In the search for MgB2-like phonon-mediated superconductors we have carried out a systematic density functional theory study of the Ca-B system, isoelectronic to Mg-B, at ambient and gigapascal pressures. A remarkable variety of candidate high-pressu
re ground states have been identified with an evolutionary crystal structure search, including a stable alkaline-earth monoboride oI8-CaB, a superconductor with an expected critical temperature (Tc) of 5.5 K. We have extended our previous study of CaB6 [Phys. Rev. Lett. 108, 102501 (2012)] to nearby stoichiometries of CaB[6+x], finding that extra boron further stabilizes the proposed B24 units. Here an explanation is given for the transformation of cP7-CaB6 into the more complex oS56 and tI56 polymorphs at high pressure. The stability of the known metallic tP20 phase of CaB4 at ambient pressure is explained from a crystal structure and chemical bonding point of view. The tP20 structure is shown to destabilize at 19 GPa relative to a semiconducting MgB4-like structure due to chemical pressure from the metal ion. The hypothetical AlB2-type structure of CaB2, previously shown to have favorable superconducting features, is demonstrated here to be unstable at all pressures; two new metallic CaB2 polymorphs with unusual boron networks stabilize at elevated pressures above 8 GPa but are found to have very low critical temperatures (Tc ~1 K). The stability of all structures has been rationalized through comparison with alkaline-earth analogs, emphasizing the importance of the size of the metal ion for the stability of borides. Our study illustrates the inverse correlation between the thermodynamic stability and superconducting properties and the necessity to carefully examine both in the design of new synthesizable superconducting materials.
Density functional theory calculations have been used to identify stable layered Li-$M$-B crystal structure phases derived from a recently proposed binary metal-sandwich (MS) lithium monoboride superconductor. We show that the MS lithium monoboride g
ains in stability when alloyed with electron-rich metal diborides; the resulting ordered Li$_{2(1-x)}M_x$B$_2$ ternary phases may form under normal synthesis conditions in a wide concentration range of $x$ for a number of group-III-V metals $M$. In an effort to pre-select compounds with the strongest electron-phonon coupling we examine the softening of the in-plane boron phonon mode at $Gamma$ in a large class of metal borides. Our results reveal interesting general trends for the frequency of the in-plane boron phonon modes as a function of the boron-boron bond length and the valence of the metal. One of the candidates with a promise to be an MgB$_2$-type superconductor, Li$_2$AlB$_4$, has been examined in more detail: according to our {it ab initio} calculations of the phonon dispersion and the electron-phonon coupling $lambda$, the compound should have a critical temperature of $sim4$ K.
