Magnetoinfrared Spectroscopy of Landau Levels and Zeeman Splitting of Three-Dimensional Massless Dirac Fermions in ${\mathrm{ZrTe}}_5$

We present a magnetoinfrared spectroscopy study on a newly identified three-dimensional (3D) Dirac semimetal ${\mathrm{ZrTe}}_5$. We observe clear transitions between Landau levels and their further splitting under a magnetic field. Both the sequence of transitions and their field dependence follow quantitatively the relation expected for 3D massless Dirac fermions. The measurement also reveals an exceptionally low magnetic field needed to drive the compound into its quantum limit, demonstrating that ${\mathrm{ZrTe}}_5$ is an extremely clean system and ideal platform for studying 3D Dirac fermions. The splitting of the Landau levels provides direct, bulk spectroscopic evidence that a relatively weak magnetic field can produce a sizable Zeeman effect on the 3D Dirac fermions, which lifts the spin degeneracy of Landau levels. Our analysis indicates that the compound evolves from a Dirac semimetal into a topological line-node semimetal under the current magnetic field configuration.

Figure 1

The relative reflectivity of ${\mathrm{ZrTe}}_5$ under magnetic field, as a function of energy. The spectra are shifted upward by equal intervals corresponding to different $B$.

Figure 2

The wave number dependent relative reflectivity $R(B)/R(0)$ under magnetic field of 2 T. $n=0\dots 5$ point to six different peaks in sequence. The inset shows the linear dependence of the transition energies between Landau levels on $\sqrt{n}+\sqrt{n+1}$. The dashed line is a guide to the eyes.

Figure 3

The pseudocolor photograph of the relative reflectivity $R(B)/R(0)$ as functions of wave number and $\sqrt{B}$. The dashed lines are linear fittings of the peak energies dependent on $\sqrt{B}$.

Figure 4

Two proposed scenarios. The left panel (a) shows the splitting of Landau levels simply caused by the Zeeman effect. The strong spin-orbit coupling could lead to a mixing of spin-up and spin-down components. So the split $+$ (solid lines) and—(dashed lines) levels do not have pure spin-up and spin-down components. This would allow inter-Landau level transitions to occur with opposite signs, however, weak in intensity. The purple dashed line is the Fermi energy $E_F$. A Zeeman field without orbital effect will transform 3D Dirac node into line nodes in this case [17]. The right panel (b) represents the Landau levels of a Weyl semimetal induced by the magnetic field. The crossing points of $n=0$ Landau levels with the horizontal axis are the would-be Weyl points, if the orbital effect of the magnetic field is ignored. The solid lines and dashed lines represent the two sets of Landau levels from the two Weyl nodes with opposite chirality. Transitions between Landau levels of opposite chirality will have weaker intensity. In both panels, the red solid arrows represent transitions between Landau levels of the same spin or chirality, whereas the green dashed arrows indicate different spin or chirality.

Figure 5

The magnetic field dependent energy difference of $E_3-E_1$ and $E_4-E_2$. They represent the Landau level splittings for the conduction and valence bands, respectively.