G. Montambaux, “Artificial graphenes: Dirac matter beyond condensed matter”, COMPTES RENDUS PHYSIQUE, vol. 19, p. 285-305, 2018.Abstract
After the discovery of graphene and of its many fascinating properties, there has been a growing interest for the study of ``artificial graphenes{''}. These are totally different and novel systems that bear exciting similarities with graphene. Among them are lattices of ultracold atoms, microwave or photonic lattices, ``molecular graphene{''} or new compounds like phosphorene. The advantage of these structures is that they serve as new playgrounds for measuring and testing physical phenomena that may not be reachable in graphene, in particular the possibility of controlling the existence of Dirac points (or Dirac cones) existing in the electronic spectrum of graphene, of performing interference experiments in reciprocal space, of probing geometrical properties of the wave functions, of manipulating edge states, etc. These cones, which describe the band structure in the vicinity of the two connected energy bands, are characterized by a topological ``charge{''}. They can be moved in the reciprocal space by appropriate modification of external parameters (pressure, twist, sliding, stress, etc.). They can be manipulated, created or suppressed under the condition that the total topological charge be conserved. In this short review, I discuss several aspects of the scenarios of merging or emergence of Dirac points as well as the experimental investigations of these scenarios in condensed matter and beyond. (C) 2018 Published by Elsevier Masson SAS on behalf of Academie des sciences.
G. Montambaux, “Generalized Stefan-Boltzmann Law”, FOUNDATIONS OF PHYSICS, vol. 48, p. 395-410, 2018.Abstract
We reconsider the thermodynamic derivation by L. Boltzmann of the Stefan law and we generalize it for various different physical systems whose chemical potential vanishes. Being only based on classical arguments, therefore independent of the quantum statistics, this derivation applies as well to the saturated Bose gas in various geometries as to ``compensated{''} Fermi gas near a neutrality point, such as a gas of Weyl Fermions. It unifies in the same framework the thermodynamics of many different bosonic or fermionic non-interacting gases which were until now described in completely different contexts.
J. - N. Fuchs, Piechon, F., and Montambaux, G., “Landau levels, response functions and magnetic oscillations from a generalized Onsager relation”, SCIPOST PHYSICS, vol. 4, p. 024, 2018.Abstract
A generalized semiclassical quantization condition for cyclotron orbits was recently proposed by Gao and Niu {[}1], that goes beyond the Onsager relation {[}2]. In addition to the integrated density of states, it formally involves magnetic response functions of all orders in the magnetic field. In particular, up to second order, it requires the knowledge of the spontaneous magnetization and the magnetic susceptibility, as was early anticipated by Roth {[}3]. We study three applications of this relation focusing on two-dimensional electrons. First, we obtain magnetic response functions from Landau levels. Second we obtain Landau levels from response functions. Third we study magnetic oscillations in metals and propose a proper way to analyze Landau plots (i.e. the oscillation index n as a function of the inverse magnetic field 1 = B) in order to extract quantities such as a zero-field phase-shift. Whereas the frequency of 1 = B-oscillations depends on the zero-field energy spectrum, the zero-field phase-shift depends on the geometry of the cell-periodic Bloch states via two contributions: the Berry phase and the average orbital magnetic moment on the Fermi surface. We also quantify deviations from linearity in Landau plots (i.e. aperiodic magnetic oscillations), as recently measured in surface states of three-dimensional topological insulators and emphasized by Wright and McKenzie {[}4].
G. Montambaux, Lim, L. - K., Fuchs, J. - N., and Piechon, F., “Winding Vector: How to Annihilate Two Dirac Points with the Same Charge”, PHYSICAL REVIEW LETTERS, vol. 121, p. 256402, 2018.Abstract
The merging or emergence of a pair of Dirac points may be classified according to whether the winding numbers which characterize them are opposite (+- scenario) or identical (++ cenario). From the touching point between two parabolic bands (one of them can be flat), two Dirac points with the same winding number emerge under appropriate distortion (interaction, etc.), following the ++ scenario. Under further distortion, these Dirac points merge following the +- scenario, that is corresponding to opposite winding numbers. This apparent contradiction is solved by the fact that the winding number is actually defined around a unit vector on the Bloch sphere and that this vector rotates during the motion of the Dirac points. This is shown here within the simplest two-band lattice model (Mielke) exhibiting a flat band. We argue on several examples that the evolution between the two scenarios is general.