A sphere and a cube can be deformed into one another without cuts or stitches. A mug and a glass cannot because, to deform the first into the second, the handle needs to be broken. Topology is the branch of mathematics that formalises this difference between mugs and glasses, extending it also to abstract spaces with many dimensions. A new theory developed by scientists at SISSA in Trieste has succeeded in establishing a new relationship between the presence or absence of “handles” in the space of the arrangements of atoms and molecules that make up a material, and the propensity of the latter to conduct electricity. According to this theory, the insulating materials “equipped with handles” can conduct electricity as well as metals, while retaining typical properties of insulators, such as transparency.
The research, which has just been published in the journal Physical Review X, has thrived in the fascinating world of topology, an abstract discipline that gives a potent handle (pun intended!) to some of the most exotic properties of matter. In this way, scientists at the School of Trieste have investigated how to estimate the charge transport and the currents in generic ionic fluids rigorously, in line with the quantum nature of the material.
They have thus developed a theory to explain physical phenomena which have been known for more than a century but which until now lacked a rigorous interpretative base and predictive framework, thereby laying the foundations for major technological developments, for example in the field of thermoelectric materials.