Orbital magnetism in coupled-bands models

Abstract

We develop a gauge-independent perturbation theory for the grand potential of itinerant electrons in twodimensional tight-binding models in the presence of a perpendicular magnetic field. At first order in the field, we recover the result of the so-called modern theory of orbital magnetization and, at second order, deduce a new general formula for the orbital susceptibility. In the special case of two coupled bands, we relate the susceptibility to geometrical quantities such as the Berry curvature. Our results are applied to several two-band systems-either gapless or gapped. We point out some surprising features in the orbital susceptibility-such as in-gap diamagnetism and parabolic band-edge paramagnetism-coming from interband coupling. From this we draw general conclusions on the orbital magnetism of itinerant electrons in multiband tight-binding models.

Statistical mechanics approach to the electric polarization and dielectric constant of band insulators

“…Such an approach was, for example, proposed in [32] for both the electric and magnetic responses. Whereas it works well for the magnetic field, allowing to compute the magnetization and the orbital magnetic susceptibility [7], it encounters severe difficulties in the case of an electric field. In particular, [32] have to assume that the finite-field polarization is given by the Zak phase in order to use their method but can not derive this fundamental relation.…”

Geometrical contributions to the exchange constants: Free electrons with spin-orbit interaction

“…For completeness, we mention that it has been shown that Eq. (2) needs to be modified for the calculation of OMS from tight-binding models [27,28]. We do not discuss these modifications here.…”

“…We have mentioned in the previous section that the Fukuyama formula for OMS needs to be modified for tight-binding models [27,28]. We expect similar modifications to be necessary when exchange constants are computed from tight-binding models, but we leave the discussion of these modifications for future work.…”

Orbital magnetic susceptibility of graphene andMoS2

“…A paramagnetic orbital response also occurs necessarily around van Hove singularities [15] and in Dirac systems the sublattice isospin degree of freedom gives rise to a contribution that can be interpreted as the traditional Pauli paramagnetism [16]. Moreover, in contrast to previous approaches via the PeierlsLandau formula [17] and its generalization to multiband systems, interband (or better geometrical) processes turn out to play a crucial role, e.g., filled bands need not be magnetically inert [9,18]. In this context, it was shown that the band structure does not allow us to uniquely determine the magnetic response of a solid, in stark contrast with the Peierls-Landau approach, i.e., different systems with an identical band structure can display completely opposite orbital magnetic responses [19].…”

“…In this context, it was shown that the band structure does not allow us to uniquely determine the magnetic response of a solid, in stark contrast with the Peierls-Landau approach, i.e., different systems with an identical band structure can display completely opposite orbital magnetic responses [19]. The topological aspects of the band structure partly encoded in the Berry curvature play an important role in this scenario [7,9]. In fact, using the semiclassical wave-packet approach, a complete discussion about the several contributions to the magnetic susceptibility including purely geometrical terms was recently presented in Ref.…”