Bosonization approach to the edge reconstruction in a two-dimensional quantum dot

We consider the edge reconstruction of electrons in a two-dimensional harmonic trap under a strong magnetic field. In this system the edge reconstruction occurs as a result of competition between electron-electron interaction and confining potential. To describe it, we develop a bosonization scheme for two-dimensional electron systems. With this method we obtain the excitation spectrum and confirm that the edge reconstruction occurs when the value of the magnetic field reaches the critical value. We also show that the edge reconstruction depends on the number of electrons too.