Superconductivity: why can't the resistance reach 0?

Question

When we study electricity in high school we examine the resistance of conductors and its relation with temperature. Diagrams show the relationship at the beginning is pretty much a linear with temperature but at very low temperatures its starts to curve in such why it never reaches zero but it is close and the book explains it "At low temperatures it starts to curve because the conductor is not of pure material it has particles of other elements and their effect starts at low temperature and that is way it was linear beforehand"

My question is how do these other elements stop it from reaching 0 and why don't they have the same effect on our conductive the whole time why does it only show at 159.7K and even less?

The explanation is that as temperature is reduced, the movement of the atoms is slowed which attributes to a lower chance of the electrons' movement being slowed because of bumping into atoms increasing their speed which means it has less resistance.

Why can't the resistance reach zero?

Answer 1

In the following, I will focus on what amount of correctness may be extracted from your book statement and what it refers to in my understanding.

There are very many factors at play in the determination of resistance of a material. This being said, let us imagine that the system you are considering is a metal. Then, you may consider that some electrons are free to move as in an electron gas, and are subject to the potential of the atoms which make up the crystal. In such a system, and contrary to intuition, if the crystal is perfect, resistance should be 0. This is because perfect crystal means perfect translational symmetry, and in this framework, you may show that the electrons' velocity is a constant.

Where does resistivity come from then? The answer is in the preceding paragraph: from the imperfections of the crystalline lattice. Your book refers to two such imperfection sources:

1. The motion of the atomic nuclei which, when they vibrate, make the translational symmetry of the crystal imperfect. In simpler terms, this is temperature: when T increases, the atomic motion increases, the crystal imperfections are more important, and resistivity increases. That this relationship is linear or not is another matter which I will not consider here.
2. When T goes down, the atoms which make up the atomic lattice move less and less. At absolute 0 we should expect them to be "frozen", and resistivity therefore should be zero. This does not happen so, because once the resistivity coming from the atomic motion is small enough, then the resistivity coming from other imperfections of the lattice become visible. Here your book refers to impurities of the crystal, which always exist in nature - replacing an atom of Si in a silicon crystal by some other element, or having some lacking atom, breaks the translational symmetry of the system, and therefore induces resistivity.

The resistivity coming from impurities is small, and has a very very weak T dependence. For all practical purposes it may be considered constant. Therefore, it only shows up at very low temperatures, because for higher temperatures, it is dominated by the resistivity contribution coming from atomic motion.

Of course all of this is oversimplified, and even the obvious looking statement that electrons "bump into atoms" is totally wrong at the microscopic level, but as a very first approach, this conveys a few concepts on the origin of resistivity and some of its temperature dependence.

Answer 2

Anything that disturbs the trajectory of a DC current electron shows up as resistance. A pure and perfect crystal lattice has thermal vibrations. Electrons scatter off phonons. Current electrons scatter off valence electrons. Electrons have spin-1/2. They are fermions. Only two can occupy a common energy level. A macroscopic current contains stacked high energy electrons

Now go to a BCS supercon. The supercurrent is a degenerate sea of spin-1 boson Cooper pairs with conjugate momenta. A naive model would have the spin-antipaired electrons zooming in opposite directions, with their center of mass drift being the supercurrent. DEGENERATE. To elevate the degenerate Bose sea to a higher energy state is to elevate all of it - or none. It propagates past small stuff without interaction, without DC resistance.

The forgoing is a obviously a poor model. AC supercons are dissipative, spin vorrtices in Type II supercons, magnetic field quenching, etc. It does hint at why a normal current must have resistance and a supercurrent need not.