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Dirac semimetal thin films in in-plane magnetic fields

In this work we study the effects of in-plane magnetic fields on thin films of the Dirac Semimetal (DSM) \ce{Na2Bi} where one of the in-plane directions is perpendicular to the $k$-separation between the two Weyl points for each spin orientation. We show numerically that the states localized near the surface of these thin films are related to the Fermi arc states in semi-infinite slabs. Due to the anisotropy between the two in-plane directions, the application of a magnetic field along these directions have differing effects. A field parallel to the $k$ space separation between the Weyl points leads to a broadening of the surface state band and a formation of an energy plateau, while a perpendicular field shifts the energy where the hole and particle bands meet upwards and sharpens the tips of the bands. We illustrate the effects of these changes to the bandstructure by studying the transmission from a source segment without a magnetic field to a drain segment with a field with the field and interface at various in-plane directions.