Spherical atoms have the highest geometrical symmetry, and thus exhibit the high multiplicity of quantum states known as degeneracy. It has long been believed that the symmetry of any polyatomic species cannot exceed that of a sphere due to geometrical limitations. However, scientists from the Tokyo Institute of Technology have now shown that an inflated tetrahedron (far left) can exhibit anomalous degeneracy that surpasses that of spherical atoms. Image: Nature Communications.
Spherical atoms have the highest geometrical symmetry, and thus exhibit the high multiplicity of quantum states known as degeneracy. It has long been believed that the symmetry of any polyatomic species cannot exceed that of a sphere due to geometrical limitations. However, scientists from the Tokyo Institute of Technology have now shown that an inflated tetrahedron (far left) can exhibit anomalous degeneracy that surpasses that of spherical atoms. Image: Nature Communications.

Scientists at the Tokyo Institute of Technology in Japan have theoretically demonstrated that special tetrahedron nanostructures composed of certain metals have a higher degree of symmetry than the geometrical symmetry of spherical atoms. Nanomaterials with unique and unprecedented electrical and magnetic properties arising from this symmetry could now be developed and used in next-generation electronic devices. The scientists report their findings in a paper in Nature Communications.

Studying symmetry, one of the most fundamental concepts in physics and chemistry, can facilitate a deeper understanding of the laws shaping our universe. Being broadly spherical, atoms naturally have the highest degree of geometrical symmetry.

An interesting property often arising from symmetry is a high degree of degeneracy – a characteristic of quantum energy levels wherein a given energy level can correspond simultaneously to two or more different states in a quantum system. Degeneracy gives rise to properties including high conductivity and magnetism, which could be exploited to create novel electronic materials.

Unfortunately, given the limitations of geometrical symmetry, no substance is known to have a higher degree of degeneracy than spherical atoms. But what if substances could have a different type of symmetry leading to a higher degree of degeneracy? How could such a symmetry be explained?

Kimihisa Yamamoto and his colleagues at the Tokyo Institute of Technology set out to demonstrate the existence of metal nanomaterials with such novel types of symmetry. The team inferred that special inflated tetrahedron structures made of metal atoms such as zinc and magnesium may have a special type of symmetry arising not from geometrical properties but from the dynamic characteristics of the system.

"We have demonstrated that realistic magnesium, zinc and cadmium clusters having a specific tetrahedral framework possess anomalous higher-fold degeneracies than spherical symmetry," explains Yamamoto.

The team employed a tight-binding model analysis, validated with density functional theory calculations, to identify the general conditions for the bonding interactions between the atoms (the ‘transfer integrals’) that give rise to the predicted dynamical symmetry. "Surprisingly, the degeneracy condition can be represented as an elegant square-root mathematical sequence involving the ratios of the transfer integrals," says Yamamoto. "It is also impressive that this sequence has already been discovered by Theodorus in ancient Greece, independently of materials science."

This research demonstrated that nanomaterials with a degree of symmetry higher than that of spherical atoms can be realized. The super-degenerate quantum states resulting from this dynamical symmetry could be exploited in multiple ways, such as by designing new materials with unprecedented conductivity or magnetic properties, heralding the next generation of electronic devices.

This story is adapted from material from the Tokyo Institute of Technology, with editorial changes made by Materials Today. The views expressed in this article do not necessarily represent those of Elsevier. Link to original source.