Isotropic low-temperature upper critical field in (Ba,K)Fe$_2$As$_2$

Furious activity has been generated by the discovery of superconductivity in the iron-arsenic-based compounds ReFeAs(O,F) (Re = lanthanide) and (A,K)Fe$_2$As$_2$ (A=Ba, Sr). Superconducting $T_{\rm c}$s as high as 55~K have been observed, provoking comparisons with the ``high $T_{\rm c}$'' cuprates. The layered crystal structure of the cuprates led to speculations that reduced dimensionality is necessary for ``high-temperature'' superconductivity; at first sight, the iron-arsenic compounds, which also possess layered structures, give additional credence to this idea. However, we report measurements in magnetic fields of up to 60~T, necessary to overcome the large upper critical fields, that demonstrate that the superconducting properties of single crystals of (Ba,K)Fe$_2$As$_2$ are in fact rather three dimensional. This is markedly different from the highly anisotropic properties of all previously-known layered superconductors (e.g. the cuprates and the crystalline organic metals); we suggest that it is attributable to the distinctive electronic structure of the iron-arsenide compounds. Our measurements indicate that in contrast to the assumptions based on the cuprates, reduced dimensionality is not a prerequisite for ``high-temperature'' superconductivity.