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

This study reports the detailed physical properties of high-quality RhGe and CoGe B20 single crystals, revealing their metallic, paramagnetic, and weakly correlated semimetal nature to establish a platform for investigating multifold fermions and helicoid-arc surface states in chiral topological semimetals.

The Gist

Imagine the world of materials science as a vast library of building blocks. Most blocks are symmetrical, like a perfect cube or a sphere. But in this paper, the researchers are looking at a very special, twisted kind of block called the B20 structure. Think of these blocks not as perfect cubes, but as screw threads or spirals. Because they are twisted (chiral), they create a unique playground for electrons, the tiny particles that carry electricity.

The scientists in this study focused on two specific "screw-thread" materials: RhGe (made of Rhodium and Germanium) and CoGe (made of Cobalt and Germanium). These materials are the "cousins" of other famous materials that have been studied before, but they are harder to make.

Here is what the researchers discovered, broken down into simple concepts:

1. The Challenge: Growing the Crystals

Making these materials is like trying to bake a cake that requires extreme pressure and heat to set properly. You can't just mix the ingredients in a bowl; you have to crush them together at 5 times the pressure of the deepest ocean and heat them to over 1,000°C.

• The Result: The team successfully grew high-quality, single crystals of RhGe and CoGe. Think of these as perfect, flawless gemstones rather than a pile of crushed dust.

2. How They Conduct Electricity (The Traffic Flow)

The researchers tested how electricity moves through these crystals.

• The Behavior: Both materials act like metals. Electricity flows through them easily, much like cars on a highway.
• The "Traffic Jam" Test: At very low temperatures, the electrons in RhGe behave like a calm, organized crowd (a "Fermi liquid"), moving smoothly without bumping into each other too much. CoGe is similar but has a slightly rougher road, causing a tiny bit more resistance at very low temperatures.
• The Surprise: In the past, some people thought RhGe might become a superconductor (a material that conducts electricity with zero resistance). However, these high-quality crystals showed no superconductivity. It turns out the "superconducting" behavior seen in older, lower-quality samples might have been a fluke caused by impurities or defects, like a shortcut in a road that doesn't actually exist in the real highway.

3. Magnetism (The Compass Test)

The team checked if these materials acted like magnets.

• The Finding: Neither material is a permanent magnet. They don't stick to your fridge. Instead, they are paramagnetic.
• The Analogy: Imagine a crowd of people holding compasses. In a magnet, everyone points north. In these materials, the compasses are mostly pointing in random directions, but if you bring a strong magnet nearby, they all briefly turn toward it. They are "magnetically polite" but not "magnetically obsessed."

4. The "Ghost" Particles (Topological Secrets)

This is the most exciting part for physicists, though it's abstract.

• The Concept: Inside these twisted crystals, the electrons behave like massless particles (particles with no weight) that move in very specific, protected paths.
• The Surface: The surface of these crystals is predicted to have "highways" for electrons that are different from the inside. The researchers suggest that because RhGe and CoGe are chemically similar to other famous materials (like CoSi), they likely host these exotic "topological" states.
• The Potential: Because these crystals are so pure, they provide a perfect "clean room" for scientists to study these exotic electron behaviors without the noise of impurities getting in the way.

5. Why the Difference Between RhGe and CoGe?

Even though they are cousins, they have different personalities:

• RhGe: It has very high "mobility," meaning electrons zip through it very fast. It has a strong response to magnetic fields (Magnetoresistance).
• CoGe: It has more "traffic" (more electrons) but they move slower. It also has a tiny bit of extra Cobalt mixed in, which acts like a small speed bump, causing a slight increase in resistance at very low temperatures.

The Bottom Line

The paper is essentially a quality control report on two new, high-grade materials. The researchers say:

1. We made perfect crystals of RhGe and CoGe.
2. They are metals that conduct electricity well.
3. They are not superconductors (at least not in these pure forms).
4. They are not magnets.
5. They are perfect candidates for future experiments to study the weird, twisted world of "topological" physics, where electrons act like ghosts moving through a maze.

The study doesn't promise a new gadget or a medical cure today; instead, it provides the raw, high-quality ingredients that other scientists will need to build those future discoveries.

Technical Summary

Technical Summary: Physical Properties of RhGe and CoGe Single Crystals Synthesized under High Pressure

Problem Statement
Chiral topological semimetals, particularly noncentrosymmetric cubic B20 compounds, represent a frontier in topological materials research due to their potential to host multifold fermions and exotic surface states. While transition-metal silicides like CoSi and RhSi have been extensively studied, their germanide counterparts, RhGe and CoGe, remain underexplored. Previous investigations into these materials have been limited by the significant challenges associated with synthesizing high-quality single crystals, which require high-pressure and high-temperature conditions. Furthermore, existing literature presents conflicting findings: polycrystalline RhGe was reported to exhibit weak itinerant ferromagnetism and superconductivity, whereas CoGe was described as a Pauli paramagnet. The lack of reliable single-crystal data has hindered a definitive understanding of their intrinsic electronic and magnetic properties.

Methodology
To address the synthesis challenges, the authors employed a high-pressure and high-temperature (HPHT) method using a cubic anvil apparatus. High-purity elemental precursors were homogenized with specific stoichiometric ratios (Rh:Ge = 1:1.2 with excess Ge as a flux; Co:Ge = 1:1) and sealed in hexagonal boron nitride (hBN) capsules to prevent reaction with the container. The samples were compressed to 5 GPa and subjected to specific thermal cycles (ramping to 1250 °C for RhGe and 1100 °C for CoGe, followed by slow cooling and quenching).

The resulting single crystals were characterized using:

• Structural Analysis: Powder X-ray diffraction (PXRD) with Rietveld refinement, Laue backscattering diffraction for orientation, and scanning electron microscopy (SEM) with energy-dispersive X-ray (EDX) spectroscopy for chemical composition.
• Transport Measurements: Electrical resistivity ($\rho_{xx}$) and Hall resistivity ($\rho_{yx}$) were measured using a superconducting magnetic system up to 9 T.
• Magnetic and Thermodynamic Measurements: Magnetic susceptibility ($\chi$) was measured via SQUID magnetometry, and specific heat ($C_p$) was measured using a physical property measurement system.

Key Results

1. Crystal Structure and Quality: Both RhGe and CoGe crystallize in the noncentrosymmetric cubic B20 structure (space group $P2_13$). Rietveld refinement confirmed phase purity, and Laue diffraction patterns exhibited sharp spots, indicating high structural integrity. EDX analysis revealed RhGe to be nearly stoichiometric, while CoGe contained a slight excess of Cobalt (Co:Ge $\approx$ 1.25:1), suggesting the presence of Co defects.
2. Transport Properties:
   • Metallic Behavior: Both compounds exhibit metallic behavior. RhGe shows a residual resistivity ratio (RRR) of ~27, while CoGe has an RRR of ~2.
   • Fermi-Liquid Behavior: At low temperatures, RhGe follows a $T^{2.05}$ dependence in resistivity, and CoGe follows a $T^{2.06}$ dependence between 40–70 K, indicating Fermi-liquid behavior.
   • Low-Temperature Anomalies: CoGe displays a subtle resistivity upturn below 25 K, attributed to electron-electron interactions (EEI) in the presence of disorder (likely the excess Co defects), rather than weak localization or the Kondo effect, as confirmed by positive magnetoresistance.
   • Carrier Concentration and Mobility: Both materials are electron-type semimetals with low carrier concentrations ($n_a \approx 4.5 \times 10^{20}$ cm$^{-3}$ for RhGe and $3.5 \times 10^{20}$ cm$^{-3}$ for CoGe at 2 K). RhGe exhibits significantly higher mobility ($\mu \approx 2366$ cm$^2$ V$^{-1}$ s$^{-1}$ at 2 K) compared to CoGe ($\mu \approx 359$ cm$^2$ V$^{-1}$ s$^{-1}$).
   • Magnetoresistance (MR): RhGe shows a large positive MR (~600% at 2 K) that diminishes with temperature, fitting a power law $MR \propto H^{1.75}$. CoGe exhibits weak positive MR (<3%).
3. Magnetic and Thermodynamic Properties:
   • Paramagnetism: Both compounds are paramagnetic. RhGe shows weak temperature-independent Pauli paramagnetism. CoGe displays similar behavior above 50 K but exhibits a slight upturn below 50 K, likely due to trace magnetic impurities from the excess Co.
   • Absence of Superconductivity: Contrary to previous reports on polycrystalline RhGe, no superconducting transition was observed in the RhGe single crystals down to 1.8 K. This is confirmed by the absence of a diamagnetic signal in susceptibility and no specific heat jump.
   • Specific Heat: The electronic specific heat coefficients ($\gamma$) are small for both materials (0.40 mJ mol$^{-1}$ K$^{-2}$ for RhGe and 0.24 mJ mol$^{-1}$ K$^{-2}$ for CoGe), indicating weak electronic correlations compared to magnetic B20 systems like FeGe or MnGe.

Significance and Claims
The paper claims that the successful synthesis of millimeter-sized, high-quality RhGe and CoGe single crystals provides a robust material platform for exploring topological phenomena. The authors assert that these materials are paramagnetic metals with low carrier densities, consistent with theoretical predictions of nonmagnetic behavior and rigid band approximation similarities to CoSi.

Crucially, the study resolves previous controversies by demonstrating that the superconductivity and ferromagnetism reported in polycrystalline RhGe are absent in high-quality single crystals, likely due to subtle compositional differences or residual strain in polycrystals. The authors conclude that RhGe and CoGe, being isoelectronic to CoSi and RhSi, should exhibit similar band topologies, including long Fermi arcs. However, differences in spin-orbit coupling strength and surface environments may lead to distinct surface state connectivities and instabilities. Consequently, these crystals serve as a necessary prerequisite for future angle-resolved photoemission spectroscopy (ARPES) studies to investigate the evolution of multifold fermions and helicoid-arc surface states in B20 systems. The work also highlights the ongoing challenges and sensitivity of discovering superconductivity in B20-structured materials.