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Multiband character of $β$-FeSe: Angular dependence of the magnetoresistance and upper critical field

We studied $ab$-plane transport properties in single crystals of the superconductor $β$-FeSe up to 16 T. In the normal state, below 90 K, the crystals present a strongly anisotropic positive magnetoresistance that becomes negligible above that temperature. In the superconducting state (T$_c$=8.87(5) K) the upper critical field anisotropy $H$$_{c2}$$\parallel$$ab$ / $H$$_{c2}$$\parallel$$c$ changes with temperature and the angular dependence of the dissipation for fixed temperatures and fields reflects a strongly anisotropic behavior. Our results make evident that multiband effects are needed to describe the measured transport properties. We model the magnetoresistance and upper critical field behavior with a two-band model showing that the diffusivities ratio parameter remains unchanged going from the normal to the superconducting state.