Landau diamagnetic response in metals as a Fermi surface effect

Abstract

It is demonstrated that the Landau diamagnetism of the free electron gas and a monovalent metal can be considered as a Fermi surface effect. Only a relatively small number of electron states close to the Fermi surface are diamagnetically active whereas the majority of the electron states inside the Fermi surface are diamagnetically inert. This partitioning of the occupied electron states is driven by the structure of Landau levels, around which one can introduce magnetic tubes in the reciprocal space. Completely filled magnetic tubes do not change their energy in an applied magnetic field, and only partially occupied magnetic tubes in the neighborhood of the Fermi surface exhibit a diamagnetic response. Using this partitioning of the occupied electron states we derive a general expression for the steady diamagnetic susceptibility, for calculation of which one needs to know the shape of the Fermi surface and the energy gradient on it. The method is applied to alkali metals, whose Fermi surfaces and energy gradients have been obtained from ab initio band structure calculations. It has been found that the Landau diamagnetic susceptibility is anisotropic depending on the direction of the applied magnetic field with respect to the Fermi surface. This effect is more pronounced for Li and Cs, whose Fermi surfaces show a noticeable deformation from the spherical shape. The method opens a new route for ab initio calculations of the Landau diamagnetism of metals or intermetallic compounds. In the case of free electron gas it is shown that this approach also fully describes the oscillatory de Haas -van Alphen part of the diamagnetic susceptibility. Small oscillations of the Fermi energy found in the model are caused by redistribution (inflow or outflow) of electrons from the equatorial region of the Fermi surface.

Saddle point anomaly of Landau levels in graphenelike structures

“…In the magnetic field with rational flux f = p/q the saddle point structure of minibands does not affect the magnetic response of graphene in the magnetic field, which is dominated by the contribution from electron states at the Fermi level. This is in line with the general conclusion that the diamagnetic response for 3D metals is caused by a narrow region near the Fermi level [32]. Therefore, a statement about possible dHvA oscillations due to the irregular character of Landau levels at ǫ M made on the basis of semiclassical picture [20] is not confirmed by our calculations.…”

“…9, where the pattern of Landau minibands is approximately conserved in shape and simply shifts upward as a whole on decreasing H. As discussed in Ref. [32] all fully occupied Landau levels situated below the Fermi energy do not contribute to the diamagnetic effect.…”

Fantastic flat bands and where to find them: The CoSn-type compounds

“…For a spherical Fermi surface, this is expected to be isotropic and proportional to the density of states at the Fermi energy [1,2]. Anisotropy can arise when the totaled magnetization contributions of Landau-orbits on non-spherical Fermi surfaces are strongly dependent on field direction [55]. This had little bearing on our investigation of flat bands so we did not investigate further.…”