Edge and pn interface states in graphene

Abstract

In 2017 Overweg et al found new oscillation pattern in conductance when magnetic field rise up to 0 5(T) Although this pattern can be simulated by tight-binding model physical mechanism in this pattern have not understood So they want to find analytical solution and check conductance changing by this solution After they used tight-binding model to simulate many different set up oscillation pattern disappear when energy in leads are fixed According to this result they thought that oscillating pattern have relation to bulk Landau level In this research I try to solve edge states interface states and bulk states in graphene 2DEG is easier system than graphene I will solve 2DEG first and use conclusion from 2DEG to describe graphene situation First I will introduce what edge states interface states and bulk states are And how these three different states are distinguished I suppose that two different potential model using to describe material boundary and junction respectively After some mathematical process band structure and eigenfucntions can be found I pick 4 different points in different situations to plot current densities and check these 4 points whether edge states interface states or bulk states In addition to analytical solutions I also use KWANT to calculate numerical solutions After compare analytical and numerical solutions we find that they have good overlap It means analytical solutions can be used to find correct band structure and quantum states

Date of Award	2019
Original language	English
Supervisor	Ming-Hao Liu (Supervisor)