On the zero-field orbital magnetic susceptibility of Bloch electrons in graphene-like solids: Some rigorous results

Abstract

Starting with a nearest-neighbors tight-binding model, we rigorously investigate the bulk zero-field orbital susceptibility of a non-interacting Bloch electrons gas in graphene-like solids at fixed temperature and density of particles. In the zero-temperature limit and in the semiconducting situation, we derive a complete expression which holds for an arbitrary number of bands with possible degeneracies. In the particular case of a two-bands gapped model, all involved quantities are explicitly written down. Besides the formula that we obtain have the special feature to be suitable for numerical computations since it only involves the eigenvalues and associated eigenfunctions of the Bloch Hamiltonian, together with the derivatives (up to the second order) w.r.t. the quasi-momentum of the matrix-elements of the Bloch Hamiltonian. Finally we give a simple application for the two-bands gapped model by considering the case of a dispersion law which is linear w.r.t. the quasi-momentum in the gapless limit. Through this instance, the origin of the singularity, which expresses as a Dirac delta function of the Fermi energy, implied by the McClure's formula in monolayer graphene is discussed.

Orbital magnetism in coupled-bands models

“…A trick [23,24] to circumvent this problem is to define a new "twisted" Green's functiong bỹ g ij = e iϕ ij g ij , (12) then expand G in terms ofg and, finally, reintroduce g in order to recover a gauge-independent expression for the diagonal elements of G. One easily shows that…”

“…(23), which allows us to obtain the susceptibility formula, Eq. (24), whereas the third line allows us to recover the susceptibility formula, Eq.…”

Geometric orbital susceptibility: Quantum metric without Berry curvature

“…Many different approaches were developped to calculate the orbital susceptibility in multiband systems (see discussion in 25,39). Compact but abstract orbital susceptibility formulas were obtained using Green's function techniques.…”

Graphene, Graphene-Derivatives and Composites: Fundamentals, Synthesis Approaches to Applications

“…Materials required for bio imaging must have properties likehigh specificity, non-poisonous, and sensitivity which are displayed by graphene quantum dots (GQDs). Besides, they demonstrate extraordinary photophysical and spectrofluorometric properties needed for producing images of biological segments [16]. Graphene also found applications in photodynamic therapy (PDT), which is a non-intrusive technique for cancer therapy.…”