Although niobium borides have been extensively studied
on their
mechanical properties, a systematic investigation on their potential
metastable phases, superconducting excitations, and spin Hall effects
(SHE) is still lacking. Herein, we carry out a global structure search
in the Nb-B system based on the evolutionary algorithm and density
functional theory. Thermodynamical, dynamical, mechanical, and quasiharmonic
approximation investigations unveil four new phases, Nb<sub>3</sub>B<sub>5</sub>, Nb<sub>2</sub>B<sub>5</sub>, Nb<sub>3</sub>B<sub>7</sub>, and Nb<sub>5</sub>B<sub>4</sub>, which are promising candidates
for experimental preparations. Moreover, the superconducting transitions
of all Nb-B compounds are performed from electron–phonon calculations.
In addition, all Nb-B compounds are predicted to be topologically
nontrivial. More intriguingly, Nb<sub>2</sub>B<sub>5</sub> is unveiled
as a promising noncentrosymmetric superconductor to explore topological
superconducting excitation. Furthermore, nonzero spin Hall conductivity
(SHC) tensor elements of all Nb-B compounds are predicted, and NbB
is predicted to own a maximal SHC value of 320 (ℏ/<i>e</i>) (S/cm) among all Nb-B compounds. Our theoretical results fill in
the gap on superconducting and SHC parameters of Nb-B binaries, demonstrating
that Nb-B binaries are a potential choice to explore superconducting
excitations and topological states and to investigate the SHE.