Bipolar Conduction as the Possible Origin of the Electronic Transition in Pentatellurides: Metallic vs Semiconducting Behavior

The pentatellurides ${\mathrm{ZrTe}}_5$ and ${\mathrm{HfTe}}_5$ are layered compounds with one-dimensional transition-metal chains that show a not-yet-understood temperature-dependent transition in transport properties as well as recently discovered properties suggesting topological semimetallic behavior. Here, we report magnetotransport properties for two kinds of ${\mathrm{ZrTe}}_5$ single crystals grown with the chemical vapor transport (CVT) and the flux method (Flux), respectively. They show distinct transport properties at zero field: The CVT crystal displays a metallic behavior with a pronounced resistance peak and a sudden sign reversal in thermopower at approximately 130 K, consistent with previous observations of the electronic transition; in striking contrast, the Flux crystal exhibits a semiconducting-like behavior at low temperatures and a positive thermopower over the whole temperature range. For both samples, strong effects on the transport properties are observed when the magnetic field is applied along the orthorhombic $b$ and $c$ axes, i.e., perpendicular to the chain direction. Refinements on the single-crystal x-ray diffraction and the measurements of energy dispersive spectroscopy reveal the presence of noticeable Te vacancies in the CVT samples, while the Flux samples are close to the stoichiometry. Analyses on the magnetotransport properties confirm that the carrier densities of the CVT sample are about two orders higher than those of the Flux sample. Our results thus indicate that the widely observed anomalous transport behaviors in pentatellurides actually take place in the Te-deficient samples. For the stoichiometric pentatellurides, our electronic structure calculations show narrow-gap semiconducting behavior, with different transport anisotropies for holes and electrons. For the degenerately doped $n$-type samples, our transport calculations can result in a resistivity peak and crossover in thermopower from negative to positive at temperatures close to those observed experimentally due to a combination of bipolar effects and different anisotropies of electrons and holes. Our present work resolves the long-standing puzzle regarding the anomalous transport behaviors of pentatellurides, as well as the electronic structure in favor of a semiconducting state.

Popular Summary

The transition metal pentatelluride ${\mathrm{ZrTe}}_5$ exhibits highly unusual changes in electrical behavior. There is a strong resistivity peak as a function of temperature, along with a very large thermopower that changes sign when the resistivity peaks. Large thermopower means that a large electrical voltage can be generated when a temperature difference is imposed across the material. This potentially provides a new and, until now, never-understood thermoelectric mechanism for cooling electronics and other applications. Researchers also debate whether ${\mathrm{ZrTe}}_5$ is a topological insulator (a material that conducts electricity only on its surface) or a Dirac semimetal (where electrons behave as if they have no mass). We exploit new synthesis methods to study the charge transport in ${\mathrm{ZrTe}}_5$ of much more perfect samples than previously attainable. Our analysis not only explains the electrical behavior but also reveals that ${\mathrm{ZrTe}}_5$ is actually a semiconductor.

We grew ${\mathrm{ZrTe}}_5$ crystals using the two main growth techniques: the chemical vapor transport method and the flux method. Crystals grown via chemical vapor transport showed the expected electrical behavior. However, crystals grown with the flux method acted like semiconductors, and the thermopower remained positive. We traced this difference to the onset of bipolar conduction, which arises from a simultaneous thermal excitation of electrons and holes in a narrow-gap semiconductor, in the presence of telluride vacancies introduced by the chemical vapor transport method.

This semiconducting state and a highly unusual electronic structure, where electrons and holes move most easily in different directions, explain the long-standing puzzle of the resistivity peak and sign change of the thermopower.

Figure 1

(a) Crystal structure of ${\mathrm{ZrTe}}_5$. (b) ${\mathrm{ZrTe}}_5$ crystals grown with the CVT and Flux methods. (c) A schematic drawing of the sample stage for thermopower measurements. (d) The thermopower stage with a ${\mathrm{ZrTe}}_5$ crystal on it. This stage can be inserted into the piston-cylinder cell for high-pressure thermopower measurements up to 2.5 GPa.

Figure 2

Temperature dependence of (a) resistivity $\rho (T)$ and (b) thermopower $S(T)$ in zero magnetic field for the ${\mathrm{ZrTe}}_5$ crystals grown with the CVT and Flux methods. The vertical dashed line marks the characteristic temperature $T_p$ of CVT sample.

Figure 3

Temperature dependence of resistivity $\rho (T)$ and thermopower $S(T)$ for the CVT sample with magnetic field applied along the three principal axes.

Figure 4

Temperature dependence of resistivity $\rho (T)$ and thermopower $S(T)$ for the Flux sample with magnetic field applied along the three principal axes.

Figure 5

Field dependences of (a) longitudinal magnetoresistance $\mathrm{MR}=[\rho (H)/\rho (0\mathrm{T})-1]\times 100\%$ and (b) Hall resistivity ${\rho }_{xy}$ for the CVT sample at various temperatures. Temperature dependence of the (c) carrier density $n$ and (d) mobility $\mu$ are extracted from the fitting to the Hall conductivity ${\sigma }_{xy}$. The resistivity data measured on the same sample are also shown in panel (c).

Figure 6

Field dependences of (a) longitudinal magnetoresistance $\mathrm{MR}=[\rho (H)/\rho (0\mathrm{T})-1]\times 100\%$ and (b) Hall resistivity ${\rho }_{xy}$ for the Flux sample at various temperatures. Temperature dependence of the (c) carrier density $n$ and (d) mobility $\mu$ are extracted from the fitting to the Hall conductivity ${\sigma }_{xy}$. The resistivity data are also shown in panel (c).

Figure 7

(a) Total electronic density of states (DOS) of ${\mathrm{ZrTe}}_5$ on a per-formula unit basis. Note the asymmetry between electrons and holes. (b) Band energy isosurfaces 0.05 eV from the band edges for ${\mathrm{ZrTe}}_5$. The $\mathrm{\Gamma }$ point is at the center of the depicted zones, while the $k_x$ direction is along the horizontal axis for the left panel, while the right panel shows a tilted view. Hole surfaces below the valence band maximum are in blue, while electron surfaces above the conduction band minimum are in red. Note the very different structure of the hole and electron sheets. (c) Band structure of ${\mathrm{ZrTe}}_5$; note the semiconducting character. (d) Brillouin zone path for the band structure.

Figure 8

Transport function $\sigma /\tau$ along the three crystallographic directions for ${\mathrm{ZrTe}}_5$.

Figure 9

(a) The $a$-axis $S(T)$ for various doping levels as obtained in the constant-scattering-time approximation for ${\mathrm{ZrTe}}_5$. (b) The $a$-axis resistivity transport function, $\rho$ (see text) for ${\mathrm{ZrTe}}_5$. (c) The $a$-axis resistivity transport function on a log scale comparing $n$-type doped and undoped material.