In the realm of energy research, two scientists from the University of Texas at Austin, Christopher A. Leong and Bitan Roy, have delved into the intriguing world of hyperbolic lattices and their potential implications for energy materials. Their work, published in the journal Physical Review B, explores the behavior of electrons in these unique structures and the phenomena that emerge under certain conditions.
Leong and Roy began by examining a simple model of electrons hopping between nearest neighbors on hyperbolic lattices, which are structures with a constant negative curvature. These lattices, known as {10,3} and {14,3}, exhibit a vanishing density of states, meaning that there are no available electron states at certain energies. This is a significant departure from the more familiar honeycomb lattice, which has been extensively studied in the context of graphene and other two-dimensional materials.
The researchers then introduced a twist to their model by spatially modulating the hopping amplitude, which is the likelihood of an electron jumping from one site to another. This modulation preserves the underlying rotational symmetries of the lattices but effectively couples the electrons to time-reversal symmetric axial magnetic fields. These strain-induced fields give rise to a flat band near zero energy, a phenomenon that has been observed in other systems but not previously in hyperbolic lattices.
The flat band triggers the nucleation of a charge density wave, characterized by a staggered pattern of electron density between two sublattices. This is akin to the behavior of electrons in a strained honeycomb lattice, where similar phenomena have been observed. Moreover, the researchers found that weak Coulomb repulsions between electrons can lead to the formation of the Haldane phase, which features intra-sublattice circulating currents with a net zero magnetic flux. This phase is named after physicist F. Duncan Haldane, who predicted its existence in certain two-dimensional systems.
The researchers also explored the effects of a weak on-site Hubbard repulsion, which is a type of electron-electron interaction that occurs when electrons are on the same site. They found that this repulsion can destabilize the flat bands, leading to the formation of a magnetic phase that supports both antiferromagnetic and ferromagnetic orders. In this phase, the magnetization in the bulk and boundary cancel each other out, but the Néel order, a type of antiferromagnetic order, is of the same sign everywhere, resulting in a global antiferromagnet.
Finally, Leong and Roy investigated the effects of non-Hermiticity, which arises from an imbalance in the hopping amplitudes between two sublattices in opposite directions. They found that this non-Hermiticity can substantially boost the magnitudes of the various orders they observed, provided that all the eigenvalues in the noninteracting system are real. This phenomenon, which they term non-Hermitian amplification of axial magnetic catalysis, could have significant implications for the design of new energy materials.
While the practical applications of this research for the energy industry are not immediately clear, the insights gained into the behavior of electrons in hyperbolic lattices could potentially inform the development of new materials for energy storage, conversion, and transmission. Moreover, the phenomena observed in this study could shed light on the behavior of electrons in other complex systems, paving the way for future breakthroughs in energy research. The research was published in Physical Review B, a leading journal in the field of condensed matter physics.
This article is based on research available at arXiv.