Physical properties of RhGe and CoGe single crystals synthesized under high pressure

Chiral topological semimetals hosting multifold fermions and exotic surface states represent a frontier in topological materials research. Among them, noncentrosymmetric cubic B20 compounds-notably transition-metal silicides and germanides-offer a unique platform for realizing symmetry-protected topological phases and unconventional optoelectronic responses. Here, we report the physical properties of RhGe and CoGe single crystals with B20 structure in detail. Transport measurements reveal metallic behavior with characteristic Fermi-liquid scaling at low temperatures, while magnetization results confirm paramagnetism in both compounds. In addition, both of materials exhibit low carrier concentrations with small electronic specific heat coefficient, indicating their semimetal feature with weak electronic correlations. Such high-quality CoGe and RhGe single crystals provide a material platform to explore the evolution of multifold fermions and the instability of helicoid-arc surface states with spin-orbit coupling and surface environment in B20 material systems.

💡 Research Summary

The authors report a comprehensive study of single‑crystal RhGe and CoGe, both crystallizing in the non‑centrosymmetric cubic B20 structure (space group P2₁3). The crystals were grown under high pressure (5 GPa) and high temperature (RhGe at 1250 °C, CoGe at 1100 °C) using a cubic‑anvil apparatus with hBN capsules to avoid reactions with the flux. Powder X‑ray diffraction together with Rietveld refinement confirmed phase‑pure B20 structures, yielding lattice parameters a = 0.4859 nm for RhGe and a = 0.4640 nm for CoGe. Single‑crystal Laue patterns showed sharp cubic symmetry, indicating high crystal quality. Energy‑dispersive X‑ray spectroscopy revealed near‑stoichiometric RhGe (Rh:Ge ≈ 1.08:1) and a slight Co excess in CoGe (Co:Ge ≈ 1.25:1), suggesting the presence of Co‑related defects.

Electrical resistivity measurements displayed metallic behavior for both compounds. In the low‑temperature range (20–70 K) the resistivity follows ρ(T)=ρ₀+ATⁿ with n≈2, characteristic of a Fermi‑liquid. RhGe exhibits a high residual‑resistivity ratio (RRR≈27) and a low residual resistivity (≈70 µΩ cm at 70 K), whereas CoGe shows a much lower RRR≈2 and a modest upturn in resistivity below ~25 K. The upturn in CoGe follows a σ∝T¹ᐟ² dependence, indicative of electron‑electron interaction in a disordered system, likely linked to the excess Co defects.

Magnetization data confirm that both materials are Pauli paramagnets. RhGe shows a temperature‑independent susceptibility, while CoGe displays a weak Curie‑Weiss upturn below 50 K, corresponding to a tiny concentration (<2 %) of magnetic impurities, plausibly the excess Co atoms. No superconducting transition is observed down to 1.8 K in either compound, consistent with the absence of a specific‑heat anomaly.

Magnetoresistance (MR) measurements reveal striking differences. RhGe shows a large positive MR (~600 % at 2 K, 9 T) that decays rapidly with temperature and follows MR∝H¹·⁷⁵, suggesting multiband transport with both electron and hole contributions. CoGe, in contrast, exhibits a weak positive MR (<3 % over the entire temperature and field range), consistent with previous polycrystalline reports. Hall effect measurements indicate dominant electron carriers for both compounds. At 2 K the apparent carrier densities are n≈4.5×10²⁰ cm⁻³ (RhGe) and n≈3.5×10²⁰ cm⁻³ (CoGe). The carrier mobility of RhGe is exceptionally high (μ≈2366 cm² V⁻¹ s⁻¹ at 2 K) but drops sharply with increasing temperature, whereas CoGe reaches a modest peak μ≈370 cm² V⁻¹ s⁻¹ near 25 K and then decreases slowly.

Specific‑heat measurements from 2 K to 300 K show that both compounds approach the Dulong‑Petit limit at high temperature. Low‑temperature data fit Cₚ/T=γ+βT², yielding electronic specific‑heat coefficients γ=0.40 mJ mol⁻¹ K⁻² (RhGe) and γ=0.24 mJ mol⁻¹ K⁻² (CoGe). These values are comparable to those of nonmagnetic B20 semimetals such as CoSi and are an order of magnitude smaller than those of magnetic B20 compounds (e.g., MnGe, FeGe), indicating weak electron correlations. The Debye temperatures derived from β are Θ_D≈357 K (RhGe) and Θ_D≈403 K (CoGe), the latter being higher due to the lighter Co atom.

Overall, the study establishes RhGe and CoGe as high‑quality, nonmagnetic B20 semimetals with low carrier concentrations, weak electronic correlations, and distinct transport signatures. RhGe’s high mobility and large MR point to a multiband electronic structure with strong spin‑orbit coupling effects, while CoGe’s modest mobility and disorder‑induced electron‑electron interaction reflect its off‑stoichiometry. These properties make the crystals excellent platforms for probing symmetry‑protected multifold fermions, helicoid‑arc surface states, and their evolution under spin‑orbit coupling or surface modifications, thereby advancing the experimental exploration of topological phenomena in chiral B20 materials.