Theory of Emergent Inductance and Capacitance in Topological Insulator Thin Films.

The theory of emergent inductance in magnetic materials is based upon the modification of Faraday's law of electromagntic inducance proposedby Barnes and Maekawa in the context of spin-motive forces (SMF). Descrbed will be a theory of emergent inductance of the surface state of a nominally non-magnetic two dimensional topolocical insulator (TI). The reality of emergent inductance is over a hunderd years old with a quartz crystal being the classical example. Such a crystal is voltage driven and corersponds to an emergent series LCR circuit implying that a quatrz crystal is not a useful inductance at low frequency. In contrast the current driven magnetic and topological systems represent a parallel LCR circuit. An emergent L is always accompanied by a C and losses by an R. The SMF and equivent LCR circuit of a TI require the evalaution of the spin off-diagonal Berrry connection A_s. It is exciting that experiment on such equivalent LCR circuits represents a significant critical illustration of spin Berry phase phyics. It is found the observed would be negative L values observed experimentally in magnets reflects the effect of the C of a parallel LCR circuit with appropriate parameters. A number of experimental predictions will be made.