Condensed Matter Seminar - Structure of the Single-Electron Wavefunction and Ground States in Flat Electronic Bands

Because of its flat energy bands, the two-dimensional electron gas exhibits a rich set of ground states, commonly classified in two different classes. Fractional quantum Hall states form one class of ground states; numerous fractional states support Abelian excitations, but the most interesting ones host non-Abelian excitations. Charge ordered ground states, such as the Wigner solid, electronic bubbles, and electronic stripe phases form a second class of ground states. In this talk I will highlight the profound influence of the structure of the single-electron wavefunction on the formation of these two classes of ground states in the twodimensional electron gas hosted in GaAs/AlGaAs quantum wells. In particular, I will discuss two recent experimental findings: a) the quantum phase transition from a non-Abelian fractional state to a stripe phase when the single-electron wavefunction has a single node and b) the proliferation of bubbles for single-electron wavefunctions with a complex nodal structure.