Room temperature Planar Hall effect in nanostructures of trigonal-PtBi2

Abstract

Trigonal-PtBi2 has recently garnered significant interest as it exhibits unique superconducting topological surface states due to electron pairing on Fermi arcs connecting bulk Weyl nodes. Furthermore, topological nodal lines have been predicted in trigonal-PtBi2, and their signature was measured in magnetotransport as a dissipationless, i.e. odd under a magnetic field reversal, anomalous planar Hall effect. Understanding the topological superconducting surface state in trigonal-PtBi2 requires unravelling the intrinsic geometric properties of the normal state electronic wavefunctions and further studies of their hallmarks in charge transport characteristics are needed. In this work, we reveal the presence of a strong dissipative, i.e. even under a magnetic field reversal, planar Hall effect in PtBi2 at low magnetic fields and up to room temperature. This robust response can be attributed to the presence of Weyl nodes close to the Fermi energy. While this effect generally follows the theoretical prediction for a planar Hall effect in a Weyl semimetal, we show that it deviates from theoretical expectations at both low fields and high temperatures. We also discuss the origin of the PHE in our material, and the contributions of both the topological features in PtBi2 and its possible trivial origin. Our results strengthen the topological nature of PtBi2 and the strong influence of quantum geometric effects on the electronic transport properties of the low energy normal state.

Figures (6)

• Figure 1: a,b: Brillouin zone showing the 12 symmetry-related Weyl nodes in band 48 (see Veyrat2024 closest to the Fermi level, with colour-encoded chirality. c: Band structure along the $\Gamma M$ line (left panel) and from $\Gamma$ to the Brillouin zone boundary through the blue Weyl node closest to the $\Gamma M$ line.
• Figure 2: a,b: Typical angular dependence of the conventional planar Hall effect, in Cartesian (a) and polar (b) coordinates. Both the longitudinal (anisotropic magnetoresistance, $R_{xx}$, blue) and transverse (planar Hall effect, $R_{yx}$, red) resistances exhibit a $\pi$-periodic angular dependence, with a $\pi/4$-offset between them. The origin of the oscillation is set by the direction of the electric field (current).
• Figure 3: a,b,c: Optical pictures and sample configurations for D4 (41 nm), D1 (70 nm) and D2 (126 nm). The measurements related to each sample is shown below it. d-i: In-plane magnetic field ($B_y-B_z$) mappings of the longitudinal ($R_{xx}$, d,e,f) and transverse ($R_{yx}$, g,h,i) resistances. All mappings were measured simultaneously by sweeping $B_{||,1}$) at fixed $B_{||,2}$, and increasing $B_{||,2}$ in steps of 50 mT. All mappings show the expected four-fold symmetry expected for the PHE, with sample-orientation-dependent phase and $\pi/4$ shift between longitudinal and transverse configurations. j-l: Angular dependence of $R_{xx}$ (top panels) and $R_{yx}$ (bottom panels) extracted from the mappings d-i, for a field $B = 1.5$ T corresponding to the black circles. The data is well fitted by the PHE model (in red, see \ref{['eq: PHE_fit']}). The phase of the oscillations in each sample can be correlated to the presumed current orientation in the sample.
• Figure 4: a,c: Angular dependence at 14 T and 5 K (a) or 300 K (c) of the longitudinal ($R_{xx}$, top panels) and transverse ($R_{yx}$, bottom panels) resistances for sample D1, in Cartesian coordinates. Fits to the PHE model (\ref{['eq: PHE_fit']} are shown in red (a) and blue (c). b,d: Same data as in a,c, in polar coordinates. The dashed-line represents the orientation of the current estimated from the data.
• Figure 5: a,b: Angular dependence of the longitudinal ($R_{xx}$, top panels) and transverse ($R_{yx}$, bottom panels) resistances of samples D1 at 5K and multiple fields from 1T to 14T (a) and at 14T and multiple temperatures from 5K to 300K (b). The plots are shifted vertically for visibility, to share a minimum at 0 $\Omega$. c,d: Field (c) and temperature (d) dependence of the PHE amplitude $\Delta \rho$ extracted from fits of the data in (a,b) with \ref{['eq: PHE_fit']} for samples D1 (blue diamonds and dashed-red line, respectively), and for sample D2 (green diamonds and dashed-magenta line, respectively, see SM). The field dependence of $\Delta \rho$ is well fitted with a sub-quadratic power law for both samples. The temperature dependence of $\Delta \rho$ cannot be fitted with an exponential decay law, and is fitted with a power law.