Anomalous Nernst effect and field-induced Lifshitz transition in the Weyl semimetals TaP and TaAs

The discovery of Weyl fermions in transition-metal monoarsenides/phosphides without inversion symmetry represents an exceptional breakthrough in modern condensed matter physics. However, exploring the inherent nature of these quasiparticles is experimentally elusive because most of the experimental probes rely on analyzing Fermi arc topology or controversial signatures such as the appearance of the chiral anomaly and the giant magnetoresistance. Here, we show that the prototypical type-I Weyl semimetals TaP and TaAs possess a giant anomalous Nernst signal with a characteristic saturation plateau beyond a critical field which can be understood as a direct consequence of the finite Berry curvature originating from the Weyl points. Our results thus promote the Nernst coefficient as an ideal bulk probe for detecting and exploring the fingerprints of emergent Weyl physics.

Figure 1

(a) Schematic picture of the Berry curvature originated from right-handed (blue) and left-handed (red) Weyl points. The Weyl points always appear as a pair with opposite chirality separated by $\mathrm{\Delta }k$ in the $k$ space and they act as a source or sink of Berry curvature (outward or inward arrows). (b) Schematic picture of the folding between the energy-dependent Fermi distribution function (blue) and entropy density (red) with the diverging Berry curvature (red shaded area) near the Weyl point. The gray shaded area marks the thermal energy $k_{B}T$. The ANE is particularly large and sensitive to a variation of the chemical potential if the gray and red shaded areas overlap, i.e., $\tilde{\mu }\approx k_{B}T$, which is highlighted in the cases (ii) and (iii).

Figure 2

Nernst effect data for (a), (b) TaP and (c), (d) TaAs. (a) and (c) show the Nernst coefficient normalized to the temperature $S_{xy}/T$ as a function of $B$. In both of the compounds an anomalous contribution appears as a tendency to saturation. (b) and (d) show the Nernst coefficient $S_{xy}$ as a function of the temperature $T$. In both compounds we find a crossover between two different temperature regimes which appears as a change of slope with a broadened maximum. The red dotted lines in (a) and (c) represent guides for the eyes. The black dashed lines in (a) and (c) show the results of the phenomenological fit, which well reproduces the experimental data for all the $T$. Shubnikov–de Haas oscillations appear in the $S_{xy}/T$ vs $B$ curves of TaP at low temperature and they are visible up to 60 K [29].

Figure 3

Temperature dependence of the amplitude of the anomalous part of the Nernst coefficient normalized to the temperature $S_0^A/T$ for TaP (red) and TaAs (black). A crossover between two different regimes is clearly observable in the abrupt change of $S_0^A/T$ that occurs in TaP and TaAs around 150 and 100 K, respectively. Inset: Temperature dependence of $S_0^A$ for TaP (red) and TaAs (black) without temperature normalization. A broadened maximum exists at around $T=80$ K and $T=50$ K in TaP and TaAs, respectively.

Figure 4

Schematic behavior of the chemical potential $\mu$ in a Dirac/Weyl semimetal. (a) In zero field the energy dispersion shows only one single Dirac node which is placed in the $\mathrm{\Gamma }$ point. (b) Application of magnetic field $B$ leads to the appearance of two nodes whose $k$-space separation is proportional to $B$. A shift of $\mu$, indicated by the dotted lines, is induced to conserve the particle number under variation of $B$. The downshift of $\mu$ is responsible for the observed strong variation of the Nernst coefficient for $B<B_s$, where $B_s$ is the saturation field of the Nernst coefficient. (c) For $B>B_s$ a Lifshitz transition occurs and two separated Fermi surfaces appear. (d) By further rising $B>B_s$ the Weyl cone distance increases without changing the $k$-space volume. Hence, the conservation of the particle number (area between the dashed lines) is already achieved if $\mu$ remains almost fixed. As a consequence, the anomalous Nernst coefficient $S_{xy}^A$ will also not change, as highlighted in (e).