Strained hyperbolic Dirac fermions: Zero modes, flat bands, and competing orders

TL;DR

This paper explores how strain-induced axial magnetic fields in hyperbolic lattices create flat bands and induce various electronic orders, revealing new phenomena in Dirac fermions on curved spaces with potential non-Hermitian effects.

Contribution

It introduces a spatially modulated hopping pattern on hyperbolic lattices that preserves symmetries and couples to axial magnetic fields, leading to novel flat bands and magnetic phases.

Findings

Strain induces flat bands near zero energy in hyperbolic lattices.

Weak Coulomb interactions lead to charge density waves and circulating currents.

Non-Hermitian effects can significantly amplify these electronic orders.

Abstract

Starting from the nearest-neighbor tight-binding model on {10,3} and {14,3} hyperbolic lattices that, for a uniform hopping amplitude, gives rise to emergent Dirac fermions on a curved space with a constant negative curvature, displaying a vanishing density of states, we propose spatially modulated hopping pattern therein that preserve the underlying 5- and 7-fold rotational symmetries, respectively, and effectively couples fermions to time-reversal symmetric axial magnetic fields. Such strain-induced axial fields produce a flat band near zero-energy, triggering nucleation of a charge density-wave, featuring a staggered pattern of fermionic density between two sublattices, and the Haldane phase fostering intra-sublattice circulating currents with a net zero magnetic flux for weak nearest- and next-nearest-neighbor Coulomb repulsions, respectively. Sufficiently weak on-site Hubbard repulsion destabilizes such flat bands toward the formation of a magnetic phase that simultaneously supports antiferromagnetic and ferromagnetic orders in the whole system. While the magnetization in the bulk and boundary cancel each other, the Ne\'el order is of the same sign everywhere, thereby yielding a global antiferromagnet. Throughout, we draw parallels between these findings and the well-studied qualitatively similar results on a 3-fold rotational symmetric strained honeycomb lattice, thereby unifying the phenomenon of axial magnetic catalysis for Dirac fermions, encompassing the ones living on the Euclidean plane. Finally, we show that with a specific class of non-Hermiticity, manifesting via an imbalance in the hopping amplitudes between two sublattices in the opposite directions, magnitudes of all these orders can be boosted substantially when all the eigenvalues in the noninteracting systems are real, staging a non-Hermitian amplification of axial magnetic catalysis.