What Makes a Diamond Pretty?
According to recent research from Columbia physicists, its brilliance and unique physical properties come from quantum geometry.
The diamond is an exceptional material. Long prized for its beauty, this crystalline form of carbon is the hardest naturally occurring substance, and, despite being an excellent insulator that resists the flow of electricity, it can store ample electrical energy.
A diamond’s unique properties are somewhat surprising, given where carbon’s position on the periodic table. Sitting just above silicon and sharing the same crystalline structure, a diamond should behave like a semiconductor. Instead, it has a very large band gap, which reflects the amount of energy needed for electrons to enter what’s known as the conduction band. A large barrier is typical of insulators, but unlike most materials with a similarly sized band gap, diamonds have covalent, rather than ionic, bonds.
Diamonds are indeed atypical insulators, but this cannot be explained by looking only at energy levels. Rather, according to new research from Columbia theoretical physicist Raquel Queiroz, it’s a reflection of a diamond’s quantum geometry, an emerging mathematical language to describe an electron’s waveform. That geometry also turns out to contribute dramatically to a diamond’s brilliance.
In a new study published in Nature Communications, Queiroz, with Columbia Physics PhD student Ilia Komissarov and collaborator Tobias Holder from Tel Aviv University, explore how insulating materials' properties relate to what is known as the quantum metric—a concept in quantum geometry that estimates how far electrons are typically found from the atom they originate from. Insulators don’t carry an electrical current because their electrons remain tightly bound to that originating atom. However, these electrons still oscillate in place and can become polarized in response to an electromagnetic field, allowing insulators to store electrical energy as capacitors. The research team demonstrated that how easily a material can be polarized—and thus, its dielectric constant, which measures its capacity to store electrical energy—increases with the magnitude of its quantum metric.
“This gives us a clear guideline for predicting dielectric constants for different materials without hard computations, which is a goal for many engineering applications,” said Queiroz.
The results also connect condensed matter physics, which deals with the properties of solid crystals, with chemical intuition. In chemistry, the uncertainty of an electron's location reflects the chemical bond between atoms in a molecule. Ionic molecules share electrons unequally, resulting in a smaller quantum metric than covalently bonded molecules, which share electrons equally.
The diamond is a macroscopically large crystal; its electrons can, therefore, be spread throughout its entire lattice. But this has made constructing mathematical tools to describe diamond bonds at microscopic levels a challenge. The answer, according to the team’s research, can again be found in the quantum metric: covalent insulators have a large metric, which results in an unexpectedly high dielectric constant compared to other usually ionic insulators with similar bandgaps, explained Queiroz.
A pretty perk? All those electrons jittering in place in the diamond lattice also offer ample opportunities for light to reflect and refract and get trapped, giving a diamond its renowned brilliance.