# Quasi-symmetry in CoSi reveals new type of topological material

Symmetry is a key concept in our understanding of the physical world around us. They way self-similar components are arranged following the guidelines of symmetry dictates their joint behavior. It is no accident that the human body evolved in a mirror-symmetric shape, as beautifully captured by Da Vinci’s work. Similarly, in material science, certain symmetries dictate the functionality of a material on the quantum level. A recent focus point in the field is to understand how certain symmetries work together to give fundamentally new responses in so-called topological materials. These materials display distinct surface and bulk properties, making them promising candidates for future application in quantum electronics.

Ever since the discovery of the quantum Hall effect (Nobel Prize 1985), symmetry has been the guiding principle in the search for topological materials. Now an international team of researchers from Germany, Switzerland, and the USA has introduced an alternative guiding principle, ‘quasi-symmetry’, which leads to the discovery of a new type of topological material with great potential for applications in spintronics and quantum technologies. This work has been published in *Nature Physics*.

As distinct from a proper symmetry which acts on the whole object uniformly, the quasi-symmetry operation acts selectively on different parts of the system. A simplified example may be an incomplete mirror image, in which some parts of the object are mirrored but others are not. Theoretically, it corresponds to a system which has exact symmetry when taking only the basic approximation into consideration while additional approximative terms break such symmetry. In the electronic band structure of a solid, this enforces finite but parametrically small energy gaps at some low-symmetry points in momentum space.

In their new work, the researchers demonstrate that quasi-symmetry in the semi-metal CoSi stabilizes tiny energy gaps over a large near-degenerate plane. This is reflected in the way the electrons are bent into circular motion by a magnetic field, known as quantum oscillations. The application of in-plane strain breaks the crystal symmetry which gaps only the corresponding degenerate points but the quasi-symmetry-protected points remain intact, observable by new magnetic breakdown orbits. These results demonstrate one of the most important features of quasi-symmetry: its robustness against chemical and physical perturbations.

Most of the topological materials discovered in recent years require precise engineering of their chemical composition for them to be relevant for future technological applications. In contrast, quasi-symmetries eliminate the need for such fine tuning as the topological features can be found at any arbitrary chemical potential. Moreover, quasi-symmetry-protected topological materials are robust against any physical deformation which breaks the crystalline symmetry. Moreover, quasi-symmetry-protected topological materials are robust against physical deformations which break the crystalline symmetry, a key prerequisite for their technological application via thin-film processes.

These features demonstrate a new class of topological materials with increased resilience to perturbations, which simplifies their use in technology. The researchers believe that this first example represents an important step towards uncovering topological materials beyond the usual space group classifications, which could help the community not to overlook what may be hidden in plain sight.

References:

1. Guo, C. et al. *Nat. Phys.* (2022).

2. Wilde, M.A., Pfleiderer, C. *Nat. Phys. *(2022).