Helicity-protected ultrahigh mobility Weyl fermions in NbP

Noncentrosymmetric transition-metal monopnictides, including TaAs, TaP, NbAs, and NbP, are emergent topological Weyl semimetals (WSMs) hosting exotic relativistic Weyl fermions. In this Rapid Communication, we elucidate the physical origin of the unprecedented charge carrier mobility of NbP, which can reach $1\times {10}^7{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ at 1.5 K. Angle- and temperature-dependent quantum oscillations, supported by density function theory calculations, reveal that NbP has the coexistence of $p$- and $n$-type WSM pockets in the $k_z=1.16\pi /c$ plane (W1-WSM) and in the $k_z=0$ plane near the high symmetry points $\mathrm{\Sigma }$ (W2-WSM), respectively. Uniquely, each W2-WSM pocket forms a large dumbbell-shaped Fermi surface enclosing two neighboring Weyl nodes with the opposite chirality. The magnetotransport in NbP is dominated by these highly anisotropic W2-WSM pockets, in which Weyl fermions are well protected from defect backscattering by real spin conservation associated to the chiral nodes. However, with a minimal doping of $\sim 1\%$ Cr, the mobility of NbP is degraded by more than two orders of magnitude, due to the invalidity of helicity protection to magnetic impurities. Helicity protected Weyl fermion transport is also manifested in chiral anomaly induced negative magnetoresistance, controlled by the W1-WSM states. In the quantum regime below 10 K, the intervalley scattering time by impurities becomes a large constant, producing the sharp and nearly identical conductivity enhancement at low magnetic field.

Figure 1

(a) $T$-dependent $\rho$ curves at $B=0$, showing varying sample quality. (b) Ultrahigh carrier mobility of NbP, which is sensitive to magnetic impurities. Inset: $T$-dependent Hall resistivity from 300 to 1.5 K, showing a pronounced transition from $p$-type carriers at room temperature to the coexistence of electrons and holes below 200 K.

Figure 2

Angle-dependent SdH oscillations of NbP. (a) Extremely strong SdH oscillations in NbP, with amplitudes independent of RRR. Inset: Schematic of the angle rotation. (b) Four major oscillation peaks of $F_0=6.8$ T, $F_1=13.9$ T, $F_2=31.8$ T, and $F_3=64.4$ T with $B\parallel c$. (c) Schematic of FS cross sections for different pockets with $B\parallel c$. (d) SdH oscillation peaks with $\theta ={90}^{\circ }$. (e) The evolution of $F_0,F_1,F_2$, and $F_3$ as a function of $\theta$.

Figure 3

$T$-dependent SdH oscillations and Berry's phase. (a) FFT of $T$-dependent SdH oscillations of S2. (b) $T$-dependent SdH oscillations in the field range of 8–15 T. (c) The LK model fitting of the 10.9 and 13.4 T peaks. The latter is the superposition of $F_2$ and $F_3$. (d) Deviation of Berry's phase from $\pi$ due to nonideal relativistic fermions in the W2-WSM pockets.

Figure 4

Robust chiral anomaly induced NMR in NbP as a function of $T$, showing $T$-independent NMR below 10 K and strong $T$ dependence above 30 K.