Parallel ("nested") regions of a Fermi surface (FS) drive instabilities of the electron fluid, for example the spin density wave in elemental chromium. In one-dimensional materials, the FS is trivially fully nested (a single nesting vector connects two "Fermi dots"), while in higher dimensions only a fraction of the FS consists of parallel sheets. We demonstrate that the tiny angle regime of twist bilayer graphene (TBLG) possess a phase, accessible by interlayer bias, in which the FS consists entirely of nestable "Fermi lines": the first example of a completely nested FS in a 2d material. This nested phase is found both in the ideal as well as relaxed structure of the twist bilayer. We demonstrate excellent agreement with recent STM images of topological states in this material and elucidate the connection between these and the underlying Fermiology. We show that the geometry of the "Fermi lines" network is controllable by the strength of the applied interlayer bias, and thus that TBLG offers unprecedented access to the physics of FS nesting in 2d materials. 1 arXiv:1908.08318v1 [cond-mat.mtrl-sci] 22 Aug 2019 of the FS consists of nested sheets) and notoriously difficult to control 10,11 . In contrast, the nesting exhibited by the twist bilayer is both complete (100% nested) and, as we show, can be fully controlled by tuning of the interlayer bias.This "nesting phase" of the twist bilayer is found in a large regime of angle-field space and is, remarkably, found both for the ideal twist geometry as well as the structural dislocation network that it reconstructs to at tiny angles 12-14 . The finding of a robust moiré-induced 2d "Fermi line" analogy of the 1d "Fermi dot" topology, controllable via bias, both offers unprecedented access to the physics of FS nesting, as well as highlighting the remarkable electronic structures that can be created by moiré geometries and their structural dislocation networks in 2d materials. II. RESULTS A. ModelThe physics of the tiny angle regime of the twist bilayer is an essentially multiscale problem involving both the lattice constant of graphene -the scale at which atomic relaxation 2 FIG. 1: Fully nested Fermiology in the graphene twist bilayer and the corresponding dislocation network (θ = 0.51 • , E = 90 mV/Å). Below ∼ 1 • twist bilayer graphene relaxes into an ordered network of dislocations, with the smoothly varying stacking order of the ideal twist geometry (a) becoming series of sharp AB and BA domains (b), each separated by pure shear partial dislocations with high von Mises strain (J 2 ) (c,d). Pseudo-magnetic fields of the order of 40 T are induced in the AB and BA regions with alternating sign between the latter (e,f). In the density of states (DOS) the zero mode is substantially broadened, with the valley region shifting upwards in energy (g).However, while atomic relaxation induces dramatic changes to the Fermiology in the zero mode region (l,m), in the valley region a remarkably stable Fermi topology of fully nested Fermi lines is seen (nesting vector indicated by...

We present a continuum theory of graphene treating on an equal footing both homogeneous Cauchy-Born (CB) deformation, as well as the microscopic degrees of freedom associated with the two sublattices. While our theory recovers all extant results from homogeneous continuum theory, the Dirac-Weyl equation is found to be augmented by new pseudo-gauge and chiral fields fundamentally different from those that result from homogeneous deformation. We elucidate three striking electronic consequences: (i) non-CB deformations allow for the transport of valley polarized charge over arbitrarily long distances e.g. along a designed ridge; (ii) the triaxial deformations required to generate an approximately uniform magnetic field are unnecessary with non-CB deformation; and finally (iii) the vanishing of the effects of a one dimensional corrugation seen in ab-initio calculation upon lattice relaxation are explained as a compensation of CB and non-CB deformation.

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The edge physics of graphene based systems is well known to be highly sensitive to the atomic structure at the boundary, with localized zero mode edge states found only on the zigzag type termination of the lattice. Here we demonstrate that the graphene twist bilayer supports an additional class of edge states, that (i) are found for all edge geometries and thus are robust against edge roughness, (ii) occur at energies coinciding with twist induced van Hove singularities in the bulk and (iii) possess an electron density strongly modulated by the moiré lattice. Interestingly, these "moiré edge states" exist only for certain lattice commensurations and thus the edge physics of the twist bilayer is, in dramatic contrast to that of the bulk, not uniquely determined by the twist angle. arXiv:1801.06464v1 [cond-mat.mes-hall]

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We investigate the electronic structure of realistic partial dislocation networks in bilayer graphene that feature annihilating, wandering, and intersecting partial lines. We find charge accumulation states at partials that are sensitive to Fermi energy and partial Burgers vector but not to the screw versus edge character of the partial. These states are shown to be current carrying, with the current density executing a spiral motion along the dislocation line with a strong interlayer component to the current. Close to the Dirac point localization on partials switches to localization on intersections of partials, with a corresponding complex current flow around the nodes.

We establish through analytical and numerical studies of thermodynamic quantities for noninteracting atomic gases that the isotropic three-dimensional spin-orbit coupling, the Weyl coupling, induces interaction which counters "effective" attraction (repulsion) of the exchange symmetry present in zero-coupling Bose (Fermi) gas. The exact analytical expressions for the grand potential and hence for several thermodynamic quantities have been obtained for this purpose in both uniform and trapped cases. It is enunciated that many interesting features of spin-orbit coupled systems revealed theoretically can be understood in terms of coupling-induced modifications in statistical interparticle potential. The temperature-dependence of the chemical potential, specific heat and isothermal compressibility for a uniform Bose gas is found to have signature of the incipient Bose-Einstein condensation in very weak coupling regime although the system does not really go in the Bose-condensed phase. The transition temperature in harmonically trapped case decreases with increase of coupling strength consistent with the weakening of the statistical attractive interaction. Anomalous behavior of some thermodynamic quantities, partly akin to that in dimensions less than two, appears for uniform fermions as soon as the Fermi level goes down the Dirac point on increasing the coupling strength. It is suggested that the fluctuation-dissipation theorem can be utilized to verify anomalous behaviors from studies of long-wavelength fluctuations in bunching and antibunching effects.

We show that the physics of deformation in α-, β-, and 6, 6, 12-graphyne is, despite their significantly more complex lattice structures, remarkably close to that of graphene, with inhomogeneously strained graphyne described at low energies by an emergent Dirac-Weyl equation augmented by strain induced electric and pseudo-magnetic fields. To show this we develop two continuum theories of deformation in these materials: one that describes the low energy degrees of freedom of the conical intersection, and is spinor valued as in graphene, and one describing the full sub-lattice space. The spinor valued continuum theory agrees very well with the full continuum theory at low energies, showing that the remarkable physics of deformation in graphene generalizes to these more complex carbon architectures. In particular, we find that deformation induced pseudospin polarization and valley current loops, key phenomena in the deformation physics of graphene, both have their counterpart in these more complex carbon materials. arXiv:1904.11257v1 [cond-mat.mtrl-sci]