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Superfluidity and superconductivity?

Is there any relation between the two aside from the fact that they are somewhat analogies , I see a lot of people on the internet who claim the helium (in it's superfluid state) is a also a super conductor but searching this site and Wikipedia I couldn't find anything speaking directly of this although I found statements like this "liquid helium is used to cool the superconducting material ...." which suggest the opposite .

-update: "Josephson effect has also been observed in SHeQUIDs, the superfluid Helium analog of a dc-SQUID" in case SHeQUIDs isn't a superconductor how could this be?

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3 Answers 3

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Both of them are super-interesting to study:-)

Superfluid is a low-temperature state of a quantum many-body system of electrically neutral particles (e.g. atoms). Superfluids have some amazing properties. For example, there is no dissipation (i.e. friction) and the flow is irrotational (up to quantum vortices). Theoretically it is described by a macroscopic wave-function with its absolute value related to the superfluid density and the gradient of its phase defines the superfluid velocity. In addition, in every superfluid there is also a physical Goldstone mode which costs nothing to excite.

Superconductor is like a superfluid, but the elementary particles are electrically charged (e.g. electrons). This leads to the Meissner effect, i.e. it costs energy for the magnetic field to penetrate into a superconductor. There is also no physical soft mode in the energy spectrum. Theoretically all this is explained by the Higgs mechanism.

In both cases the lowest energy quantum state is macroscopically populated which is know as Bose-Einstein condensation.

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  • $\begingroup$ Thanks for your explaination. However, I am still unclear since I saw the concept, neutral superconductor. That concepet is given in page 504 in Piers Coleman's Introduction to many-body physics. Besides, Coleman says neutral superconductor would leads to gapless Bogoliubov mode. So is the concept of neutral superconductor equivalent to superfluidity? $\endgroup$
    – xiang sun
    Commented Sep 13, 2021 at 6:44
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There is a HUGE relation between them and Bose-Einstein condensation.

I refer you to the amazingly amazing book by James Annett (which explains precisely your question):
Superconductivity, Superfluids, and Condensates

http://www.amazon.com/Superconductivity-Superfluids-Condensates-Condensed-Physics/dp/0198507569

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The superconductivity (SC) and superfluidity (SF) both have one universal origin — the Bose-Einstein-Condensation (BEC) of bosons, because BEC-bosons have a minimum and quantized kinetic energy and, thus, cannot transfer their energy to other particles by arbitrarily small portions. In case of SC a boson is an electron pair, in case of SF a boson is a neutral atom (usually — helium atom). The BEC temperature inversely depends on boson mass, so the critical temperature (Tc) of SC may be much higher than Tc of SF.

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