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Superconductivity Linked to Topology in Unexpected Way


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For many people, understanding superconductor is an ultimate goal as these materials could revolutionize much of the modern world. This is much easier said than done though, as the physics behind superconductivity is quite complicated and crosses many fields. Now researchers at Aalto University have made an unexpected discovery that links superconductivity and topology by solving a curious paradox.

Back in 1928 theories on the motions of electrons in crystals were developed and it was found that electrons in a crystal will act like electrons in free space, thanks to quantum mechanics. In the crystal though, the ordered array of atoms will make the electrons behave like they have more or less mass than normal. In superconductors, where electrons can flow without resistance, it is actually possible for the electrons to appear to have infinite mass, which is contrary to expectations as infinite mass would stop a normal particle. Under quantum mechanics though, electrons are both particles and waves and by including something called the quantum metric to characterize the electrons, the answer appears. While the apparent mass of the electrons increase within the superconductor, this metric also increases, making the electrons seem to spread across the crystal. The greater the quantum metric is, the greater the supercurrent that can be carried.

The quantum metric has a relation to the Chern number from topology, where it is an invariant. That means that without breaking the object, the value will not vary, like the number of twists in a belt. By having a nonzero value for the electrons, the electron waves will be forced to overlap, which ensures superconductivity. The next step for this research could be to test the prediction in ultracold gases.

Source: Aalto University

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