Edge reconstructions in 2D electron gas in magnetic field

We are interested in studying physics near the edge of a 2D electron gas system in perpendicular magnetic field. It has already been studied in nu=1,2,3 in GaAs system with magnetic field , when the confining potential is made smoother near the edge then electrons near the edge reconstructs itself in order to screen the background potential. We use Hartree Fock Method to find the ground state of the system. To do this we consider a semi-infinite cylindrical geometry, along the x-axis we have a boundary and along the curved edge is y-axis. Then after writing the Hartree Fock(HF) Hamiltonian, which is a matrix, we solve this Hamiltonian self-consistently to get the ground-state of the system using armadillo and boost package in c++. The input files for the main code (c++) are generated by python codes which uses numpy and scipy. We want to use the cluster for the following two projects:

1. To study nu=4 case for GaAs system. We try to find out the ground state near the edge for different smoothness of background potential and different strength of the electron-electron interaction.
2. To study the excitations of the nu=2 and 3 case using time dependent Hartree fock approximation (TDHF).

Students

Amartya Saha, Graduate Student

Jincheng An, Added on MCC cluster, 06/06/2023

Aimee Toscano, Added on LCC cluster, 06/21/2023

Edges in Interacting Moire Systems

When two two-dimensional systems with slightly mismatched lattice constants (or that differ by a small rotation) are laid on top of each other, a moire pattern with a much larger unit cell iwith thousands of atoms is formed. This approximate periodicity can lead to a band reconstruction in the bulk, leading to very flat bands. It is well-known that interactions in flat bands can cause exotic ground states to be stabilized. In twisted bilayer graphene, it is known that at a certain "magic" twist angle between the two layers, the central bands are almost completely flat. A variety of ground states, such as Mott insulators, superconductors, and Chern insulators, have been seen experimentally. In this project we will systematically explore the edge states of such strongly interacting systems in the ribbon geometry. The Hartree-Fock approximation will be used to treat the interactions. Because of the large size of the moire unit cell (thousands of atoms) the work will be intensely computational, hence the request for cluster time.

Students

Mainak Das, Graduate, Added 03/29/2023 on MCC cluster

Faculty

Dr. Ganpathy Murthy (murthy@pa.uky.edu)

Software

Armadillo c++
Boost c++
Vectors c++
Numpy (python)
Scipy (python)

Collaborators

Dr. Sumathi Rao, Harish Chandra Research Institute, Jhunsi, Allahabad India
Suman Jyoti De, Harish Chandra Research Institute, Jhunsi, Allahabad India

Grant

NSF(DMR-1306897)

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