Related papers: Functional renormalization group for a large moir\…
We present a renormalization group analysis of two-dimensional interacting fermion systems with a closed and partially flat Fermi surface. Numerical solutions of the one-loop flow equations show that for a bare local repulsion, the system…
Twisted bilayer graphene exhibits isolated, relatively flat electronic bands near charge neutrality when the interlayer rotation is tuned to specific magic angles. These small misalignments, typically below 1.1{\deg}, result in long-period…
Many-body effects in condensed matter yield novel quantum states when the electronic density of states is enhanced. A vivid example is flat bands, which suppress kinetic energy and let interactions dominate, when they are filled with an…
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…
Although the functional renormalization group (fRG) is by now a well-established method for investigating correlated electron systems, it is still undergoing significant technical and conceptual improvements. In particular, the motivation…
Materials with flat electronic bands often exhibit exotic quantum phenomena owing to strong correlations. Remarkably, an isolated low-energy flat band can be induced in bilayer graphene by simply rotating the layers to 1.1$^{\circ}$,…
Band engineering in twisted bilayers of the five generic two-dimensional Bravais networks is demonstrated. We first derive symmetry-based constraints on the interlayer coupling, which helps us to predict and understand the shape of the…
We investigate the renormalization group flows and fixed point structure of many coupled minimal models. The models are coupled two by two by energy-energy couplings. We take the general approach where the bare couplings are all taken to be…
It has recently been shown that quantum-confined states can appear in epitaxially grown van der Waals material heterobilayers without a rotational misalignment ($\theta=0^\circ$), associated with flat bands in the Brillouin zone of the…
The study of moir\'e engineering started with the advent of van der Waals heterostructures in which stacking two-dimensional layers with different lattice constants leads to a moir\'e pattern controlling their electronic properties. The…
We analyze the one-dimensional extended Hubbard model with a single static impurity by using a computational technique based on the functional renormalization group. This extends previous work for spinless fermions to spin-1/2 fermions. The…
Experimental demonstrations of tunable correlation effects in magic-angle twisted bilayer graphene have put two-dimensional moir\'e quantum materials at the forefront of condensed-matter research. Other twisted few-layer graphitic…
Renormalization group methods are used to study the low-energy behavior of the unscreened Coulomb interaction in a one-dimensional electron system. By applying a GW approximation, a strong wavefunction renormalization is found in the model,…
The generalized tight-binding model, based on the subenvelope functions of distinct sublattices, is developed to investigate the magnetic quantization in sliding bilayer graphenes. The relative shift of two graphene layers induces a…
Moir\'e materials with flat electronic bands provide a highly controllable quantum system for studies of strong-correlation physics and topology. In particular, angle-aligned heterobilayers of semiconducting transition metal dichalcogenides…
We present a two-step method specifically tailored for band structure calculation of the small-angle moir\'{e}-pattern materials which contain tens of thousands of atoms in a unit cell. In the first step, the self-consistent field…
One-dimensional (1D) moir\'e superlattices provide a new route to engineering reduced-dimensional electronic states in van der Waals materials, yet their electronic structure and microscopic origin remain largely unexplored. Here, we…
We introduce approximate, functional renormalization group based schemes to obtain correlation functions in pure excited eigenstates of large fermionic many-body systems at arbitrary energies. The algorithms are thouroughly benchmarked and…
Experimental advances in the fabrication and characterization of few-layer materials stacked at a relative twist of small angle have recently shown the emergence of flat energy bands. As a consequence electron interactions become relevant,…
We review some aspects of the renormalization group method for interacting fermions. Special emphasis is placed on the application of scaling theory to quasi-one-dimensional systems at non zero temperature. We begin by introducing the…