Pressure tuning the Fermi surface topology of the Weyl semimetal NbP

We report on the pressure evolution of the Fermi surface topology of the Weyl semimetal NbP, probed by Shubnikov–de Haas oscillations in the magnetoresistance combined with ab initio calculations of the band structure. Although we observe a drastic effect on the amplitudes of the quantum oscillations, the frequencies only exhibit a weak pressure dependence up to 2.8 GPa. The pressure-induced variations in the oscillation frequencies are consistent with our band-structure calculations. Furthermore, we can relate the changes in the amplitudes to small modifications in the shape of the Fermi surface. Our findings show evidence of the stability of the electronic band structure of NbP and demonstrate the power of combining quantum-oscillation studies and band-structure calculations to investigate pressure effects on the Fermi surface topology in Weyl semimetals.

Figure 1

Temperature dependence of the normalized electrical resistivity $\rho /{\rho }_{295\mathrm{K}}$ in zero magnetic field.

Figure 2

(a) and (b) Magnetoresistance at 2 K for selected pressures in the two configurations $B\parallel c$ and $B\parallel a$, respectively.

Figure 3

(a) ${\mathrm{MR}}_{\mathrm{symm}}$ for $S_{B\parallel a}$ with $B\parallel I$. The inset shows the pressure effects on ${\mathrm{MR}}_{\mathrm{symm}}$ at 9 T for $S_{B\parallel a}$. (b) Antisymmetrized MR of sample $S_{B\parallel c}$, which is a measure of the Hall coefficient $R_H$ (see text for details).

Figure 4

(a) Shubnikov–de Haas oscillations as a function of the inverse magnetic field taken at different pressures for $S_{B\parallel c}$. The oscillatory part was extracted by the subtraction of a third-order polynomial background. (b) and (c) Temperature dependence of the fast Fourier transform of the SdH oscillations under pressures of 0.02 and 2.47 GPa for $B\parallel c$.

Figure 5

(a) Oscillatory part of MR as a function of the inverse magnetic field taken at different pressures for the sample $S_{B\parallel a}$. (b) and (c) Fast Fourier transform of the SdH oscillations as a function of temperature under pressures of 0.02 and 2.47 GPa for $B\parallel a$.

Figure 6

(a) and (b) Pressure dependence of the experimental SdH (solid symbols) and calculated quantum-oscillation frequencies (dashed lines) for $B\parallel c$ and $B\parallel a$, respectively. The size of the bullets gives an estimate of the error in the determination of the oscillation frequencies as shown in Figs. 4 and 5. (c) and (d) Illustration of the calculated Fermi surface pockets [left (blue): electron; right (violet): hole pockets]. The extremal orbits identified in our experimental data, $\alpha , {\alpha }_2, {\alpha }_2^{\prime }, \beta , \gamma , E{1}^{\prime }, H{1}^{\prime }, H2, H{2}^{\prime }$, and $H{2}^{\prime \prime }$ are indicated. The gray dashed lines mark those extremal orbits that are not confirmed experimentally. Band structures along the line connecting a pair of Weyl points for (e) W2 and (f) W1 at different pressures. The dashed line marks the Fermi energy set to zero.