# What is the drift velocity of an electron in a superconductor?

How is it,when compared to drift velocity in a conductor?

• – Farcher Sep 18 '18 at 5:40

Drift velocity of electrons is a concept dependent on the solid state model assumed for a solid. Here is a microscopic view of current Where drift velocity can be defined .

Even though conductors are best described with the band theory of solids, this microscopic view makes sense as charge moves in steps in the lattice dimensions.

For superconductivity, models exist where the behavior of electrons carrying the charge is not as the above picture.

BCS theory applies directly to superconductors such as Nb3Ge (Tc = 23K) in which the electrons are bound together by their interaction with the vibrations of the underlying lattice: one electron in the pair polarizes the lattice by attracting the nuclei towards it, leaving a region of excess positive charge (a potential well) into which a second electron is attracted - the positively charged nuclei thus mediate an attraction between the negatively charged electrons. Only electrons within the vibrational frequency of Ef can be paired by this interaction, and so only a small fraction of the electrons become superconducting.

I suppose that for the not bonded electrons, if a field is applied the drift velocity will be the one defined at the top. Otherwise a specific model is needed for the drift velocity of charge carriers in a superconducting circuit. Note that Ohms law does not apply as the resistance is zero, and an applied electric field will destroy superconductivity.

This paper uses the drift velocity of charge carriers in a superconductor in a specific model.

This measurement states :

The drift velocity, in agreement with the theory, turned out to be proportional to the current density and independent of the configuration of the normal and superconducting layer.

Thus the drift velocity is the one of the material, of course at the low temperatures of superconductivity. There exists a temperature dependence : This is for a semiconductor, Gemanium, but a7 slight dependence exists also in metals as far as I can check.

• Please summarise the paper which you linked or at least tell me what to read. I am just starting to study superconductors. – Krishna Deshmukh Oct 6 '18 at 15:59
• you should read the linked paper, it is simple enough arxiv.org/ftp/arxiv/papers/1012/1012.0879.pdf – anna v Oct 9 '18 at 8:26

Below I copied part of the Wiki article that explains drift veolcity. The term σ refers to the conductivity which for a material in superconducting mode would be very large. Therefore it would seem that the drift velocity would be much higher than for ordinary conducting materials. The rest of the variables are of course important, but you did not specify the specific counductor material. Ordinary materials only drift at a less than a millimeter per second so even in a superconductor it would still be very much less than the speed of light.

From wiki:

In terms of the basic properties of the right-cylindrical current-carrying metallic ohmic conductor, where the charge-carriers are electrons, this expression can be rewritten as[citation needed]:

where, u is again the drift velocity of the electrons, in m⋅s−1; m is the molecular mass of the metal, in kg; ΔV is the voltage applied across the conductor, in V; ρ is the density (mass per unit volume) of the conductor, in kg⋅m−3; e is the elementary charge, in C; f is the number of free electrons per atom. ℓ is the length of the conductor, in m; and

# σ is the electric conductivity of the medium at the temperature considered, in S/m

drift velocities in superconducting materials were about the same as for good conductors like copper wire. So somewhere in the neighborhood of .1 to 1 mm/sec.