Theory of Metal-Insulator Transitions in Graphite under High Magnetic Field

Zhiming Pan, Xiao-Tian Zhang, Ryuichi Shindou

Published 2018-02-28Version 1

Graphite under high magnetic field exhibits consecutive metal-insulator (MI) transitions as well as re-entrant insulator-metal (IM) transition in the quasi-quantum limit at low temperature. We employ models with electron pocket(s) and hole pocket(s), to construct a bosonized Hamiltonian that comprises of displacement field along the field direction and its conjugate fields. Using a renormalization group argument, we show that there exists a critical interaction strength above which a umklapp term becomes relevant and the system enters excitonic insulator phase with a long-range ordering of spin superfluid phase field ("spin nematic excitonic insulator"). When a pair of electron and hole pockets get smaller in size, a quantum fluctuation of the spin superfluid phase becomes progressively large and eventually distabilizes the excitonic insulator phases, resulting in the re-entrant IM transition. The strength of the quantum fluctuation is quantified by the Luttinger parameters of the pockets, while the Luttinger parameters are shown to be related with the critical exponent of the $T=0$ IM (and also MI) transition point. We further show that the exponent can be experimentally determined by an infrared optical spectroscopy. This lets us propose a "test experiment" for our theory of the re-entrant IM transition. We explain field- and temperature-dependences of in-plane resistivity by surface transports via chiral surface Fermi arc states and its coupling with gapless Goldstone modes associated with the spin nematic orderings.