In some materials, when many electrons interact very strongly, they behave collectively like a quantum fluid with unusual properties. One example is a Fractional Quantum Hall state, which occurs in a two-dimensional system under a strong magnetic field. In this state, the electrons form a topologically ordered quantum fluid that supports unusual collective excitations.

A Fractional Chern Insulator aims to recreate the same type of physics without requiring such a strong magnetic field. Instead, the crystal lattice and electronic band structure are engineered to mimic the effects of the magnetic field.

The electron fluid has an internal geometric structure that describes how electrons are correlated with one another. When this internal geometry oscillates collectively, it produces a special excitation known as a graviton mode.

In this work, the authors developed new mathematical tools and performed large-scale computer simulations to search for graviton modes in lattice-based systems. They then smoothly transformed a known Fractional Quantum Hall state into a Fractional Chern Insulator and showed that the graviton mode persists throughout the transition.

Graviton modes were already known to exist in Fractional Quantum Hall systems and have recently been observed experimentally. However, it was unclear whether they could survive in a Fractional Chern Insulator because the crystal lattice breaks some of the symmetries that are thought to protect these excitations.

The authors found that graviton modes do survive on the lattice. They showed that the Fractional Chern Insulator graviton is not a completely new excitation, but is continuously connected to the graviton found in Fractional Quantum Hall systems. They also found that the graviton decays much more slowly than many researchers expected, meaning it remains a well-defined excitation. Finally, the work suggests that graviton modes could provide a valuable experimental signature for identifying exotic topological phases such as Fractional Chern Insulators.

“It is remarkable how geometric excitations can govern the behavior of inherently discrete lattices, demonstrating unexpected universal features of topological quantum matter.“ – Zi Yang Meng, The University of Hong Kong, and Marcello Dalmonte, Università di Bologna.

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Fractional charge and fractional statistics in the quantum Hall effects by D E Feldman and Bertrand I Halperin (2020)