Electron Pumping Transport In The α-T₃ Lattice

Recently,the superconductivity discovered in the twisted bilayer graphene has ignited the research interest in the 2D Dirac materials with a flat band.Although the electrons in the flat band itself do not directly contribute the electron transport properties of the system,the electron transport in the neighboring Dirac band would be greatly affected.In this thesis,we are dedicated to studying the quantum pumping effect of theα-T₃ lattice which possesses a flat band without any energy dispersion.α-T₃ lattice is an interpolate between the Graphene lattice（α=0）and the Dice lattice（α=1）and has valley-degenerate Dirac bands together with a flat band,which crosses the Dirac band exactly at the Dirac point.The Berry phase of Dirac electrons in theα-T₃ lattice is dependent on the value of.In this thesis,we focus on theα=1 case and study the quantum pump effect of the Dirac electron by taking the flat band into account.The introduced mass terms of the Dirac electrons are taken as the pumping parameters that vary slowly with time.Two mass terms dubbed asandare considered,and theterm breaks the electron-hole symmetry but theterm reverses this symmetry.By use of the adiabatic pump formula,we calculated the pump current in the adiabatic approximation.It is shown that themass term cannot bring in any pump current,whereas thepump parameter can lead to a quantized charge pump effect in that an integral number of charges are pumped out in a pump cycle.The physics origin is ascribed to the topological interface state forming between the two parameter regions in themass term case.For themass term case,there is no topological interface state forming in the system so that no such a quantized charge can be pumped out.Since the topological interface state can evolve with time so as to transport a unit charge moving in the system and this process is similar to the famous Thouless quantum pump.Finally,we concluded that the pump effect of the Dirac electrons in theα-T₃ lattice would be severely affected by the existing flat band.