The%20Pippard%20coherence%20length

1
The Pippard coherence length
In 1953 Sir Brian Pippard considered
He concluded
1. N/S boundaries have positive surface
energy
The superconducting electron density ns cannot
change rapidly with position...
2. In zero magnetic field
superconducting transitions in pure
superconductors can be as little as 10-5K
wide
.it can only change appreciably of a distance of
?10-4cm,
The boundary between normal and superconducting
regions therefore cannot be sharp.
Thus all electrons in the sample must
participate in superconductivity and there must
be long range order or coherence between the
electrons
..ns has to rise from zero at the boundary to a
maximum value over a distance ?
3. Small particles of superconductors
have penetration depths greater than those
of bulk samples
? is the Pippard coherence length
Therefore superconducting electron densities must
change at a relatively slow rate through the
sample
Lecture 5
2
The Pippard coherence length
The superconducting electron density ns cannot
change rapidly with position...
.it can only change appreciably of a distance of
?10-4cm,
The boundary between normal and superconducting
regions therefore cannot be sharp.
..ns has to rise from zero at the boundary to a
maximum value over a distance ?
? is the Pippard coherence length
Lecture 5
3
Surface energy considerations
We now have two fundamental length scales of the
superconducting state
The penetration depth, ?, is the length scale
over which magnetic flux can penetrate a
superconductor
The coherence length, ?, is the length scale over
which the superelectron density can change
which changes on the length scale of ?
which changes on the length scale of ?
Lecture 5
4
Positive and negative surface energy
For ? gt ?
For ? lt ?
Surface energy is positive Type I
superconductivity
Surface energy is negative Type II
superconductivity
Lecture 5
5
Conditions for Type II Superconductivity
If the surface energy is negative we expect Type
II superconductivity
Normal cores ,flux lines or vortices will
appear and arrange themselves into an hexagonal
lattice due to the repulsion of the associated
magnetic dipoles
? radius over which superconductivity is
destroyed
? radius of vortex
Lecture 5
6
The Lower and Upper Critical Fields
(A more rigorous G-L treatment shows ? must be
greater than ?2 -see later lectures)
Hc1 is known as the lower critical field
As some magnetic flux has entered the sample it
has lower free energy than if it was perfectly
diamagnetic, therefore a field greater than Hc is
required to drive it fully normal
Note for Nb, ?1
This field, Hc2, is the upper critical field.
Lecture 5
7
Ginzburg-Landau Theory
Everything we have considered so far has treated
superconductivity semi-classically
However we know that superconductivity must be a
deeply quantum phenomenon
In the early 1950s Ginzburg and Landau developed
a theory that put superconductivity on a much
stronger quantum footing
Their theory, which actually predicts the
existence of Type II superconductivity, is based
upon the general Landau theory of second order
or continuous phase transitions
In particular they were able to incorporate the
concept of a spatially dependent superconducting
electron density ns, and allowed ns to vary with
external parameters
Lecture 5
8
Landau Theory of Phase Transitions
We find M0 for TgtTCM M?0 for TltTCM
Any second order transition can be described in
the same way, replacing M with an order parameter
that goes to zero as T approaches TC
Lecture 5
9
The Superconducting Order Parameter
We have already suggested that superconductivity
is carried by superelectrons of density ns
ns could thus be the order parameter as it goes
to zero at Tc
This complex scalar is the Ginzburg-Landau order
parameter
Lecture 5
10
Free energy of a superconductor
? and ? are parameters to be determined,and it is
assumed that ? is positive irrespective of T and
that ? a(T-Tc) as in Landau theory
Lecture 5