Related papers: Universal principles of moir\'e band structures
In the first two papers of this series, we characterized the structure of maximally random jammed (MRJ) sphere packings across length scales by computing a variety of different correlation functions, spectral functions, hole probabilities,…
Although not as wide, and popular, as that of quantum mechanics, the investigation of fundamental aspects of statistical mechanics constitutes an important research field in the building of modern physics. Besides the interest for itself,…
Magnetism and superconductivity are physical phenomena whose foundations are rooted in quantum mechanics and whose technological applications do not cease to surprise us. In this article we describe a class of magnetic materials, we call…
We show how Carrollian symmetries become important in the construction of one-dimensional fermionic systems with all flat-band spectra from first principles. The key ingredient of this construction is the identification of Compact Localised…
We review the intriguing many-body physics resulting out of the interplay of a single, local impurity and the two-particle interaction in a one-dimensional Fermi system. Even if the underlying homogeneous correlated system is taken to be…
In this work, major principles of the mathematical constitution of space and the principles of construction of the physical space are presented. Generalized conceptions of distances and dimensionality evaluation are proposed, together with…
Two-dimensional atomic crystals can radically change their properties in response to external influences such as substrate orientation or strain, resulting in essentially new materials in terms of the electronic structure. A striking…
Hyperuniform states of matter are correlated systems that are characterized by an anomalous suppression of long-wavelength (i.e., large-length-scale) density fluctuations compared to those found in garden-variety disordered systems, such as…
The recent observation of correlated phases in transition metal dichalcogenide moir\'e systems at integer and fractional filling promises new insight into metal-insulator transitions and the unusual states of matter that can emerge near…
Flat bands in moir\'e superlattices provide a fertile ground for correlated and topological phases, governed by their quantum geometric properties. While the valley-based paradigm captures key features in select materials, it breaks down in…
Even though organic conductors have complicated crystalline structure with low symmetry and large unit cell, band structure calculations predict multiband quasi-two dimensional electronic structure yielding very simple Fermi surface in most…
In many-body systems with U(1) global symmetry, the charge fluctuations in a subregion reveal important insights into entanglement and other global properties. For subregions with sharp corners, bipartite fluctuations have been predicted to…
The piecewise linearity condition on the total energy with respect to the total magnetization of finite quantum systems is derived, using the infinite-separation-limit technique. This generalizes the well-known constancy condition, related…
The underlying mathematical structures of gauge theories are known to be geometrical in nature and the local and global features of this geometry have been studied for a long time in mathematics under the name of fibre bundles. It is now…
Flat bands amplify correlation effects and are of extensive current interest. They provide a platform to explore both topology in correlated settings and correlation physics enriched by topology. Recent experiments in correlated kagome…
We develop a comprehensive method to construct analytical continuum models for moir\'e systems directly from first-principle calculations without any parameter fitting. The core idea of this method is to interpret the terms in the continuum…
Topological properties of materials, as manifested in the intriguing phenomena of quantum Hall effect and topological insulators, have attracted overwhelming transdisciplinary interest in recent years. Topological edge states, for instance,…
We consider a family of periodic scalar operators for which one can define flat bands in the sense of Floquet-Bloch theory. One puzzling question originating in recent physics literature is a quantisation rule for the values of parameters…
We compute parameters characterizing many-body quantum chaos for a critical Fermi surface without quasiparticle excitations. We examine a theory of $N$ species of fermions at non-zero density coupled to a $U(1)$ gauge field in two spatial…
Motivated by recent observation of the quantum spin Hall effect in monolayer germanene and twisted bilayer transition-metal-dichalcogenides (TMDs), we study the topological phases of moir\'e twisted bilayers with time-reversal symmetry and…