Grigorii P. Mikitik

We propose a four-band model describing the electron energy spectra near the Weyl points in the topological semimetals of the TaAs family (TaAs, TaP, NbAs, NbP). This model takes into account the fact that these Weyl points result from the band-contact lines which would exist in the mirror-reflection planes of these materials if the spin-orbit interaction were absent in them. Within this model, we obtain conditions for the existence of the Weyl points, determine their positions in the Brillouin zone, and derive the explicit formula for dispersion of the bands along the straight line connecting the two close Weyl points with opposite topological charges. Using NbP as an example, the values of the parameters defining the model spectrum are found. The obtained results show that for the semimetals of the TaAs family, the charge-carriers spectrum in the vicinity of the two close Weyl points can be analyzed without complex band-structure calculations.

Using a distribution of the Meissner currents over the surface of an infinitely long superconducting slab with a rectangular cross section, the magnetic moment of the slab is calculated, taking into account corrections associated with a small but finite value of the London penetration depth λ . Since these corrections determine the shift of the resonant frequency in the tunnel-diode oscillator technique, formulas for determining λ within this technique are derived for the slab. These formulas are valid for any aspect ratio of its cross section, and they differ from those that are often used in analyzing experimental data. Specifically, it is shown that the sharp edges of the slab can cause a large frequency shift proportional to the change in the value of λ 2 / 3 . Although this result complicates the extraction of a temperature dependence of λ from the frequency shift, it also opens up additional possibilities for determining the London penetration depth. In particular, under certain conditions, it is possible not only to measure the changes in λ with temperature, but also to estimate its absolute value.

Using a known distribution of the Meissner currents over the surface of an infinitely long superconducting slab with a rectangular cross section, we find an applied magnetic field at which vortices begin to penetrate into the superconductor. This vortex-penetration field is determined by an interplay of the geometrical and Bean-Livingston barriers. The obtained results enable one to find the lower critical field and the London penetration depth from measurements of the magnetic induction on the surface of the superconducting slab, using, e.g., the micro-Hall probes. Published by the American Physical Society 2024

We develop a theory of the magnetostriction for metals with small charge-carrier pockets of their Fermi surfaces. As an example, we consider LuAs that has a cubic crystal structure. The theory quite well describes the known experimental data on the magnetostriction of this metal. The obtained results also clearly demonstrate that the dilatometry can be used for detecting tiny Fermi surface pockets that are not discerned by traditional methods based on investigations of the Shubnikov–de Haas and de Haas–van Alphen effects.

Thus far, a detection of the Dirac or Weyl fermions in topological semimetals remains often elusive, since in these materials conventional charge carriers exist as well. Here, measuring a field-induced length change of the prototype Weyl semimetal TaAs at low temperatures, we find that its c-axis magnetostriction amounts to relatively large values whereas the a-axis magnetostriction exhibits strong variations with changing the orientation of the applied magnetic field. It is discovered that at magnetic fields above the ultra-quantum limit, the magnetostriction of TaAs contains a linear-in-field term, which, as we show, is a hallmark of the Weyl fermions in a material. Developing a theory for the magnetostriction of noncentrosymmetric topological semimetals and applying it to TaAs, we additionally find several parameters characterizing the interaction between the relativistic fermions and elastic degrees of freedom in this semimetal. Our study shows how dilatometry can be used to unveil Weyl fermions in candidate topological semimetals.

We demonstrate a unique approach to test the signature of the nodal-line physics by thermodynamic methods. By measuring magnetic susceptibility in ZrSiS we found an intriguing temperature-driven crossover from dia- to paramagnetic behavior. We show that the anomalous behavior represents a real thermodynamic signature of the underlying nodal-line physics through the means of chemical pressure (isovalent substitution of Zr for Hf), quantum oscillations, and theoretical modeling. The anomalous part of the susceptibility is orbital by nature, and it arises due to the vicinity of the Fermi level to a degeneracy point created by the crossing of two nodal lines. Furthermore, an unexpected Lifshitz topological transition at the degeneracy point is revealed by tuning the Fermi level. The present findings in ZrSiS give an attractive starting point for various nodal-line physics-related phenomena to be tested by thermodynamic methods in other related materials.

We consider the semiclassical quantization condition for the energy of an electron in a magnetic field in the case when the electron orbit lies on a Fermi-surface pocket surrounding the Weyl point of a topological semimetal and analyze the constant γ appearing in this condition. It is shown that this constant has the universal value, γ = 0, independent on the tilt of the Weyl spectrum. Since the constant γ for an extremal cross section of the Fermi surface determines the phase of quantum oscillations, this result explains why measurements of the phase permit one to find Weyl points in crystals even though the extremal cross section of the pocket does not pass through this point, and the appropriate Berry phase of the orbit differs from π.