The ratio of the Zeeman splitting to the cyclotron energy ($M=Delta E_{rm Z}/hbar omega_{rm c}$) for hole-like carriers in bismuth has been quantified with a great precision by many experiments performed during the past five decades. It exceeds 2 when the magnetic field is along the trigonal axis and vanishes in the perpendicular configuration. Theoretically, however, $M$ is expected to be isotropic and equal to unity in a two-band Dirac model. We argue that a solution to this half-a-century-old puzzle can be found by extending the $kcdot p$ theory to multiple bands. Our model not only gives a quantitative account of magnitude and anisotropy of $M$ for hole-like carriers in bismuth, but also explains its contrasting evolution with antimony doping pressure, both probed by new experiments reported here. The present results have important implications for the magnitude and anisotropy of $M$ in other systems with strong spin-orbit coupling.
Ternary iron arsenide EuFe$_2$As$_2$ with ThCr$_2$Si$_2$-type structure has been studied by magnetic susceptibility, resistivity, thermopower, Hall and specific heat measurements. The compound undergoes two magnetic phase transitions at about 200 K and 20 K, respectively. The former was found to be accompanied with a slight drop in magnetic susceptibility (after subtracting the Curie-Weiss paramagnetic contribution), a rapid decrease in resistivity, a large jump in thermopower and a sharp peak in specific heat with decreasing temperature, all of which point to a spin-density-wave-like antiferromagnetic transition. The latter was proposed to be associated with an A-type antiferromagnetic ordering of Eu$^{2+}$ moments. Comparing with the physical properties of the iso-structural compounds BaFe$_2$As$_2$ and SrFe$_2$As$_2$, we expect that superconductivity could be induced in EuFe$_2$As$_2$ through appropriate doping.
Chemical doping has recently become a very important strategy to induce superconductivity especially in complex compounds. Distinguished examples include Ba-doped La$_2$CuO$_4$ (the first high temperature superconductor), K-doped BaBiO$_3$, K-doped C$_{60}$ and Na$_{x}$CoO$_{2}cdot y$H$_{2}$O. The most recent example is F-doped LaFeAsO, which leads to a new class of high temperature superconductors. One notes that all the above dopants are non-magnetic, because magnetic atoms generally break superconducting Cooper pairs. In addition, the doping site was out of the (super)conducting structural unit (layer or framework). Here we report that superconductivity was realized by doping magnetic element cobalt into the (super)conducting-active Fe$_2$As$_2$ layers in LaFe$_{1-x}$Co$_{x}$AsO. At surprisingly small Co-doping level of $x$=0.025, the antiferromagnetic spin-density-wave transition in the parent compound is completely suppressed, and superconductivity with $T_csim $ 10 K emerges. With increasing Co content, $T_c$ shows a maximum of 13 K at $xsim 0.075$, and then drops to below 2 K at $x$=0.15. This result suggests essential differences between previous cuprate superconductor and the present iron-based arsenide one.
