We combine transport, magnetization, and torque magnetometry measurements to investigate the electronic structure of ZrTe5, a system that is thought to be near a topological phase transition. At fields beyond the quantum limit, we observe a magnetization reversal from paramagnetic to diamagnetic response, which is characteristic of a Dirac semimetal. However, on increasing temperature across a corresponding transport anomaly, all signatures of this Dirac-like nature are completely suppressed, providing the first thermodynamic evidence of a possible topological phase transition in this compound. ZrTe5 may thus provide a rare, experimentally accessible example in which such phase transitions can be studied directly.

Although Weyl fermions have proven elusive in high-energy physics, their existence as emergent quasiparticles has been predicted in certain crystalline solids in which either inversion or time-reversal symmetry is broken. Recently they have been observed in transition metal monopnictides (TMMPs) such as TaAs, a class of noncentrosymmetric materials that heretofore received only limited attention. The question that arises now is whether these materials will exhibit novel, enhanced, or technologically applicable electronic properties. The TMMPs are polar metals, a rare subset of inversion-breaking crystals that would allow spontaneous polarization, were it not screened by conduction electrons. Despite the absence of spontaneous polarization, polar metals can exhibit other signatures of inversion-symmetry breaking, most notably second-order nonlinear optical polarizability, χ (2) , leading to phenomena such as optical rectification and second-harmonic generation (SHG). Here we report measurements of SHG that reveal a giant, anisotropic χ (2) in the TMMPs TaAs, TaP and NbAs. With the fundamental and second-harmonic fields oriented parallel to the polar axis, the value of χ (2) is larger by almost one order of magnitude than its value in the archetypal electro-optic materials GaAs and ZnTe, and in fact larger than reported in any crystal to date.

The elastic modulus c44 of a single crystal of the Weyl semimetal TaAs was investigated by measuring relative changes in the sound velocity under application of a magnetic field up to 10 T. Using an ultrasonic pulsed-echo technique, we studied the shear response of the crystal when the angle between the sound wave propagation and the magnetic field is changed. We observe a broken tetragonal symmetry at fields above 6 T, an anisotropy that is likely related to a longitudinal negative magnetoresistance and therefore might provide evidence of the chiral anomaly, one of the main topological signatures of this class of materials. We also observe quantum oscillations in the sound velocity whose frequencies vary with magnetic field orientation. A fan diagram of Landau level indices reveals topological and trivial Berry phases, depending on the field orientation, indicating a sensitivity to different Fermi surface pockets that do or do not enclose Weyl nodes, respectively.

Kondo insulators have recently aroused great interest because they are promising materials that host a topological insulator state caused by the strong electron interactions. Moreover, recent observations of the quantum oscillations in the insulating state of Kondo insulators have come as a great surprise. Here, to investigate the surface electronic state of a prototype Kondo insulator YbB12, we measured the transport properties of single crystals and microstructures. In all samples, the temperature dependence of the electrical resistivity is insulating at high temperatures and the resistivity exhibits a plateau at low temperatures. The magnitude of the plateau value decreases with reducing sample thickness, which is quantitatively consistent with the surface electronic conduction in the bulk insulating YbB12. Moreover, the magnetoresistance of the microstructures exhibits a weak-antilocalization effect at low field. These results are consistent with the presence of a topologically protected surface state, suggesting that YbB12 is a candidate material for a topological Kondo insulator. The high field resistivity measurements up to µ0H = 50 T of the microstructures provide supporting evidence that the quantum oscillations of the resistivity in YbB12 occurs in the insulating bulk.

The second-order conductivity of a material, σ(2), relating current to the square of electric field, is nonzero only when inversion symmetry is broken, unlike the conventional linear conductivity. Second-order nonlinear optical responses are thus powerful tools in basic research as probes of symmetry breaking; they are also central to optical technology as the basis for generating photocurrents and frequency doubling. The recent surge of interest in Weyl semimetals with acentric crystal structures has led to the discovery of a host of σ(2)-related phenomena in this class of materials, such as polarization-selective conversion of light to dc current (photogalvanic effects) and the observation of giant second-harmonic generation (SHG) efficiency in TaAs at photon energy 1.5 eV. Here, we present measurements of the SHG spectrum of TaAs, revealing that the response at 1.5 eV corresponds to the high-energy tail of a resonance at 0.7 eV, at which point the second harmonic conductivity is approximately 200 times larger than seen in the standard candle nonlinear crystal, GaAs. This remarkably large SHG response provokes the question of ultimate limits on σ(2), which we address by a new theorem relating frequency-integrated nonlinear response functions to the third cumulant (or "skewness") of the polarization distribution function in the ground state.