Abstract
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 ℤ2 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 changes magnetic properties of the dual system. This is justified by showing increasing susceptibility and the spontaneous magnetization with increasing impurity parameter.
Highlights
There is a holographic study about the crossover between WAL and WL phases [14, 15] by adding Chern-Simons like coupling with impurity and gauge field
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 Z2 symmetry and time reversal symmetry in a 2+1 dimensional system with momentum relaxation
Summary
In order to compare real experimental data quantitatively, the hysteric magnetoconductance should be averaged over all the fragments Such a research including fragmentation average could be an interesting study but it is beyond the scope of the present work. In addition to these electric conductivities, we study hysteresis curves of the Seebeck coefficient S and the Nernst signal N which have never been measured yet in the TIs, to our knowledge These quantities are important to see the magnetic properties of materials, such as, anomalous Hall effect. It can be conjectured that these phenomenological order parameters may be related to real scalar hair and magnetization of the black brane in the holographic point of view It can be an intersting study about the relation between the bulk and boundary quantities. This independent check of the magnetization confirms that the magnetization current (3.12) is the correct expression
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