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A plethora of unconventional localization phenomena and fractal features of linear spectrum observed in quasiperiodic structures have been accompanied by a long-standing quest for the geometrical elements and structures that permit tilings…
A new method for finding electronic structure and wavefunctions of electrons in quasiperiodic potential is introduced. To obtain results it uses slightly modified Schrodinger equation in spaces of dimensionality higher than physical space.…
The strict geometric rules that define aperiodic tilings lead to the unique spectral and transport properties of quasicrystals, but also limit our ability to design them. In this Letter, we explore a novel example of a continuously tunable…
A two-dimensional system of soft particles interacting via a two-length-scale potential is studied. Density functional theory and Brownian dynamics simulations reveal a fluid phase and two crystalline phases with different lattice spacing.…
We report on a theoreticl study of the electronic structure of quasiperiodic, quasi-one-dimensional systems where fully three dimensional interaction potentials are taken into account. In our approach, the actual physical potential acting…
Models of superconductors having a quasi-one-dimensional crystal structure based on the convoluted into a tube Ginzburg sandwich, which comprises a layered dielectric-metal-dielectric structure, have been suggested. The critical crystal…
Moir\'e materials, typically confined to stacking atomically thin, two - dimensional (2D) layers such as graphene or transition metal dichalcogenides, have transformed our understanding of strongly correlated and topological quantum…
Electrons navigate more easily in a background of ordered magnetic moments than around randomly oriented ones. This fundamental quantum mechanical principle is due to their Bloch wave nature and also underlies ballistic electronic motion in…
After providing a concise overview on quasicrystals and their discovery more than a quarter of a century ago, I consider the unexpected interplay between nanotechnology and quasiperiodic crystals. Of particular relevance are efforts to…
The creation of moir\'e superlattices in twisted bilayers of two-dimensional crystals has been utilised to engineer quantum material properties in graphene and transition metal dichalcogenide (TMD) semiconductors. Here, we examine the…
The moir\'e Hubbard model describes correlations in certain homobilayer twisted transition metal dichalcogenides. Using exact diagonalization and density matrix renormalization group methods, we find magnetic Mott insulating and metallic…
Quasiperiodic potentials can be used to interpolate between localization and delocalization in one dimension. With the rise of optical platforms engineering dipolar interactions, a key question is the stability of quasicrystalline phases…
Over the past decade, a combination of crystal structure prediction techniques and experimental synthetic work has thoroughly explored the phase diagrams of binary hydrides under pressure. The fruitfulness of this dual approach is…
Moir\'e superlattices - periodic orbital overlaps and lattice-reconstruction between sites of high atomic registry in vertically-stacked 2D layered materials - are quantum-active interfaces where non-trivial quantum phases on novel…
Twisted bilayers of two-dimensional (2D) materials are proving a fertile ground for investigating strongly correlated electron phases. This is because the moir\'e pattern introduced by the relative twist between layers introduces…
According to electronic structure theory, bilayer graphene is expected to have anomalous electronic properties when it has long-period moir\'e patterns produced by small misalignments between its individual layer honeycomb lattices. We have…
We study the lattice configuration and electronic structure of a double moir\'{e} superlattice, which is composed of a graphene layer encapsulated by two other layers in a way such that the two hexagonal moir\'{e} patterns are arranged in a…
Topological phases of matter have sparked an immense amount of activity in recent decades. Topological materials are classified by topological invariants that act as a non-local order parameter for any symmetry and condition. As a result,…
The supermoir\'e lattice, arising from the interference of multiple moir\'e patterns, dramatically reshapes the electronic band structure by introducing new minibands and modifying band dispersion. Concurrently, strong electronic…
Motivated by recent experimental findings, we investigate the possible occurrence and characteristics of quasicrystalline order in two-dimensional mixtures of point dipoles with two sorts of dipole moments. Despite the fact that the dipolar…