Applied Mathematics & Quantum Matter Double Seminar: Modelling of 2D Moiré Materials

The joint applied mathematics and quantum matter double-seminar on modelling of 2D moiré materials will feature talks by Mitchell Luskin (University of Minnesota) and Ziyan (Zoe) Zhu (Boston College).

This talk wil be followed by a reception and informal discussion at 5:00pm.

Speaker: Mitchell Luskin, University of Minnesota
Title: Mathematics and Physics at the Moiré Scale 
Abstract: Placing a two-dimensional lattice on another with a small rotation gives rise to periodic “moiré” patterns on a superlattice scale much larger than the original lattice. The Bistritzer-MacDonald (BM) model attempts to capture the electronic properties of twisted bilayer graphene (TBG) by an effective periodic continuum model over the bilayer moiré pattern. We use the mathematical techniques developed to study waves in inhomogeneous media to identify a regime where the BM model emerges as the effective dynamics for electrons modeled as wave-packets spectrally concentrated at the monolayer Dirac points of linear dispersion, up to error that we rigorously estimate. Using measured values of relevant physical constants, we argue that this regime is realized in TBG at the first “magic" angle where the group velocity of the wave packet is zero and strongly correlated electronic phases (superconductivity, Mott insulators, etc.) are observed. We will also present models of TBG which account for the effects of mechanical relaxation; we couple our relaxed BM model with interacting TBG models. We find that our systematic relaxation model gives quantitative differences from earlier simplified models.

About Mitchell Luskin
Mitchell Luskin develops mathematical models and computational methods for solid mechanics, molecular dynamics, and electronic structure for the mechanical and electromagnetic properties of materials. His current research focuses on quantum materials, especially 2D moiré heterostructures.

Speaker: Ziyan (Zoe) Zhu, Boston University
Title: Microscopic theory for electron-phonon coupling in twisted bilayer graphene
Abstract: The origin of superconductivity in twisted bilayer graphene -- whether phonon-driven or electron-driven -- remains unresolved, in part due to the absence of a quantitative and efficient model for electron-phonon coupling (EPC). In this work, we develop a first-principles-based microscopic theory to calculate EPC in twisted bilayer graphene for arbitrary twist angles without requiring a periodic moiré supercell. Our approach combines a momentum-space continuum model for both electronic and phononic structures with a generalized Eliashberg-McMillan theory beyond the adiabatic approximation. Using this framework, we find that the EPC is strongly enhanced near the magic angle. The superconducting transition temperature induced by low-energy phonons peaks at  around 1 K, and remains finite for a range of angles both below and above the magic angles. We predict that superconductivity persists up to 1.4˚, where superconductivity has been recently observed despite the dispersive electronic bands. Beyond a large density of states, we identify a key condition for strong EPC: resonance between the electronic bandwidth and the dominant phonon frequencies. We also show that the EPC strength of a specific phonon corresponds to the modification of the moiré potential. In particular, we identify several -phonon branches that contribute most significantly to the EPC, which are experimentally detectable via Raman spectroscopy.

About Zoe Zhu
Zoe Zhu develops numerical models to predict and understand emergent quantum phenomena by studying the coupling between lattices, electrons, and spins. Her multiscale framework bridges atomistic simulations with the mesoscopic properties of large aperiodic quantum materials. She aims to guide experimental searches for exotic phases of matter, from superconductivity to topological states.