Effects of frustration and localization of states in the Penrose lattice

Flat-bands in translated and twisted bilayer Penrose quasicrystals

Correlated phases in Moiré materials together with the flat-bands in twisted systems play a central role to explain superconductivity in the new twisted bilayer graphene. In this paper, flat-bands are shown to exist in both translated and twisted bilayer of quasicrystals. Such flat-bands arise for different displacements and twisting angles of two-coupled Penrose lattices where Moiré patterns are also shown. Moiré patterns analyzed in this work have at least two inverted worms showing an interference pattern going along the five-fold axes of the pentagon. In order to analyze the behavior of the flat band, our study has been done for fixed interference worm directions but increasing the worm interference density, and for fixed worm interference density but increasing the number of worm directions. In case of rotations, the Moiré patterns that occurs for special angles such asπ/5, 2π/5, 3π/5, 4π/5 andπare discussed in detail because they clearly show flat-bands along with quasicrystalline electronic states at the Fermi level.

Flat bands without twists: periodic holey graphene

Holey Graphene(HG) is a widely used graphene material for the synthesis of high-purity and highly crystalline materials. The electronic properties of a periodic distribution of lattice holes are explored here, demonstrating the emergence of flat bands. It is established that such flat bands arise as a consequence of an induced sublattice site imbalance, i.e. by having more sites in one of the graphene's bipartite sublattice than in the other. This is equivalent to the breaking of a path-exchange symmetry. By further breaking the inversion symmetry, gaps and a nonzero Berry curvature are induced, leading to topological bands. In particular, the folding of the Dirac cones from the hexagonal Brillouin zone (BZ) to the holey superlattice rectangular BZ of HG, with sizes proportional to an integerntimes the graphene's lattice parameter, leads to a periodicity in the gap formation such thatn≡0(mod 3). A low-energy hamiltonian for the three central bands is also obtained revealing that the system behaves as an effectiveα-T3graphene material. Therefore, a simple protocol is presented here that allows for obtaining flat bands at will. Such bands are known to increase electron-electron correlation effects. Therefore, the present work provides an alternative system that is much easier to build than twisted systems, allowing for the production of flat bands and potentially highly correlated quantum phases.

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

This is an update of a previous review (Naumiset al2017Rep. Prog. Phys.80096501). Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials were considered. We surveyed (i) methods to induce valley and sublattice polarisation (P) in graphene, (ii) time-dependent strain and its impact on graphene's electronic properties, (iii) the role of local and global strain on superconductivity and other highly correlated and/or topological phases of graphene, (iv) inducing polarisationPon hexagonal boron nitride monolayers via strain, (v) modifying the optoelectronic properties of transition metal dichalcogenide monolayers through strain, (vi) ferroic 2D materials with intrinsic elastic (σ), electric (P) and magnetic (M) polarisation under strain, as well as incipient 2D multiferroics and (vii) moiré bilayers exhibiting flat electronic bands and exotic quantum phase diagrams, and other bilayer or few-layer systems exhibiting ferroic orders tunable by rotations and shear strain. The update features the experimental realisations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of elemental 2D ferroelectric bismuth, and 2D multiferroic NiI2. The document was structured for a discussion of effects taking place in monolayers first, followed by discussions concerning bilayers and few-layers, and it represents an up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials.

Real Space Theory for Electron and Phonon Transport in Aperiodic Lattices via Renormalization

Structural defects are inherent in solids at a finite temperature, because they diminish free energies by growing entropy. The arrangement of these defects may display long-range orders, as occurring in quasicrystals, whose hidden structural symmetry could greatly modify the transport of excitations. Moreover, the presence of such defects breaks the translational symmetry and collapses the reciprocal lattice, which has been a standard technique in solid-state physics. An alternative to address such a structural disorder is the real space theory. Nonetheless, solving 1023 coupled Schrödinger equations requires unavailable yottabytes (YB) of memory just for recording the atomic positions. In contrast, the real-space renormalization method (RSRM) uses an iterative procedure with a small number of effective sites in each step, and exponentially lessens the degrees of freedom, but keeps their participation in the final results. In this article, we review aperiodic atomic arrangements with hierarchical symmetry investigated by means of RSRM, as well as their consequences in measurable physical properties, such as electrical and thermal conductivities.

Electronic and optical properties of strained graphene and other strained 2D materials: a review

This review presents the state of the art in strain and ripple-induced effects on the electronic and optical properties of graphene. It starts by providing the crystallographic description of mechanical deformations, as well as the diffraction pattern for different kinds of representative deformation fields. Then, the focus turns to the unique elastic properties of graphene, and to how strain is produced. Thereafter, various theoretical approaches used to study the electronic properties of strained graphene are examined, discussing the advantages of each. These approaches provide a platform to describe exotic properties, such as a fractal spectrum related with quasicrystals, a mixed Dirac-Schrödinger behavior, emergent gravity, topological insulator states, in molecular graphene and other 2D discrete lattices. The physical consequences of strain on the optical properties are reviewed next, with a focus on the Raman spectrum. At the same time, recent advances to tune the optical conductivity of graphene by strain engineering are given, which open new paths in device applications. Finally, a brief review of strain effects in multilayered graphene and other promising 2D materials like silicene and materials based on other group-IV elements, phosphorene, dichalcogenide- and monochalcogenide-monolayers is presented, with a brief discussion of interplays among strain, thermal effects, and illumination in the latter material family.

Noncollinear magnetic order in quasicrystals

Based on Monte Carlo simulations, the stable magnetization configurations of an antiferromagnet on a quasiperiodic tiling are derived theoretically. The exchange coupling is assumed to decrease exponentially with the distance between magnetic moments. It is demonstrated that the superposition of geometric frustration with the quasiperiodic ordering leads to a three-dimensional noncollinear antiferromagnetic spin structure. The structure can be divided into several ordered interpenetrating magnetic supertilings of different energy and characteristic wave vector. The number and the symmetry of subtilings depend on the quasiperiodic ordering of atoms.