Effect of many-body quantum fluctuations on matrix Berry phases of a two-dimensional n-type semiconductor quantum dot

In the presence of spin-orbit coupling and inversion symmetry of the lateral confinement potential a single electron does not exhibit matrix Berry phases in quasi-two-dimensional semiconductor quantum dots. In such a system we investigate whether many-body correlation effects can lead to finite matrix Berry phases. We find that the transformation properties of many-electron wavefunctions under two-dimensional inversion operation do not allow finite matrix Berry phases. This effect is exact and is independent of the form of electron-electron interactions. On the other hand, quasi-two-dimensional semiconductor quantum dots with lateral confinement potential without inversion symmetry can have finite matrix Berry phases. We find that many-body quantum fluctuations can change matrix Berry phases significantly in such systems.