How a tetrahedral substance can be more symmetrical than a spherical atom

A new type of symmetry.

Quantum states of various symmetrical species. Spherical atoms have the highest geometrical symmetry, and thus exhibit the high multiplicity of quantum states, usually called degeneracy. It has long been believed that any polyatomic species cannot exceed a sphere due to geometrical limitations. However, an inflated tetrahedron exhibits the anomalous degeneracy surpassing spherical atoms.
Quantum states of various symmetrical species. Spherical atoms have the highest geometrical symmetry, and thus exhibit the high multiplicity of quantum states, usually called degeneracy. It has long been believed that any polyatomic species cannot exceed a sphere due to geometrical limitations. However, an inflated tetrahedron exhibits the anomalous degeneracy surpassing spherical atoms.

Atoms normally have the most elevated level of geometrical symmetry, relating to the spherical symmetry. A fascinating property frequently emerging from symmetry is a high level of degeneracy—a normal for quantum energy levels wherein a given energy level can relate all the while to at least two unique states in a quantum system.

Degeneracy offers ascend to properties including high conductivity and magnetism, which could be exploited to make novel electronic materials. Tragically, given the restrictions of geometrical symmetry, no substance is known to have a higher level of degeneracy than spherical atoms.

Be that as it may, imagine a scenario in which substances could have an alternate sort of symmetry prompting a higher level of degeneracy. How could such symmetry be clarified?

Scientists at Tokyo Tech, including Prof. Kimihisa Yamamoto, set out to demonstrate the existence of metals with such types of symmetry. They construed that uncommon inflated tetrahedron structures made of particular metal atoms, for example, zinc and magnesium, may have an exceptional kind of symmetry emerging not from geometrical properties but rather from the dynamic attributes of the system.

Dynamical symmetry in inflated tetrahedron structures. Ratios of the transfer integrals (which quantify bonding interactions) between the atoms that give rise to dynamical symmetry in the inflated tetrahedron structures shown on the right.
Dynamical symmetry in inflated tetrahedron structures.
Ratios of the transfer integrals (which quantify bonding interactions) between the atoms that give rise to dynamical symmetry in the inflated tetrahedron structures shown on the right.

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

For the study, scientists used a tight-binding model analysis, validated with density functional theory calculations, to identify the general condition regarding the bonding interactions between atoms (the “transfer integrals”) giving rise to the predicted dynamical symmetry.

Prof. Yamamoto added, “Surprisingly, the degeneracy condition can be represented as an elegant square-root mathematical sequence involving the ratios of the transfer integrals (Fig. 2). It is also impressive that this sequence has already been discovered by Theodorus in ancient Greece, independently of materials science.”

This exploration showed that nanomaterials with a level of symmetry higher than that of spherical atoms can be figured it out. The super-degenerate quantum states coming about because of this dynamical symmetry could be misused in various courses, for example, planning new materials with exceptional conductivity or magnetic properties, proclaiming the next generation of electronic gadgets.

The study is published in the journal Nature Communications.