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 timereversal 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 first find the Landau-level spectrum by fixing the Landau gauge; then we compute the emergent Chern-Simons theory for a weak-electromagnetic-field regime. The corresponding Hall conductivity reveals an atypical quantum Hall effect, which can be simulated in an artificial Lieb lattice.

p -Band Engineering in Artificial Electronic Lattices

“…We now turn our attention to lifting the energy degeneracy of the p x -and p y -like orbitals at all sites by introducing an asymmetry in the lattice sites [43]. Specifically, we break the four-fold rotational symmetry by increasing the width of artificial-atom sites 1 and 2 in the y-direction by √ 3a (pink arrow in Fig.…”

Comment on "Chern-Simons theory and atypical Hall conductivity in the Varma phase''

“…As a first result, in the Section II in Ref. [1], the authors showed that the dynamics of the charge carriers on that Lieb lattice in low-energy regime present a relativisticlike behavior, correctly described by Duffin-Kemmer-Petiau-like hamiltonian (DKP). Disregarding irrelevant constants, this effective hamiltonian is expressed in a simplified version as (see equation (4) in Ref.…”

“…In an interesting Letter, Menezes et al [1] analized the topological response of a effective bosonic theory defined on the Lieb lattice which is minimally coupled to an external U (1) gauge field in 2 + 1 dimensions. To this purpose, the authors consider a tight-binding hamiltonian with three different species of (pseudo-) gapped fermions (see equations ( 1)-(3) in Ref.…”

“…To this purpose, the authors consider a tight-binding hamiltonian with three different species of (pseudo-) gapped fermions (see equations ( 1)-(3) in Ref. [1]), similar to the one proposed in Ref. [2].…”

“…Disregarding irrelevant constants, this effective hamiltonian is expressed in a simplified version as (see equation (4) in Ref. [1])…”