Chern-Simons theory and atypical Hall conductivity in the Varma phase

Abstract

In this letter, we analyze the topological response of a fermionic model defined on the Lieb lattice in presence of an electromagnetic field. The tight-binding model is built in terms of three species of spinless fermions and supports a topological Varma phase due to the spontaneous breaking of time-reversal symmetry. In the low-energy regime, the emergent effective Hamiltonian coincides with the so-called Duffin-Kemmer-Petiau (DKP) Hamiltonian, which describes relativistic pseudospin-0 quasiparticles. By considering a minimal coupling between the DKP quasiparticles and an external Abelian gauge field, we calculate both the Landau-level spectrum and the emergent Chern-Simons theory. The corresponding Hall conductivity reveals an atypical quantum Hall effect, which can be simulated in an artificial Lieb lattice.

5 pages, 3 figures; New version with an improved discussion about our findings

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Cited by in corpus (5)

• p-band engineering in artificial electronic lattices
• Topological Phases for Extended Objects: Semiclassical Phase-Space Approach with Tensorial Coordinates
• Remarks on the ($2+1$)-dimensional Duffin-Kemmer-Petiau oscillator in an external magnetic field
• Comment on "Chern-Simons theory and atypical Hall conductivity in the Varma phase''
• Parity Anomaly of Lattice Maxwell Fermions in Two Spatial Dimensions