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dfree & d-imp
The program dfree calculates the gap, free-energy difference, and the second
derivative of the free-energy difference as a function of temperature and external
field for both s- and d-wave superconductors and for various film thicknesses.
Features and Description
The figure shows the numerical results of the upper stability limit (superheating
field) and of the lower stability limit (supercooling field) for a thickness
parameter s_d=77 and an impurity parameter of t_+=350 as a function of temperature
compared to the experimental results for Al (V. Yu. Butko, P. W. Adams, and E. I.
Meletis, Phys. Rev Lett. 83, 3725 (1999)).
The free-energy difference between the superconducting and normal state can be used
to calculate the thermodynamic critical field of a superconductor. It is the field
at which the free-energy of the normal state equals that of the superconducting
state.
From the gap as a function of temperature and external magnetic field, one can
calculate the supercooling and superheating limits of the superconductor.
Increasing and decreasing the external field does not result in the same
thermodynamic critical fields, which is a hysteresis-effect. Superconductivity may
break down at a higher field if the field is zero and turned up, than the onset of
superconductivity is, when turning the field down from a higher value.
The difference between s- and d- wave superconductors lies in the order parameter
(energy gap). The gap of an s-wave superconductor is the same for all wave-vectors
k, while that of a d-wave superconductor has nodes and is thus a function of k.
This results in similar, but different superconducting properties, including a
slightly higher upper critical field for d-wave superconductors.
In a superconductor, two electrons with opposite spin pair up to build a so-called
Cooper-pair. When an external field is switched on, there are two mechanisms that
break up the Cooper-pair: paramagnetic and orbital pair-breaking.
Assuming that the external field lies in the superconducting plane, only
paramagnetic pair-breaking takes effect in a 2d superconductor. Increasing the film
thickness causes an increase in the orbital pair-breaking effect and reduces the
upper critical field, which means that the field, at which superconductivity breaks
down, gets smaller. The same happens when increasing the tilt-angle of the external
field from parallel to perpendicular.
Impurities have the opposite effect. As the mean electron-path is lessened because
of scattering on impurity-sites, orbital pair-breaking is lessened and the upper
critical field increases. d-imp considers the effect of impurity scattering.
Download
The latest version of free_energy is 1.0
free_energy source package:free_energy-v1.tar.gz
Installation
- Unpack the tarball:
tar -zxvf free_energy*.tar.gz
- Compile the program:
make dfree && make d-imp
- To run the program use:
dfree dfree.cfg temperaturefile outputname or
d-imp d-imp.cfg temperaturefile outputname
- Read the README.dfree and README.d-impfor details on how to use this programs.
Documentation and Results
A comprehensive documentation on the mathematical and physical background and
results of the programs hc2, hc2d, fflo and free_energy can be read in the
dissertation of Sherryl Manalo
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