Signatures of possible surface states in TaAs

We study Shubnikov–de Haas oscillations in single crystals of TaAs and find a previously undetected two-dimensional quantum oscillation that does not belong to the bulk Fermi surface. We cannot find an impurity phase consistent with our observations, and extensive diffraction measurements have not shown the presence of known impurity phases. We conjecture that the frequency originates from surface states that are sensitive to surface disorder. One candidate is the interference of coherent quasiparticles traversing two distinct Fermi arcs on the [001] crystallographic surface. The frequency and effective mass quantitatively agree with predictions of density functional theory and previous angle-resolved photoemission spectroscopy measurements of the Fermi arcs.

Figure 1

The powder x-ray diffraction pattern from ground crystals of TaAs (blue) can be well fit by the calculated spectrum of TaAs (red). All observed peaks are accounted for, implying that additional phases are not present. Inset: The integrated intensity from 2500 Laue diffraction patterns taken over a $100\times 100\mu {\mathrm{m}}^2$ area of a TaAs Hall bar device. All the peaks can be well indexed by TaAs, and no indications of any impurity phases are present.

Figure 2

A quantum oscillatory frequency in high-mobility TaAs. (a) The longitudinal magnetoresistivity (top) and Hall resistivity (bottom) of a polished 33-$\mu \mathrm{m}$ Hall bar device at 2 and 10 K with field applied along the [001] direction, normal to the device plane. SdH oscillations from the bulk Fermi surface are easily distinguishable. (b) The subtracted resistivities from (a). In addition to the bulk SdH oscillations, a high-frequency oscillation can be observed to start around 8 T with a frequency of 285 T. (c) The resistivity as a function of temperature, showing metallic behavior and a residual resistivity ratio of 56. Inset: The tetragonal crystal structure of TaAs. Ta atoms are shown in red, and As atoms are in blue.

Figure 3

The two-dimensional nature of the high-frequency quantum oscillations. (a) The derivative of the Hall resistivity plotted as a function of inverse magnetic field at different field angles. As the field is rotated into the plane of the Hall bar, the additional oscillation increases in frequency and moves to higher field. (b) The angle dependence of the oscillatory frequency shows the $1/cos\left(\theta \right)$ dependence characteristic of a two-dimensional cyclotron orbit. Inset: The angle dependence of the low-frequency oscillations is in good agreement with what has been measured in bulk samples of TaAs [12].

Figure 4

Temperature and high field dependence. (a) Temperature dependence of the SdH oscillations with field along the [001] direction and a 10 K background subtraction. (b) The oscillatory amplitudes can be fit to the Lifshitz-Kosevich form to extract the cyclotron effective mass. The low-frequency bulk oscillations show an effective mass of $0.066m_e$, and the high-frequency 285-T oscillations show a much larger effective mass of $0.5m_e$. (c) The high-frequency SdH oscillations show an additional structure above 13 T. Beating of different frequencies, common in multiband systems, causes the oscillation amplitude to appear to decrease with increasing field. (d) A Fourier transform shows two frequencies emerging at 274 and 287 T, in close agreement with expectations of DFT (see Fig. 8).

Figure 5

The magnetic torque measured on a sample cut from the same crystal that was used in Fig. 3. There is no indication of the 285-T oscillation as field is rotated from the [001] axis to the [100] axis.

Figure 6

Surface contribution to the conductivity. (a) Longitudinal and (b) Hall resistivities show a nontrivial thickness dependence. Resistivities were calculated using bulk geometrical factors. For a purely bulk conductivity, this would cause the curves to collapse. In addition, the SdH oscillations in the transverse magnetoresistivity appear to show a phase inversion between the 14 $\mu \mathrm{m}$/43 $\mu \mathrm{m}$ devices and 130 $\mu \mathrm{m}$/272 $\mu \mathrm{m}$ devices. Insets: The thickness dependence can be well modeled with a parallel-channel conductance model incorporating both surface and bulk contributions into device resistance. This model captures the overall shape and ordering of the resistivity curves and the phase inversion of the SdH oscillations. Temperature-dependent resistivities for each device are shown in Ref. [20]. Note field is always applied perpendicular to the current, so that extrinsic effects like current jetting are negligible.

Figure 7

(a) The thickness dependence of the 285-T oscillation appears to be nonmonotonic in device thickness. This may be the result of damaging the surface and reducing surface carrier mobility with subsequent polishing steps. (b) The bulk oscillations start at approximately the same field regardless of device thickness, indicating that the bulk mobility does not change significantly.

Figure 8

Theoretical expectations of the quantum interference orbits. DFT calculation of the [001] Fermi surface of TaAs showing both trivial and Fermi arc surface states. The interference orbit between two Fermi arcs on the same surface is highlighted in orange. The area enclosed agrees closely with the SdH oscillation frequency observed in transport. The orbit near $\overline{X}$ is 7% larger than the equivalent orbit near $\overline{Y}$, in remarkable agreement with the frequency splitting we observe at high field [Fig. 4].