  Recently, unconventional materials (or obstructed atomic insulators) have
attracted much attention owing to the unconventional feature of mismatch
between Wannier centers and atomic positions. In this paper, we demonstrate
that the trigonal selenium and tellurium host an unconventional nature in both
electronic and phonon spectra. In electronic band structures, the band
representation (BR) decomposition for occupied bands has to contain the
essential BR of $A@3b$, and the real-space invariant is $\delta_1@3b=-1$. The
$\pi$ Zak phase suggests that the one-dimensional Se/Te chain is a chiral
Su-Schrieffer-Heeger chain. The effective magnetism can be induced by $p$
states at ends. More importantly, a large shift current is obtained in Se
quantum well. In addtion, in phonon spectra, three sets of phonon bands are
well separated and assigned to $B@3b$, $B@3a$, and $A@3b$ BRs, respectively.
Thus, the obstructed phonon states are predicted on the (0001) surface. As the
prototypes of unconventional materials in both electronic and phonon spectra,
our findings could create much interest in the study of obstructed surface
electronic and phonon states in these novel materials.
