Hysteric Magnetoconductance

In this paper we study a hysteric phase transition from weak localization phase to hysteric magnetoconductance phase using gauge/gravity duality. This hysteric phase is triggered by a spontaneous magnetization related to $\mathbb{Z}_2$ symmetry and time reversal symmetry in a 2+1 dimensional system with momentum relaxation. We derive thermoelectric conductivity formulas describing non-hysteric and hysteric phases. At low temperatures, this magnetoconductance shows similar phase transitions of topological insulator surface states. We also obtain hysteresis curves of Seebeck coefficient and Nernst signal. It turns out that our impurity parameter plays a role of magnetic impurity. This is justified by showing increasing susceptibility and the spontaneous magnetization with increasing impurity parameter.