General relation between stacking order and Chern index: A topological map of minimally twisted bilayer graphene - Theil, Simon; Fleischmann, Maximilian; Gupta, R.; Rost, Fabian; Wullschläger, Florian; Sharma, S.; Meyer, Bernd; Shallcross, S. (Physical Review B, 2021)
We derive a general relation between the stacking vector u describing the relative shift of two layers of bilayer graphene and the Chern index. We find C = nu(1 - sign(vertical bar V-AB vertical bar - vertical bar V-BA vertical bar)), where nu is a valley index and vertical bar V-alpha beta vertical bar the absolute value of the u dependent stacking potentials that uniquely determine the interlayer interaction; AA stacking plays no role in the topological character. With this expression we show that while ideal and relaxed minimally twisted bilayer graphene appear so distinct as to be almost different materials, their Chern index maps are, remarkably, identical. The topological physics of this material is thus strongly robust to lattice relaxations.
CRIS-Team WoS Importer:2021-09-17

Nonperturbative theory of effective Hamiltonians for deformations in two-dimensional materials: Moire systems and dislocations - Rost, Fabian; Gupta, R.; Fleischmann, Maximilian; Weckbecker, Dominik; Ray, Nicolas; Olivares, J.; Vogl, Michael; Sharma, S.; Pankratov, Oleg; Shallcross, Sam (Physical Review B, 2019)
We demonstrate that there exists a continuum Hamiltonian H(r, p) that is formally the operator equivalent of the general tight-binding method, inheriting the associativity and Hermiticity of the latter operator. This provides a powerful and controlled method of obtaining effective Hamiltonians via Taylor expansion with respect to momentum and, optionally, deformation fields. In particular, for fundamentally nonperturbative defects, such as twist faults and partial dislocations, the method allows the deformation field to be retained to all orders, providing an efficient scheme for the generation of transparent and compact Hamiltonians for such defects. We apply the method to a survey of incommensurate physics in twist bilayers of graphene, graphdiyne, MoS2, and phosphorene. For graphene we are able to reproduce the "reflected Dirac cones" of the 30 degrees quasicrystalline bilayer found in a recent angle-resolved photoemission spectroscopy experiment, and we show that it is an example of a more general phenomenon of coupling by the moire momentum. We show that incommensurate physics is governed by the decay of the interlayer interaction on the scale of the single-layer reciprocal lattices, and demonstrate that incommensurate scattering effects lead to a very rapid broadening of band manifolds as the twist angle is tuned through commensurate values.
CRIS-Team WoS Importer:2021-10-18

Perfect and Controllable Nesting in Minimally Twisted Bilayer Graphene - Fleischmann, Maximilian; Gupta, Reena; Wullschläger, Florian; Theil, Simon; Weckbecker, Dominik; Meded, Velimir; Sharma, Sangeeta; Meyer, Bernd; Shallcross, Sam (Nano Letters, 2020)
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) possesses 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 two-dimensional (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 TBLG offers unprecedented access to the physics of FS nesting in 2D materials.
CRIS-Team Scopus Importer:2020-02-07
Keywords: Fermi surface nesting; Graphene; helical network; twist bilayer

Straintronics beyond homogeneous deformation - Gupta, Reena; Rost, Fabian; Fleischmann, Maximilian; Sharma, S.; Shallcross, Sam (Physical Review B, 2019)
We present a continuum theory of graphene, treating on an equal footing both the homogeneous Cauchy-Born (CB) deformation and 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 pseudogauge 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 is explained as a compensation of CB and non-CB deformation.
CRIS-Team WoS Importer:2021-10-18