Unconventional excitations and orbital-driven low-energy dispersions in chiral topological semimetals PdAsS, PdSbSe, and PdBiTe: a first-principles study

This first-principles study reveals that the chiral topological semimetals PdAsS, PdSbSe, and PdBiTe host diverse unconventional higher-fold excitations and numerous type-II Weyl nodes, with their low-energy dispersions and orbital characteristics significantly modulated by constituent elements and spin-orbit coupling.

The Gist

Imagine the world of solid materials not as a static block of stuff, but as a bustling, three-dimensional city where electrons are the citizens. Usually, these electrons move in predictable lanes, like cars on a highway. But in a special class of materials called Chiral Topological Semimetals, the "traffic laws" are completely different. The electrons here behave like exotic particles that don't exist in our everyday high-energy universe, but they thrive in the crystal structures of these materials.

This paper is a digital exploration (using a super-powerful computer simulation called "first-principles study") of three specific materials: PdAsS, PdSbSe, and PdBiTe. Think of these three as siblings in a family. They share the same house layout (the same crystal structure), but they have different personalities because they are made of different ingredients (different atoms).

Here is the breakdown of what the researchers found, using simple analogies:

1. The "Traffic Jams" (Nodes)

In normal materials, energy bands (the lanes electrons travel in) usually just cross each other or stay separate. But in these special materials, the lanes crash into each other at specific points, creating "traffic jams" called nodes.

• The Standard Traffic: Usually, we see simple crossings (like two roads intersecting).
• The Exotic Traffic: In these materials, the roads merge in complex ways. The researchers found "multi-lane intersections" where 3, 4, or even 6 lanes meet at a single point.
  • Spin-1 Excitations: Imagine a roundabout where three roads meet.
  • Double Weyl Points: A four-way intersection with a very specific, twisted shape.
  • Rarita-Schwinger-Weyl Fermions: A complex 6-way hub that is incredibly rare and mathematically unique.

2. The "Twist" (Chirality)

These materials are chiral. Imagine a screw or a spiral staircase. It has a "handedness"—it can be right-handed or left-handed, but it can't be superimposed on its mirror image. This twist in the atomic structure is what forces the electrons to behave in these exotic ways. It's like the city streets are built on a giant spiral, forcing the traffic to flow in a specific, swirling direction.

3. The "Surprise Guests" (New Weyl Points)

The researchers expected to find these exotic intersections only at the main city centers (high-symmetry points). However, they discovered something surprising: 8 to 12 new "ghost intersections" (Type-II Weyl points) appeared in the middle of the city blocks (general momenta), even without the help of a specific force called Spin-Orbit Coupling (SOC).

• Analogy: It's like expecting to find a subway station only at the city center, but then discovering hidden, magical portals appearing randomly in the suburbs. These were never seen before in these types of materials.

4. The "Flat vs. Bumpy" Roads (Low-Energy Dispersion)

One of the most interesting findings is how the "roads" look right next to these intersections.

• The Ideal Theory: Physics theory predicts that at these special 3-way or 6-way intersections, there should be a "middle lane" that is perfectly flat (like a calm lake).
• The Reality: The researchers found that the "flatness" depends on the ingredients of the material.
  • In PdAsS and PdSbSe, the middle lane is mostly flat, just as the theory predicted.
  • In PdBiTe, the middle lane is actually bumpy (parabolic). Why? Because the atoms in PdBiTe are "hugging" each other too tightly (strong hybridization), causing the flat road to curve.
  • The Shock: In PdSbSe, the middle lane of a 6-way intersection wasn't flat or bumpy; it was a straight, steep highway! This was a complete surprise to the scientists.

5. The "Surface Bridges" (Fermi Arcs)

In topological materials, the inside (bulk) and the outside (surface) are connected in a magical way. If you cut the material open, the electrons on the surface form a bridge that connects two different "islands" of energy. These are called Fermi Arcs.

• The Finding: The researchers tried to see these bridges on the surface of all three materials.
  • In PdSbSe, the bridges were long, clear, and easy to see.
  • In the other two materials, the bridges were faint or hidden.
  • The Lesson: Just because a material has the topological charge to create a bridge doesn't mean you can see it. The "traffic flow" inside the material (bulk dispersion) can sometimes drown out the bridge, making it invisible to our eyes.

Why Does This Matter?

Think of these materials as a new kind of quantum playground.

• Spintronics: Because these electrons have a "spin" and a "twist," they could be used to build computers that are faster and use less energy.
• Light Control: These materials react uniquely to circularly polarized light (like 3D movie glasses), which could lead to better cameras or sensors.
• Design: By understanding how changing the ingredients (swapping As for Sb or Te) changes the "road shapes," scientists can now engineer materials to have exactly the properties they need for future quantum technologies.

In a nutshell: This paper is a map of a new, exotic city. The researchers found that while the city's layout (symmetry) dictates where the main intersections are, the specific "neighborhood vibes" (atomic interactions) determine whether the roads are flat, bumpy, or straight. This knowledge helps us build better tools for the quantum future.

Technical Summary

1. Problem Statement

While the theoretical dispersion of higher-fold excitations in topological semimetals is typically governed by space group symmetries, the actual behavior of quasiparticles near these nodes is significantly influenced by local structural and electronic environments (e.g., atomic arrangement, orbital overlaps, and hybridization). Previous studies on chiral topological semimetals (space group $P213$) have largely focused on high-symmetry points where degeneracies are symmetry-enforced. However, there is a lack of comprehensive understanding regarding:

• The existence of Weyl points at general momenta (not just high-symmetry lines) in these specific materials.
• How variations in constituent elements (PdAsS vs. PdSbSe vs. PdBiTe) alter the low-energy dispersion of unconventional excitations (specifically the "flat" middle bands).
• The role of Spin-Orbit Coupling (SOC) in generating new topological features and modifying existing ones.

2. Methodology

The authors employed Density Functional Theory (DFT) to perform a systematic first-principles study of three chiral materials: PdAsS, PdSbSe, and PdBiTe.

• Computational Framework: Calculations were performed using the WIEN2k package with the APW+lo basis set and the PBEsol exchange-correlation functional.
• Spin-Orbit Coupling (SOC): The study was conducted in two regimes: without SOC and with SOC treated as a perturbation.
• Node Identification: The PY-Nodes code (based on Nelder-Mead minimization) was used to locate band crossings and Weyl points throughout the full Brillouin Zone (BZ).
• Surface States: To analyze surface physics, Maximally Localized Wannier Functions (MLWFs) were constructed using Wannier90 (focusing on $p$-orbitals of As/Sb/Bi and $d$-orbitals of Pd). Surface spectra and Fermi arcs were calculated using the iterative Green's function method via WANNIERTOOLS.
• Topological Invariants: Chirality and topological charges were calculated using WloopPHI.

3. Key Contributions and Results

A. Discovery of New Weyl Points

• Without SOC: The study identified eight new Type-II Weyl points located along the $\Gamma-R$ line in all three materials. This is a significant finding as Type-II Weyl points are typically associated with SOC effects.
• With SOC: The authors discovered 12 new Type-II Weyl nodes at general momenta $(k_x, k_y, k_z)$ in all three materials. Additionally, the number of Weyl points along the $\Gamma-R$ line varied: 8 in PdAsS and PdSbSe, but none in PdBiTe, suggesting these degeneracies may be accidental rather than purely symmetry-enforced.

B. Higher-Fold Excitations and Symmetry Breaking

The materials exhibit systematic variations in physical parameters due to their constituent elements. The study characterized the following excitations:

• At $\Gamma$-point:
  • Without SOC: Spin-1 excitations.
  • With SOC: Transformed into Rarita-Schwinger-Weyl Fermions (RSWF) (spin-3/2, 4-fold degeneracy) and Type-I Weyl points.
• At $R$-point:
  • Without SOC: Double Weyl points (Charge-2, 4-fold degeneracy).
  • With SOC: Transformed into Double Spin-1 excitations (6-fold degeneracy) and Kramer's doublets.
• Energy Range: All higher-fold nodes were found within the energy range of $(-0.5, -0.85)$ eV.

C. Orbital-Driven Low-Energy Dispersions

A major contribution of this work is the analysis of how orbital hybridization deviates the low-energy dispersion from ideal theoretical models:

• Spin-1 Excitations ($\Gamma$-point): Ideally, these feature two linearly dispersing bands and a flat middle band.
  • PdAsS & PdSbSe: The middle band remains relatively flat near $\Gamma$.
  • PdBiTe: Due to strong hybridization between Pd-4d, Bi-6p, and Te-4p orbitals, the middle band becomes parabolic rather than flat.
• Double Spin-1 Excitations ($R$-point):
  • PdAsS & PdBiTe: The middle bands exhibit parabolic dispersion even at low energy scales due to hybridization.
  • PdSbSe: Surprisingly, the middle bands exhibit linear dispersion with a positive slope, attributed to rapidly changing orbital characters in this specific material.

D. Surface States and Fermi Arcs

• Surface States (SS): Two distinct types of non-trivial surface states (SS1 and SS2) were identified. SS1 connects the projections of the RSWF ($\Gamma$) and Double Spin-1 ($M$) nodes, carrying a monopole charge magnitude of 4.
• Fermi Arcs (FA):
  • PdSbSe: Exhibits the longest and cleanest Fermi arcs.
  • PdAsS & PdBiTe: Fermi arcs are faint or difficult to resolve.
  • Mechanism: The study concludes that the observability of Fermi arcs depends critically on bulk band dispersion. In PdAsS and PdBiTe, bulk bands split and disperse in a way that fills surface gaps near the monopoles, masking the Fermi arcs. This challenges the assumption that the mere presence of topological charges guarantees observable Fermi arcs.

4. Significance

• Beyond Symmetry: The work demonstrates that while space group symmetry dictates the existence of degeneracies, local electronic factors (hybridization, orbital character) dictate the nature of the dispersion (flat vs. parabolic vs. linear).
• New Topological Candidates: The identification of previously undocumented Type-II Weyl points (both along $\Gamma-R$ and at general momenta) expands the catalog of known topological materials in the $P213$ space group.
• Design Principles: The findings provide essential insights for designing topological materials for quantum applications. Specifically, the ability to tune the dispersion of middle bands (from flat to parabolic/linear) via chemical substitution (As $\to$ Sb $\to$ Bi) offers a pathway for band structure engineering.
• Experimental Guidance: The study clarifies why Fermi arcs might be invisible in certain materials despite the presence of topological charges, guiding experimentalists (e.g., in ARPES) to focus on specific surface orientations and energy ranges where bulk dispersion does not obscure surface states.

In summary, this paper bridges the gap between idealized symmetry-based models and real-material complexities, revealing that orbital-driven effects can fundamentally alter the low-energy physics of chiral topological semimetals.