1 citations · 1 across the 9 of their papers we have counts for
10 papers
Continuum Limit for One-Dimensional Moiré Relaxation
Hao Lan, Michael Hott, Jeff Calder +1
We establish convergence of minimizers for a minimal one dimensional atomic-scale model for relaxation in moiré materials to those of a one-dimensional continuum limit functional a…
Relaxation effects on Hartree-Fock ground states in twisted bilayer graphene at even integer fillings
Tianyu Kong, Alexander B. Watson, Lin Lin +2
A standard approach for studying magic angle twisted bilayer graphene (MATBG)'s correlated electronic phase diagram is to project the Coulomb interaction down to effective models o…
WKB Spectral Asymptotics for a One-Dimensional Dirac Operator with a Slowly Varying Mass Profile
Owen Sutton, Alexander B. Watson
We study the semiclassical spectral theory of a one-dimensional Dirac operator describing waves at the interface between topologically distinct media. We derive a modified Bohr-Som…
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…
Formal justification of a continuum relaxation model for one-dimensional moiré materials
Jingzhi, Zhou, Alexander B. Watson
Mechanical relaxation in moiré materials is often modeled by a continuum model where linear elasticity is coupled to a stacking penalty known as the Generalized Stacking Fault Ener…
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…
Construction and Accuracy of Electronic Continuum Models of Incommensurate Bilayer 2D Materials
Xue Quan, Alex Watson, Daniel Massatt
Single-particle continuum models such as the popular Bistritzer-MacDonald model have become powerful tools for predicting electronic phenomena of incommensurate 2D materials and th…
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…
Ergodic properties of one-dimensional incommensurate bilayer materials
Nathan J. Essner, Jeremiah Williams, Alexander B. Watson
We consider one-dimensional deterministic and random tight-binding Hamiltonians modeling electronic properties of twisted bilayer materials. When the twisted structure is incommens…