or Onsager's principle. For high concentrations of magnetic impurities, when the gaplessness condition is satisfied at absolute zero temperature, it is shown in the low-field limit that a requirement from the third law, viz., S/sub D/ ..-->.. 0 as T ..-->.. 0, is exactly satisfied, thereby giving strong support to the underlying new method for calculating S/sub D/ and other related transport properties. Combining the present results with our earlier results on S/sub D/ in the high-field limit B approx. = H/sub c//sub 2/, S/sub D/ is predicted to first rise linearly as B is lowered from H/sub c//sub 2/, and then to bend upward to approach a finite limit as B is further lowered to approach zero, for practically all concentrations of magnetic and nonmagnetic impurities. The exact amount of upward bending depends on the concentrations of the two types of impurities, but is generally larger for dirtier systems. As a side product of this work, a plausible identification is given of the physical meaning of an anomalous quantity u/sub 1/ in the set of dynamic equations first derived by Eliashberg as being proportional to the local temperature deviation from equilibrium. (AIP)},

doi = {10.1103/PhysRevB.14.4834},

url = {https://www.osti.gov/biblio/7241580},
journal = {Phys. Rev., B; (United States)},

number = ,

volume = 14:11,

place = {United States},

year = {1976},

month = {12}

}