Mass Term Effect on Fractional Quantum Hall States of Dirac Particles

This book presents the high-precision analysis of ground states and low-energy excitations in fractional quantum Hall states formed by Dirac electrons, which have attracted a great deal of attention. In particular the author focuses on the physics of fractional quantum Hall states in graphene on a hexagonal boron nitride substrate, which was recently implemented in experiments. The numerical approach employed in the book, which uses an exact numerical diagonalization of an effective model Hamiltonian on a Haldane's sphere based on pseudopotential representation of electron interaction, provides a better understanding of the recent experiments.

The book reviews various aspects of quantum Hall effect: a brief history, recent experiments with graphene, and fundamental theories on integer and fractional Hall effects. It allows readers to quickly grasp the physics of quantum Hall states of Dirac fermions, and to catch up on latest research on the quantum Hall effect in graphene.

Auteur

Kouki Yonaga is a researcher at the National Institute of Information and Communications Technology. His work mainly involves quantum many-body physics. He received his bachelor's, master's and Ph.D from Tohoku University, in 2012, 2014 and 2017 respectively. He received the Department of Physics Award in 2014 and the Tohoku University President Award in 2017.

Contenu

Introduction.- Fundamental Theory of Quantum Hall Eect.- Theoretical Model and Method.- Mass Term Eects in Spinless Dirac Particle System.- Eects of Spin, Valley, and Mass Term on Fractional Quantum Hall States.- Mass and Valley Eects on Excitation in Quantum Hall States.- Conclusion.