Related papers: Quantum Geometry and Stability of Moir\'e Flatband…
Bilayer graphene twisted at the angle of about 1.1{\deg} better known as magic angle, exhibits ultra-flat moir\'e superlattice bands that are a source of highly-tunable, exotic quantum phenomena. Such phenomena, like superconductivity,…
We present here a Hofstadter's butterfly spectrum for the magic angle twisted bilayer graphene obtained using an ab initio based multi-million atom tight-binding model. We incorporate a hexagonal boron nitride substrate and out-of-plane…
Quantum geometry characterizes the variation of wavefunctions in momentum space through their overlaps and relative phases, providing a general framework for understanding many transport and optical properties. It is generally formulated in…
Geometric analogs of Bloch oscillations studied so far have relied on Berry curvature. We show that a weakly inhomogeneous electric field adds a distinct quantum-metric term to semiclassical wavepacket dynamics, generating an oscillatory…
The Berry curvature is a geometrical property of an energy band which acts as a momentum space magnetic field in the effective Hamiltonian describing single-particle quantum dynamics. We show how this perspective may be exploited to study…
Thermoelectric transport coefficients up to linear order in the applied magnetic field are microscopically studied using Kubo-Luttinger linear response theory and thermal Green's functions. We derive exact formulas for the thermoelectric…
The complete quantum metric of a parametrized quantum system has a real part (usually known as the Provost-Vallee metric) and a symplectic imaginary part (known as the Berry curvature). In this paper, we first investigate the relation…
Band geometry plays a substantial role in topological lattice models. The Berry curvature, which resembles the effect of magnetic field in reciprocal space, usually fluctuates throughout the Brillouin zone. Motivated by the analogy with…
Moir\'e structures formed by twisting three layers of graphene with two independent twist angles present an ideal platform for studying correlated quantum phenomena, as an infinite set of angle pairs is predicted to exhibit flat bands.…
The recently introduced concept of "surface Berry plasmons" is studied in the concrete instance of a ferromagnetic conductor in which the Berry curvature, generated by spin-orbit (SO) interaction, has opposite signs for carriers parallel or…
The quantum geometric properties of a Bloch state in momentum space are usually described by the Berry curvature and quantum metric. In realistic gapped materials where interactions and disorder render the Bloch state not a viable starting…
Moir\'e materials provide a highly tunable environment for the realization of band structures with engineered physical properties. Specifically, moir\'e structures with Fermi surface flat bands - a synthetic environment for the realization…
The topology of the electronic band structure of solids can be described by its Berry curvature distribution across the Brillouin zone. We theoretically introduce and experimentally demonstrate a general methodology based on the measurement…
Geometry and topology are fundamental to modern condensed matter physics, but their precise connection in quantum systems remains incompletely understood. Here, we develop an analytical scheme for calculating the curvature of the quantum…
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…
We present a microscopic theory for the local (single site) orbital magnetization in tight-binding systems. Each occupied state of energy $\varepsilon_n$ contributes with a local orbital magnetic moment term ${\mathbf{ m}}_n({\mathbf{ r}})$…
Many graphene moir\'e superlattices host narrow bands with non-zero valley Chern numbers. We provide analytical and numerical evidence for a robust spin and/or valley polarized insulator at total integer band filling in nearly flat bands of…
We study the magnetic Bloch oscillations performed by a quantum particle moving in a two-dimensional lattice in the presence of a strong (synthetic) magnetic field and a uniform force. An elementary derivation of the Berry curvature effect…
Unlike the spin-1/2 fermions, the Lieb and Dice lattices both host triply-degenerate low-energy excitations. Here, we discuss Moir\'e structures involving twisted bilayers of these lattices, which are shown to exhibit a tunable number of…
Topological flat bands play an essential role in inducing exotic interacting physics, ranging from fractional Chern insulators to superconductivity, in moir\'e materials. In this work, we propose a design principle for realizing topological…