Magnetoplasmon resonances in polycrystalline bismuth as seen via time-domain terahertz spectroscopy

We report the magnetic-field-dependent far-infrared reflectivity of polycrystalline bismuth. We observe four distinct absorptions that we attribute to magnetoplasmon resonances, which are collective modes of an electron-hole liquid in a magnetic field and become optical and acoustic resonances of the electron-hole system in the small-field limit. Acoustic mode are only when the masses of distinct components are very different, which is the case in bismuth. In a polycrystal, where the translational symmetry is broken, a big shift of spectral weight to an acoustic plasmon is possible. This enables us to detect an associated plasma edge. Although the polycrystal sample has grains of randomly distributed orientations, our reflectivity results can be explained by invoking only two, clearly distinct, series of resonances. In the limit of zero field, the optical modes of these two series converge onto plasma frequencies measured in a monocrystal along the main optical axes.

Figure 1

(a) The Brillouin zone with the main symmetry points (adapted from Ref. [4]). b) The Fermi surface of bismuth: a hole pocket that is an ellipsoid elongated along the trigonal axis (${\text{C}}_3$) and three electron pockets distributed in a threefold-degenerate pocket around the ${\text{C}}_3$ axis. They are not perfectly aligned with the bisectrix axis (${\text{C}}_1$) but tilted by 6${}^{\circ }$. The binary axis (${\text{C}}_2$) is orthogonal to the ${\text{C}}_1$ axis.

Figure 2

(a) Far-infrared reflectivity of polycrystalline bismuth at 5.7 K as a function of frequency at various magnetic fields (each tesla). (b) and (c) Zoom of the reflectivity around 90 cm${}^{-1}$ in order to highlight ${\omega }_{-}^1$ and around 130 cm${}^{-1}$ in order to highlight ${\omega }_{-}^2$, for every 0.25 T between 0 and 7 T. (d) Reflectivity at 50 K as a function of frequency at various magnetic fields (each tesla).

Figure 3

Time-domain measurement of the normal-incidence reflectivity of polycrystalline bismuth at 4.2 K at various magnetic fields. The ratio of reflectivity in finite field divided by reflectivity at zero field is plotted. Curves are shifted for clarity.

Figure 4

The Kerr angle spectra of polycrystalline bismuth measured at 5.7 K at various magnetic fields. The curves are shifted for clarity and the offsets are the dashed lines of the same colors.

Figure 5

Geometry of a crystal grain (blue ellipse), truncated by the $x\text{−}y$ plane, in order to explain our magnetoplasmon resonances (see text).

Figure 6

Magnetic-field dependence of the observed collective modes ${\omega }_{\pm }$ at 5.7 K (left) and at 50 K (right). Solid lines are fit from Eq. (1).