Diffraction catastrophes and semiclassical quantum mechanics for Veselago lensing in graphene

We study the effect of trigonal warping on the focussing of electrons by n-p junctions in graphene. We find that perfect focussing, which was predicted for massless Dirac fermions, is only preserved for one specific sample orientation. In the general case, trigonal warping leads to the formation of cusp caustics, with a different position of the focus for graphene's two valleys. We develop a semiclassical theory to compute these positions and find very good agreement with tight-binding simulations. Considering the transmission as a function of potential strength, we find that trigonal warping splits the single Dirac peak into two distinct peaks, leading to valley polarization. We obtain the transmission curves from tight-binding simulations and find that they are in very good agreement with the results of a billiard model that incorporates trigonal warping. Furthermore, the positions of the transmission maxima and the scaling of the peak width are accurately predicted by our semiclassical theory. Our semiclassical analysis can easily be carried over to other Dirac materials, which generally have different Fermi surface distortions.Comment: 6 pages, 4 figures, plus supplemental material. Important reference added and text update

Atomistic simulations of structural and thermodynamic properties of bilayer graphene

We study the structural and thermodynamic properties of bilayer graphene, a prototype two-layer membrane, by means of Monte Carlo simulations based on the empirical bond order potential LCBOPII. We present the temperature dependence of lattice parameter, bending rigidity and high temperature heat capacity as well as the correlation function of out-of-plane atomic displacements. The thermal expansion coefficient changes sign from negative to positive above $\approx 400$ K, which is lower than previously found for single layer graphene and close to the experimental value of bulk graphite. The bending rigidity is twice as large than for single layer graphene, making the out-of-plane fluctuations smaller. The crossover from correlated to uncorrelated out-of-plane fluctuations of the two carbon planes occurs for wavevectors shorter than $\approx 3$ nm$^{-1}$Comment: 6 pages, 7 figures

Motion of domain walls and the dynamics of kinks in the magnetic Peierls potential

We study the dynamics of magnetic domain walls in the Peierls potential due to the discreteness of the crystal lattice. The propagation of a narrow domain wall (comparable to the lattice parameter) under the effect of a magnetic field proceeds through the formation of kinks in its profile. We predict that, despite the discreteness of the system, such kinks can behave like sine-Gordon solitons in thin films of materials such as yttrium iron garnets, and we derive general conditions for other materials. In our simulations we also observe long-lived breathers. We provide analytical expressions for the effective mass and limiting velocity of the kink in excellent agreement with our numerical results.Comment: 12 pages, 9 figures (incl. supp. mat.

Mechanics of thermally fluctuating membranes

Besides having unique electronic properties, graphene is claimed to be the strongest material in nature. In the press release of the Nobel committee it is claimed that a hammock made of a squared meter of one-atom thick graphene could sustain the wight of a 4 kg cat. More practically important are applications of graphene like scaffolds and sensors which are crucially dependent on the mechanical strength. Meter-sized graphene is even being considered for the lightsails in the starshot project to reach the star alpha centaury. The predicted strength of graphene is based on its very large Young modulus which is, per atomic layer, much larger than that of steel. This reasoning however would apply to conventional thin plates but does not take into account the peculiar properties of graphene as a thermally fluctuating crystalline membrane. It was shown recently both experimentally and theoretically that thermal fluctuations lead to a dramatic reduction of the Young modulus and increase of the bending rigidity for micron-sized graphene samples in comparison with atomic scale values. This makes the use of the standard F\"oppl-von Karman elasticity (FvK) theory for thin plates not directly applicable to graphene and other single atomic layer membranes. This fact is important because the current interpretation of experimental results is based on the FvK theory. In particular, we show that the FvK-derived Schwerin equation, routinely used to derive the Young modulus from indentation experiments has to be essentially modified for graphene at room temperature and for micron sized samples. Based on scaling analysis and atomistic simulation we investigate the mechanics of graphene under transverse load up to breaking. We determine the limits of applicability of the FvK theory and provide quantitative estimates for the different regimes.Comment: to appear in npj 2D Materials and Application

Dirac electrons and domain walls: a realization in junctions of ferromagnets and topological insulators

We study a system of Dirac electrons with finite density of charge carriers coupled to an external electromagnetic field in two spatial dimensions, with a domain wall (DW) mass term. The interface between a thin-film ferromagnet and a three-dimensional topological insulator provides a condensed-matter realization of this model, when an out-of-plane domain wall magnetization is coupled to the TI surface states. We show how, for films with very weak intrinsic in-plane anisotropies, the torque generated by the edge electronic current flowing along the DW competes with an effective in-plane anisotropy energy, induced by quantum fluctuations of the chiral electrons bound to the wall, in a mission to drive the internal angle of the DW from a Bloch configuration towards a N\'eel configuration. Both the edge current and the induced anisotropy contribute to stabilize the internal angle, so that for weak intrinsic in-plane anisotropies DW motion is still possible without suffering from an extremely early Walker breakdown.Comment: 18 pages, 3 figure

Electronic Structure of gated graphene and graphene ribbons

We study the electronic structure of gated graphene sheets. We consider both infinite graphene and finite width ribbons. The effect of Coulomb interactions between the electrically injected carriers and the coupling to the external gate are computed self-consistently in the Hartree approximation. We compute the average density of extra carriers, $n_{2D}$, the number of occupied subbands and the density profiles as a function of the gate potential $V_g$. We discuss quantum corrections to the classical capacitance and we calculate the threshold $V_g$ above which semiconducting armchair ribbons conduct. We find that the ideal conductance of perfectly transmitting wide ribbons is proportional to the square root of the gate voltage.Comment: 8 pages, 6 figure

Scaling behavior and strain dependence of in-plane elastic properties of graphene

We show by atomistic simulations that, in the thermodynamic limit, the in-plane elastic moduli of graphene at finite temperature vanish with system size $L$ as a power law $~ L^{-\eta_u}$ with $\eta_u \simeq 0.325$, in agreement with the membrane theory. Our simulations clearly reveal the size and strain dependence of graphene's elastic moduli, allowing comparison to experimental data. Although the recently measured difference of a factor 2 between the asymptotic value of the Young modulus for tensilely strained systems and the value from {\it ab initio} calculations remains unsolved, our results do explain the experimentally observed increase of more than a factor 2 for a tensile strain of only a few permille. We also discuss the scaling of the Poisson ratio, for which our simulations disagree with the predictions of the self-consistent screening approximation.Comment: 5 figure

Zero modes in magnetic systems: general theory and an efficient computational scheme

The presence of topological defects in magnetic media often leads to normal modes with zero frequency (zero modes). Such modes are crucial for long-time behavior, describing, for example, the motion of a domain wall as a whole. Conventional numerical methods to calculate the spin-wave spectrum in magnetic media are either inefficient or they fail for systems with zero modes. We present a new efficient computational scheme that reduces the magnetic normal-mode problem to a generalized Hermitian eigenvalue problem also in the presence of zero modes. We apply our scheme to several examples, including two-dimensional domain walls and Skyrmions, and show how the effective masses that determine the dynamics can be calculated directly. These systems highlight the fundamental distinction between the two types of zero modes that can occur in spin systems, which we call special and inertial zero modes. Our method is suitable for both conservative and dissipative systems. For the latter case, we present a perturbative scheme to take into account damping, which can also be used to calculate dynamical susceptibilities.Comment: 64 pages, 15 figure

First-principles Theory of Nonlocal Screening in Graphene

Using the quasiparticle self-consistent GW (QSGW) and local-density (LD) approximations, we calculate the q-dependent static dielectric function, and derive an effective 2D dielectric function corresponding to screening of point charges. In the q-to-0 limit, the 2D function is found to scale approximately as the square root of the macroscopic dielectric function. Its value is ~4, a factor approximately 1.5 larger than predictions of Dirac model. Both kinds of dielectric functions depend strongly on q, in contrast with the Dirac model. The QSGW approximation is shown to describe QP levels very well, with small systematic errors analogous to bulk sp semiconductors. Local-field effects are rather more important in graphene than in bulk semiconductors.Comment: 9 pages, 2 figure

Chirality-dependent transmission of spin waves through domain walls

Spin-wave technology (magnonics) has the potential to further reduce the size and energy consumption of information processing devices. In the submicrometer regime (exchange spin waves), topological defects such as domain walls may constitute active elements to manipulate spin waves and perform logic operations. We predict that spin waves that pass through a domain wall in an ultrathin perpendicular-anisotropy film experience a phase shift that depends on the orientation of the domain wall (chirality). The effect, which is absent in bulk materials, originates from the interfacial Dzyaloshinskii-Moriya interaction and can be interpreted as a geometric phase. We demonstrate analytically and by means of micromagnetic simulations that the phase shift is strong enough to switch between constructive and destructive interference. The two chirality states of the domain wall may serve as a memory bit or spin-wave switch in magnonic devices.Comment: 11 pages, 10 figures (incl. supp. mat.); Phys. Rev. Lett. (accepted