We explore the rotational degree of freedom between graphene layers via the simple prototype of the graphene twist bilayer, i.e., two layers rotated by some angle $\theta$. It is shown that, due to the weak interaction between graphene layers, many features of this system can be understood by interference conditions between the quantum states of the two layers, mathematically expressed as Diophantine problems. Based on this general analysis we demonstrate that while the Dirac cones from each layer are always effectively degenerate, the Fermi velocity $v_F$ of the Dirac cones decreases as $\theta\to 0^\circ$; the form we derive for $v_F(\theta)$ agrees with that found via a continuum approximation in Phys. Rev. Lett., 99:256802, 2007. From tight binding calculations for structures with $1.47^\circ \le \theta < 30^\circ$ we find agreement with this formula for $\theta \gtrsim 5^\circ$. In contrast, for $\theta \lesssim 5^\circ$ this formula breaks down and the Dirac bands become strongly warped as the limit $\theta \to 0$ is approached. For an ideal system of twisted layers the limit as $\theta\to0^\circ$ is singular as for $\theta > 0$ the Dirac point is fourfold degenerate, while at $\theta=0$ one has the twofold degeneracy of the $AB$ stacked bilayer. Interestingly, in this limit the electronic properties are in an essential way determined \emph{globally}, in contrast to the 'nearsightedness' [W. Kohn. Phys. Rev. Lett., 76:3168, 1996.] of electronic structure generally found in condensed matter.Comment: Article as to be published in Phys. Rev B. Main changes: K-point mapping tables fixed, several changes to presentation

We explore the consequences of a rotation between graphene layers for the electronic spectrum. We derive the commensuration condition in real space and show that the interlayer electronic coupling is governed by an equivalent commensuration in reciprocal space. The larger the commensuration cell, the weaker the interlayer coupling, with exact decoupling for incommensurate rotations and in the ! 0 limit. Furthermore, from first-principles calculations we determine that even for the smallest possible commensuration cell the decoupling is effectively perfect, and thus graphene layers will be seen to decouple for all rotation angles.

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Laser pulses induce spin-selective charge flow that we show to generate dramatic changes in the magnetic structure of materials, including a switching of magnetic order from antiferromagnetic (AFM) to transient ferromagnetic (FM) in multisub-lattice systems. The microscopic mechanism underpinning this ultrafast switching of magnetic order is dominated by spin-selective charge transfer from one magnetic sublattice to another. Because this spin modulation is purely optical in nature (i.e., not mediated indirectly via the spin-orbit interaction) this is one of the fastest means of manipulating spin by light. We further demonstrate this mechanism to be universally applicable to AFM, FM, and ferri-magnets in both multilayer and bulk geometry and provide three rules that encapsulate early-time magnetization dynamics of multisub-lattice systems.

It is shown that, using the generalized perturbation method (GPM) with screened Coulomb interactions that ensures its consistency with the force theorem, one is able to obtain effective interactions that yield an accurate and physically transparent description of configurational energetics in the framework of the Korringa-KohnRostoker method within the atomic sphere and coherent potential approximations. This is demonstrated with calculations of ordering energies, short-range order parameters, and transition temperatures in the CuZn, CuAu, CuPd, and PtCo systems. Furthermore, we show that the GPM can be used to obtain Heisenberg exchange interaction parameters, which, for instance, capture very well the magnetic configurational energy in bcc Fe.