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# A theoretical insight into an exotic phase of matter : The topological bit

Professors Ion Garate and David Sénéchal

Photo : Martin Blache collaborateur - UdeSThe bit, the minuscule information unit that characterizes our era, is the fundamental, nearly invisible, yet ubiquitous element that forms the basis of the digital universe. There are various ways to physically represent this element, such as using a hard disc or an electrical circuit on a magnetic medium. Professors Ion Garate and David Sénéchal, along with their master’s student Xinyuan Xu, who is currently pursuing a PhD at the University of Utah, present a novel model for encoding this fundamental unit, which they call the topological bit, in a recent study that was published in Physical Review B. Their concept, which takes inspiration from magnetic storage, relies on an exotic phase of matter that can only be understood in relation to topology—an unexpected field of mathematics.

First and foremost, hard discs in computers use magnetization to permanently store information; each bit is made up of a tiny area of material that has the ability to be magnetized in one of two directions. The 0 and 1 binary states, which form the foundation of digital information, are represented by these two orientations.

The researchers describe in their article a technique for encoding a small amount of information that does not rely on magnetism but rather, in a similar manner, on the topological phase of matter, a state in which electrons react to the laws of topology, a branch of mathematics that focuses on the characteristics of geometric shapes that do not change even when deformed. These are known as topological invariants. A classic example is the number of perforations in a solid: since a doughnut and a cup have only one perforation, they are topologically equivalent. Thanks to an electronic structure defined by a topological invariant, these ideas have proven crucial in explaining unusual behaviours in matter, such as topological insulators that block current internally while conducting it without loss to the surface. Topological phases are singularly robust to defects, making them particularly interesting for technological applications.

Applying pressure or luminous flux, for example, can cause an external perturbation that changes a state from “normal” to “topological.” These two states could therefore constitute the 0 and 1 of a bit. “But as soon as we stop the perturbation, the material returns to its initial point”, explains Ion Garate. Similar to how hard drives maintain their magnetized state after the removal of a magnetic field, the material must maintain its topological state following the transition in order to produce a magnetic bit analogue from a topological phase. “So the goal was to design a model – as simple as possible – to reflect this idea.”

The two professors’ one-dimensional model of their bit is based on a chain of particles that is vibrated through. By controlling the parameters of the vibrations, the links in the chain tend to group together in pairs. Then two possibilities become apparent: either there are exclusions at both ends, or all of the particles are arranged in pairs. “These two states are topologically different from the electrons’ point of view – there’s a discontinuity between them. Accordingly, they constitute the topological bit’s 0 and 1, says David Sénéchal. “The question now is how to get from one to the other.

The researchers have shown theoretically that certain perturbations (an electric field, for example) can make pairing temporarily less interesting for the particles in the chain, leaving the pairs to reform differently. Thus, they were able to compute a dynamic in which a transient perturbation can induce a permanent change of topology between two states. This permanent change of state is the key to possible materials displaying properties useful for information storage. But beyond this hypothetical application, “there is a lot of interest in the scientific community in the induction of topological phase transitions”, explains Ion Garate.

The move from theory to practice is gradual, as is frequently the case in basic research. Before the topological bit can be realized, more research is needed. Although a concrete application of this model may seem a long way off, Professor Sénéchal humorously points out that “there’s no harm in having ideas!”, reminding us that many advances are born of bold theory.