Electromagnetic response in two dimensional flat band systems

Abstract

Electromagnetic response has become the most powerful way for detecting, controlling and displaying in all kinds of electronics. The well developed band theory plays an essential role in understanding and designing semiconductor devices. However, with the discovery of fractional quantized Hall conductance and high-temperature superconductor, band theory based on mean field approximation with perturbation has been challenged because of poor prediction in those systems. The reason why mean field breaks down is generally attributed to the existence of flat bands, where the interaction cannot be seen as perturbation compared with the marginal kinetic energy of flat band particles. This new field beyond mean field called strong correlation requires researchers spare no effort to derive a reasonable numerical result or analytical explanation.

At the same time with the discover of two dimensional materials represented by graphene, study based on two dimensional materials becomes popular because of the simplicity compared with three dimensions and also the band topology rising from quantized Hall conductance. And very recently, the discovery of a new method tuning band flatness of two dimensional materials represented by twisted bilayer graphene calls researcher from strong correlation feld into this party.

In this thesis entitled electromagnetic response in two dimensional flat band systems, I will introduce my study within three typical two dimensional flat band systems, i.e., twisted bilayer graphene, twisted transition metal dichalcogenides and Landau level with moiré potential as Chapter 3, Chapter 4 and Chapter 5 respectively. Flat band limit is usually taken in analytical derivation, and determinant quantum Monte Carlo introduced in Chapter 2 together with some developments by me is the main numerical methodology in my study. Order and degeneracy of ground state, single-particle and two-particle Green’s function and excitation spectra, fnite temperature phase and phase transition, linear and nonlinear conductance are main results of this thesis for involved topics.

Finally, I would like to say this field of two dimensional strong correlation materials is still full of vigour and vitality with striking experiment or theory emerging from time to time. Some uncovered topics of my study may be mentioned at the end of corresponding chapters and left for the future research.