711 citations · 2.4k across the 77 of their papers we have counts for
15 papers · 1 filter
Interacting Twisted Bilayer Graphene with Systematic Modeling of Structural Relaxation
Tianyu Kong, Alexander B. Watson, Mitchell Luskin +1
Twisted bilayer graphene (TBG) has drawn significant interest due to recent experiments which show that TBG can exhibit strongly correlated behavior such as the superconducting and…
Higher-order continuum models for twisted bilayer graphene
Solomon Quinn, Tianyu Kong, Mitchell Luskin +1
The first-order continuum PDE model proposed by Bistritzer and MacDonald in \cite{bistritzer2011moire} accurately describes the single-particle electronic properties of twisted bil…
Mathematical foundations of phonons in incommensurate materials
Michael Hott, Alexander B. Watson, Mitchell Luskin
In some models, periodic configurations can be shown to be stable under, both, global or local perturbations. This is not the case for aperiodic media. The specific class…
Learning the local density of states of a bilayer moiré material in one dimension
Diyi Liu, Alexander B. Watson, Michael Hott +2
Recent work of three of the authors showed that the operator which maps the local density of states of a one-dimensional untwisted bilayer material to the local density of states o…
Modeling of electronic dynamics in twisted bilayer graphene
Tianyu Kong, Diyi Liu, Mitchell Luskin +1
We consider the problem of numerically computing the quantum dynamics of an electron in twisted bilayer graphene. The challenge is that atomic-scale models of the dynamics are aper…
From incommensurate bilayer heterostructures to Allen-Cahn: An exact thermodynamic limit
Michael Hott, Alexander B. Watson, Mitchell Luskin
We give a complete and rigorous derivation of the mechanical energy for twisted 2D bilayer heterostructures without any approximation beyond the existence of an empirical many-body…
Mathematical aspects of the Kubo formula for electrical conductivity with dissipation
Alexander B. Watson, Dionisios Margetis, Mitchell Luskin
In this expository article, we present a systematic formal derivation of the Kubo formula for the linear-response current due to a time-harmonic electric field applied to non-inter…
Relaxation and domain wall structure of bilayer moire systems
Paul Cazeaux, Drake Clark, Rebecca Engelke +2
Moire patterns result from setting a 2D material such as graphene on another 2D material with a small twist angle or from the lattice mismatch of 2D heterostructures. We present a…
On the Su-Schrieffer-Heeger model of electron transport: low-temperature optical conductivity by the Mellin transform
Dionisios Margetis, Alexander B. Watson, Mitchell Luskin
We describe the low-temperature optical conductivity as a function of frequency for a quantum-mechanical system of electrons that hop along a polymer chain. To this end, we invoke…
Existence of the first magic angle for the chiral model of bilayer graphene
Alexander B. Watson, Mitchell Luskin
We consider the chiral model of twisted bilayer graphene introduced by Tarnopolsky-Kruchkov-Vishwanath (TKV). TKV have proved that for inverse twist angles such that the effect…
Nonretarded edge plasmon-polaritons in anisotropic two-dimensional materials
Dionisios Margetis, Matthias Maier, Tobias Stauber +2
By an integral equation approach to the time-harmonic classical Maxwell equations, we describe the dispersion in the nonretarded frequency regime of the edge plasmon-polariton (EPP…
Incommensurate Heterostructures in Momentum Space
Daniel Massatt, Stephen Carr, Mitchell Luskin +1
To make the investigation of electronic structure of incommensurate heterostructures computationally tractable, effective alternatives to Bloch theory must be developed. In Massatt…
On the Wiener-Hopf method for surface plasmons: Diffraction from semi-infinite metamaterial sheet
Dionisios Margetis, Matthias Maier, Mitchell Luskin
By formally invoking the Wiener-Hopf method, we explicitly solve a one-dimensional, singular integral equation for the excitation of a slowly decaying electromagnetic wave, called…
Generalized Kubo Formulas for the Transport Properties of Incommensurate 2D Atomic Heterostructures
Eric Cancès, Paul Cazeaux, Mitchell Luskin
We give an exact formulation for the transport coefficients of incommensurate two-dimensional atomic multilayer systems in the tight-binding approximation. This formulation is base…
Electronic Density of States for Incommensurate Layers
Daniel Massatt, Mitchell Luskin, Christoph Ortner
We prove that the electronic density of states (DOS) for 2D incommensurate layered structures, where Bloch theory does not apply, is well-defined as the thermodynamic limit of fini…