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Complementary angle-resolved photoemission and bulk-sensitive k-resolved resonant inelastic x-ray scattering of divalent hexaborides reveal a >1 eV X-point gap between the valence and conduction bands, in contradiction to the band overlap assumed in several models of their novel ferromagnetism. This semiconducting gap implies that carriers detected in transport measurements arise from defects, and the measured location of the bulk Fermi level at the bottom of the conduction band implicates boron vacancies as the origin of the excess electrons. The measured band structure and X-point gap in CaB6 additionally provide a stringent test case for proper inclusion of many-body effects in quasi-particle band calculations.PACS numbers: 79.60.-i, 71.18.+y, 71.20.-b Great interest in the divalent hexaborides has been generated recently by the discovery of ferromagnetism (FM) in La-doped CaB 6 [1] and by exotic theoretical models to explain the unusual magnetism, e.g. that it represents the ground state of a dilute electron gas [2,3] or of a doped excitonic insulator [4][5][6][7]. Subsequent experiments have extended the observation of ferromagnetism also to the undoped systems of CaB 6 , SrB 6 and La-doped BaB 6 [8-10] raising new questions about the origins of the unusual magnetism.Central to the excitonic instability model, and indeed the starting point of most thinking about the divalent hexaborides, is the presumed existence of small band overlap between the top of the boron valence states and the bottom of the cation d-conduction band at the X-point of the simple cubic Brillouin zone appropriate to these materials. Band overlap is predicted by LDA band structure calculations [11-13] and de Haasvan Alphen (dHvA) and Shubnikov-de Haas (SdH) experiments [14][15][16] have been interpreted in this semi-metal framework.The well known need for many body corrections to the LDA in calculating semiconductor band gaps [17] calls into question the LDA band overlap result. Indeed a recent pseudopotential GW quasiparticle band calculation for CaB 6 has predicted a large 0.8 eV X-point band gap [18]. In contrast, two new all-electron GW calculations have instead predicted an intermediate 0.3 eV bandgap [19], and an unusual increased band overlap relative to LDA [20], the latter thought to be due the special character of the X-point states. The wide disparity in results for three different implementations of the GW quasiparticle band calculation scheme, which has been very successful for calculating band gaps in many common semiconductors [17], shows clearly that existing methodologies are inconsistent [21,22], applied in this case to a system with which there is no prior experience or firm experimental knowledge. Thus the question of band overlap versus a band gap (and its magnitude) is not only crucial for the novel physics of these materials but also serves as a particularly pointed test case for one of the most fundamental aspects of the modern theory of electrons in solids.In this paper we present data on divalent hexaborides...

The Fermi surfaces and single-particle spectral functions of several low-dimensional materials have been measured as part of an effort to assess the occurrence of non-Fermi-liquid behaviour in non-cuprate materials.

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