Does superconductor has zero resistance? What does it mean? Let’s debunk it
By: Sakibul Islam Sazzad
Tags: Superconductivity, Quantum Mechanics, Quantum Computing

In Oct 14, 2020 an article published in Nature on first room temperature superconductivity. I first learnt about superconductivity in a course at SUST, titled “Electrical properties of materials” aka “materials”. I almost forgot what I had learnt, so after reading the article some curiosity popped up in my mind. It happened due to two reasons-

1. One of my field of interest in Quantum Computing (QC), where photonics with a near about absolute zero temperature is used. Like way IBM generates qubit is superconducting devices, mainly a josephson junction/effect. Honeywell, IonQ uses a trap-down system that is confined to an ion to electric field and then does the controlling for quantum computing.

2. I almost forgot what I learnt in my undergrad school. To revive it, in my free time I tried to read some articles, blogs, and watch youtube lectures.

Wanted to write something that I have learnt but day by day is being a “lutha” a SUST slang to mark laziness. Now I have a sudden rush to write it up. Let’s start. Whoever has heard the word of superconductivity, he should be familiar with the term BCS theory in superconductivity. Actually BCS annotes to three Nobel Laureate Bardeen, Cooper, Shrieffer who described how a superconductivity forms in a metal. So the first question should be addressed- What is superconductivity?

Before answering that question let’s try to get an answer to one question: what is conductivity and how does it form? There are many theories to explain it, I will try to give you an intuition for a model- Drude Model in solids. Basically its model how electrons transports through a metal. It can be analogous of gases, due to temperature particles or molecules of gases scattered randomly. Pardon me, I am not digging up a core explanation rather than just trying to get the idea how the Drude model explains conductivity to metal. So if you increase the temperature of gases, random movement gets increased, it means gases engaged into collision. Same thing happens to electrons in metal. Normally there is a flowing property of electron for which it transports through the crystallines but if temperature increases this flowing property of electron gets a hindrance. This hindrance to flow electron is known as Resistance.

Now if I try to decrease the temperature what should happen? Random movement should get decreased and near about absolute zero temperature there should be no energy of the electron except vibration energy.

But a strange thing happens that there is a critical temperature for which metal shows no resistivity. Now let me tell that typically we explain that a superconductor has zero resistance. This quote has an inner meaning, let me explain. If someone looks at the Drude Model equation, he/she will find that it is a Maxwell-Boltzmann Statistics. You will find an exponential decay with respect to temperature. So what does it mean? It means if I increase the temperature, the electrons exponentially decays (if a question pops up in your mind, what does it mean exponential decays for electrons- leave it for a moment, I will explain it later), so electrons can’t travel through solids. Now do the same analogy for decrement temperature, as it has an exponential decays, for a little kelvin scale temperature electrons take such a long time to decay that we can say electrons are traveling for a infinite time

Actually this is what happens for a super-conductor. So if someone says that in a superconductor resistance is zero he wants to say that current is flowing for such a long time that electrons don’t feel any obstacles.

Now get back to the questions, what does it mean decay for electrons? Actually in solid states electrons decays through emitting phonon (quanta of vibration) or photon and its a normal activity for electrons in solids that some electrons emits phonons/photons and some other absorbs that phonon/photons. As before I said in low temperature only vibrational energy exists in crystallines. So in low temperature electrons emit phonons. In that case a strange bonding happens to two electrons. I just explained that electrons are moving for an infinite time and it also has a vibrating energy, due to this simultaneous effects it generates a scattering wave of phonons. Whenever one electron generates this wave another electron absorbs, thus they interact with each other and acts like a pair. This is what is known as “Copper Pair Electrons”. Maybe some of you noticed that I said a wave of phonons is created, so to solve this property we have the famous Schrodinger Equations, that’s how superconductivity is a quantum phenomena. Not only this let me remark a quote- “Magnetism is not only a relativistic effect but also a quantum effect”. I will try to explain the quantum phenomena of magnetism, getting bored after writing 30 minutes at stretch.

As before I said that in superconductivity current doesn’t decay, so let’s consider a round metal bar to which current is flowing. As current is flowing there must be a magnetic field. So if I apply an external magnetic field to the round metal bar what will happen?

As the metal bar has its own magnetic field so it will repel to the external magnetic field as result no external magnetic field can penetrate to the metal bar. This is known a Meisner Effect. Now if I increase the magnetization to such a critical level that it can penetrate the metal bar then this metal bar will be called a Type I superconductor.

There are some types of metal bars for which instead of full penetration it creates a hole to penetrate. To get the full penetration one needs extra magnetization forces.

These types of metal bars are known as Type-II superconductors. Actually this Type-II superconductors are used to magnetic levitations and employed to high speed train technologies.