Tunable orbital susceptibility in $\alpha$-${\cal T}_3$ tight-binding models

TL;DR

This paper investigates how tuning interband couplings in $ ext{alpha-} ext{T}_3$ models affects their orbital susceptibility, revealing transitions between diamagnetic and paramagnetic responses without altering the energy spectrum.

Contribution

The authors develop a gauge-invariant perturbative formula for orbital susceptibility in $ ext{alpha-} ext{T}_3$ models, highlighting the role of wavefunction interband effects.

Findings

Varying $ ext{alpha}$ induces diamagnetic to paramagnetic transitions.

Transitions occur at band touching points and within gaps.

Interband effects significantly influence magnetic response.

Abstract

We study the importance of interband effects on the orbital susceptibility of three bands $\alpha$-${\cal T}_3$ tight-binding models. The particularity of these models is that the coupling between the three energy bands (which is encoded in the wavefunctions properties) can be tuned (by a parameter $\alpha$) without any modification of the energy spectrum. Using the gauge-invariant perturbative formalism that we have recently developped, we obtain a generic formula of the orbital susceptibility of $\alpha$-${\cal T}_3$ tight-binding models. Considering then three characteristic examples that exhibit either Dirac, semi-Dirac or quadratic band touching, we show that by varying the parameter $\alpha$ and thus the wavefunctions interband couplings, it is possible to drive a transition from a diamagnetic to a paramagnetic peak of the orbital susceptibility at the band touching. In the presence of a gap separating the dispersive bands, we show that the susceptibility inside the gap exhibits a similar dia to paramagnetic transition.