Tuning of anomalous magnetotransport properties in half-Heusler topological semimetal GdPtBi

This study demonstrates that high-energy electron irradiation can shift the Fermi level of the half-Heusler Weyl semimetal GdPtBi by 100 meV while preserving the negative longitudinal magnetoresistance indicative of chiral magnetic anomaly, thereby confirming the robust influence of Weyl nodes on magnetotransport properties regardless of Fermi level position.

The Gist

Imagine you have a very special, high-tech highway made of a material called GdPtBi. In the world of physics, this material is a "topological semimetal." Think of it as a super-highway where electrons (the cars) can travel with almost no friction, but only if they follow very specific, exotic rules dictated by the shape of the road itself.

The scientists in this paper wanted to see what happens if they slightly change the "traffic rules" of this highway. Specifically, they wanted to test how robust these special rules are when they move the "Fermi level"—which is like the current water level in a river.

Here is the story of what they did and what they found, explained simply:

1. The Special Highway: Weyl Nodes

In this material, there are special spots on the highway called Weyl nodes. You can think of these as magical "wormholes" or "toll-free zones" where electrons can zip through without getting stuck.

• The Magic: When you apply a magnetic field, these wormholes open up.
• The Result: Electrons flowing in the same direction as the magnetic field get a super-boost, causing a phenomenon called Negative Longitudinal Magnetoresistance (NLMR). In plain English: The more you push the electrons with a magnet, the easier it is for them to flow. It's like a car that gets faster the harder you press the gas pedal, but only if you are driving in a specific magnetic lane.

2. The Experiment: The "Electron Irradiation" Hammer

The researchers wanted to know: How close do the electrons need to be to these magical wormholes for this super-speed effect to work?

To find out, they used a technique called high-energy electron irradiation. Imagine shooting a stream of tiny, high-speed bullets (electrons) at the material.

• What it does: These bullets knock atoms slightly out of place, creating tiny defects. This acts like a "tuning fork" for the material. It changes the number of charge carriers (the cars) and, crucially, shifts the water level (Fermi level) of the river.
• The Goal: They shifted the water level by about 100 meV (a tiny amount in physics, but huge for electrons). They wanted to see if the "wormholes" would still work if the water level was no longer right in the middle of them.

3. The Big Surprise: The Highway is Tough!

The scientists expected that if they moved the water level away from the wormholes, the super-speed effect (Negative Magnetoresistance) would disappear. They thought, "If the cars aren't driving through the wormhole, the magic should stop."

But that's not what happened.

Even after shifting the water level significantly, the "super-speed" effect persisted. The electrons still flowed easier when the magnetic field was applied, even though they were no longer perfectly aligned with the wormholes.

• The Analogy: It's like driving a car on a highway where the "magic boost" zone is a specific tunnel. The researchers moved the road so the cars were driving next to the tunnel instead of through it. Surprisingly, the cars still got a speed boost! It turns out the "magic" isn't just about being in the tunnel; the whole road system is tuned to give a boost.

4. The Twist: The "Anomalous Hall Effect"

While the speed boost (magnetoresistance) was stubborn and stayed strong, another effect called the Anomalous Hall Effect (a sideways push on the electrons) got very complicated.

• As they changed the water level, the sideways push changed size and direction in a messy, unpredictable way.
• Why? The researchers used computer simulations to look at the "road map" (electronic band structure). They found that the sideways push comes from two things: the wormholes and the way the roads curve and cross each other (avoided band crossing). When they moved the water level, they changed how the cars interacted with these curves, causing the complex changes.

5. The Conclusion: Why This Matters

This study is important because it shows that these special topological materials are very robust.

• The Takeaway: You don't need to be a perfectionist to use these materials. Even if the "water level" isn't perfectly tuned to the wormholes, the material still exhibits these amazing quantum properties.
• Real World Impact: This is great news for future technology like quantum computers and spintronics (super-fast electronics). It means we don't need to create perfectly pure, flawless crystals to get these benefits. As long as the material is "close enough," the magic still works.

In a nutshell: The scientists poked a special quantum material with a stick (electron irradiation) to move its internal settings. They expected the magic to break, but instead, they found the magic was surprisingly tough and kept working, proving that these materials are ready for real-world use even if they aren't perfect.

Technical Summary

Here is a detailed technical summary of the paper "Tuning of anomalous magnetotransport properties in half-Heusler topological semimetal GdPtBi."

1. Problem Statement

Topological semimetals, particularly Weyl semimetals, exhibit unique transport properties driven by topologically non-trivial states near the Fermi level ($E_F$). In the half-Heusler compound GdPtBi, magnetic fields induce Weyl nodes, leading to phenomena such as Negative Longitudinal Magnetoresistance (NLMR) (a signature of the chiral magnetic anomaly) and the Anomalous Hall Effect (AHE).

However, a significant gap exists in understanding how these topological contributions depend on the precise position of the Fermi level relative to the Weyl nodes. While external pressure and chemical doping have been used to tune $E_F$, systematic studies on how NLMR and AHE evolve as $E_F$ is shifted away from the Weyl nodes are lacking. Furthermore, it is unclear whether the topological contributions to transport are robust or fragile when the Fermi level is displaced.

2. Methodology

The study employed a combination of experimental manipulation and theoretical modeling:

• Sample Preparation: High-quality single crystals of GdPtBi were grown using a Bi-flux method. Five samples were cut from a single crystal to ensure identical initial properties.
• Fermi Level Tuning via Electron Irradiation: Instead of chemical doping, the authors used high-energy (2.5 MeV) electron irradiation to introduce defects. This technique creates Frenkel pairs (vacancy-interstitial pairs), effectively removing electrons from the valence band and shifting the Fermi level. Samples were irradiated with doses ($\phi$) ranging from 0 to 7 C/cm².
• Experimental Characterization:
  • Electrical Transport: Measurements of electrical resistivity ($\rho$), magnetoresistance (MR) in both transverse and longitudinal geometries, and the Hall effect were performed using a Quantum Design PPMS.
  • Temperature Range: Measurements were conducted at $T = 10$ K (below the Néel temperature $T_N \approx 9$ K, where AHE is prominent) and $T = 50$ K (above $T_N$, where AHE is negligible).
• Theoretical Calculations:
  • DFT: First-principles Density Functional Theory (DFT) calculations were performed using VASP with spin-orbit coupling (SOC) and the modified Becke-Johnson (mBJ) potential to model the electronic band structure.
  • Tight-Binding Model (TBM): A TBM was constructed using Wannier90 to calculate the band structure under applied magnetic fields (0–10 T) and to estimate the Anomalous Hall Conductivity (AHC).

3. Key Contributions

• Novel Tuning Mechanism: The study successfully demonstrates that high-energy electron irradiation is an effective tool for tuning the Fermi level in GdPtBi, shifting it by approximately 100 meV away from the Weyl nodes.
• Decoupling of Effects: The authors successfully separated the contributions of Weyl nodes (chiral anomaly) and avoided band crossings to the magnetotransport properties by correlating experimental shifts in $E_F$ with theoretical band structure changes.
• Quantitative Correlations: The paper establishes quantitative relationships between carrier concentration/mobility and specific magnetotransport signatures (NLMR and Transverse MR).

4. Key Results

A. Electronic Structure and Fermi Level Shift

• Resistivity: Pristine samples showed a semiconducting-to-metallic transition with a valley near $T_N$. Irradiated samples lost this valley and exhibited metallic behavior down to low temperatures, with resistivity decreasing monotonically.
• Carrier Concentration ($n_H$) and Mobility ($\mu_H$):
  • Irradiation increased the hole carrier concentration ($n_H$) by an order of magnitude (from $2.6 \times 10^{18}$to$2.2 \times 10^{19}$cm$^{-3}$).
  • Carrier mobility ($\mu_H$) decreased significantly (from $\sim 2600$ to $\sim 350$ cm$^2$/Vs) due to increased impurity scattering.
  • Both $n_H$ and $\mu_H$ saturated at irradiation doses $\ge 4.5$ C/cm².
• Fermi Level Position: By comparing experimental $n_H$ with DFT-calculated density of states, the authors determined that the Fermi level shifted from $-30$ meV (pristine) to $-130$ meV (maximal irradiation), moving it further away from the Weyl nodes located near the $\Gamma$ point.

B. Magnetoresistance (MR)

• Negative Longitudinal MR (NLMR):
  • In pristine samples, NLMR was strong ($\sim -80\%$ at 14 T, 10 K), indicating a robust chiral magnetic anomaly.
  • As the Fermi level shifted away from the Weyl nodes (increasing irradiation dose), the magnitude of NLMR decreased.
  • At high doses, NLMR became positive in weak fields and remained negative only in strong fields, or turned entirely positive at 50 K.
  • Correlation: NLMR was found to be linearly proportional to carrier concentration ($n_H$).
• Transverse MR:
  • Transverse MR decreased with increasing irradiation dose.
  • Correlation: Transverse MR followed a quadratic dependence on carrier mobility ($\mu_H^2$), consistent with semi-classical models for low-carrier systems.

C. Anomalous Hall Effect (AHE)

• Complex Evolution: The AHE exhibited non-monotonic behavior.
  • The peak magnitude of the anomalous Hall conductivity ($\sigma_{xy}^A$) initially increased with low irradiation doses (reaching a maximum of $174.2$$\Omega^{-1}$cm$^{-1}$at$\phi = 1.5$ C/cm²) before decreasing.
  • The magnetic field ($B_{max}$) at which the AHE peak occurred shifted to higher fields (from $\sim 2.5$ T to $\sim 10$ T) as the dose increased.
• Mechanism: Theoretical calculations revealed that while Weyl nodes contribute to AHE, the avoided band crossing (driven by Berry curvature) plays a dominant role, especially as the Fermi level moves away from the Weyl nodes. The complex variation of AHE with irradiation is attributed to the energy-dependent nature of the Berry curvature arising from these avoided crossings.

5. Significance and Conclusion

• Robustness of Topology: The study concludes that while the magnitude of NLMR diminishes as the Fermi level moves away from Weyl nodes, the topological influence on magnetotransport remains robust. Even with a 100 meV shift, topological signatures persist, suggesting that the "topological window" for observing these effects in half-Heusler Weyl semimetals is relatively wide.
• Dominant Mechanisms: The work clarifies that in GdPtBi, the chiral anomaly (NLMR) is sensitive to the proximity of the Fermi level to Weyl nodes, whereas the AHE is heavily influenced by avoided band crossings and Berry curvature, allowing it to persist and even enhance under specific Fermi level tuning.
• General Applicability: These findings suggest that similar tuning strategies could be applied to other half-Heusler Weyl semimetals to optimize their properties for applications in spintronics and quantum computing, where controlling topological transport without destroying the material's integrity is crucial.

In summary, this paper provides a systematic experimental and theoretical framework for understanding how defect engineering (via electron irradiation) can tune the Fermi level in topological semimetals, revealing the distinct dependencies of chiral anomaly and anomalous Hall effects on the electronic structure.