Topological superconductivity in superconducting chiral topological semimetals with parallel spin-momentum locking

arXiv:2408.00202 · cond-mat.supr-con · Submitted 2024-07-31 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Topological superconductivity in superconducting chiral topological semimetals with parallel spin-momentum locking".

Mira: Chiral topological semimetals present a fascinating platform for intrinsic unconventional superconductivity because their unique Fermi surface spin textures, characterized by parallel spin-momentum locking, favor zero-momentum intranode superconductivity.

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So we're looking at the paper "Topological superconductivity in superconducting chiral topological semimetals with parallel spin-momentum locking." Basically, it dives into how these specific materials can host intrinsic unconventional superconductivity because of their unique Fermi surface textures and spin orientations.

Mira: Right, Kai, the core thesis seems to be that these chiral systems favor zero-momentum intranode superconductivity because of the parallel spin-momentum locking on the Fermi surface. That's a big claim because it suggests a specific pairing mechanism is naturally favored in this environment.

Lev: From my side, if we can realize this, we need to think about how robust that zero-momentum pairing is against decoherence in a real setup; I'm wondering how much thermal noise would destabilize that gapped state.

Kai: Exactly, Lev. The paper suggests this isn't just some theoretical curiosity; it points toward a mechanism for intrinsic SC that we might be able to probe experimentally by looking at the resulting topological states.

Mira: And what fascinates me is how they link the symmetry constraints of chiral crystals to the location of Weyl nodes, specifically finding them exactly at time-reversal-invariant momenta, which sets up a very specific arena for pairing.

Lev: That constraint on node location is interesting because it simplifies the topology we have to deal with when trying to implement any kind of Majorana physics on actual hardware.

Kai: So, the paper claims that this combination—Weyl nodes at TRIM points and parallel spin-momentum locking—leads directly to these distinct topological superconducting phases, including both first-order and second-order types.

Mira: That's the key finding: the specific material properties dictate whether we get a first-order time-reversal invariant topological superconducting phase or a second-order one depending on how the pairing symmetries interact.

Lev: When you talk about those different orders, are we talking about something that could be practically mapped onto existing qubit architectures or if it's purely an abstract topological concept?

Kai: The authors explore the interplay between s± and d+id pairings, showing how a mixture of these can lead to both a first-order TSC phase and a second-order one with chiral Majorana states.

Mira: The modeling uses an effective odd-parity pairing model where the order parameter is written as (k) = zero + s eta s(k) + d eta d(k), and this framework shows the competition between these different pairings <ref:2408.00202#pg1>.

Lev: The reliance on that effective model means we have to be very careful about the approximations made there; how does that mean-field approach hold up when you try to translate it to a system with genuine disorder?

Kai: The paper suggests that the dominance of s±-wave pairing under certain conditions can lead straight into that first-order TSC phase, which is a specific topological outcome.

Mira: And then they show how adding the d+id-wave component allows for the realization of that second-order topological superconductor characterized by chiral Majorana hinge modes crossing at two momenta if you have open Fermi surfaces.

Paper summary: Lev: Hinge modes crossing at two momenta sounds like something that would require incredibly precise control over the Hamiltonian parameters to even observe, let alone maintain coherence.

Kai: The implication here is that we aren't just looking at one type of topological state; we can tune the pairing symmetry by adjusting the system parameters to switch between these distinct phases.

Mira: That tuning capability is what makes this platform attractive for intrinsic superconductivity research because it shows a direct link between microscopic structure and macroscopic topological properties.

Lev: For error correction, I guess that means we'd need robust methods to protect the specific topological state we want to maintain against those competing pairing symmetries.

Kai: Ultimately, the paper is demonstrating that this chiral environment provides a unique protection mechanism for zero-momentum intranode SC pairing, extending it beyond what you see in achiral Weyl semimetals.

Mira: It’s confirming that the constraints imposed by chiral symmetry are not just about where nodes are located, but fundamentally about how they dictate the pairing symmetries that emerge.

Lev: So, if we take this as a blueprint for future experiments, what's the immediate next step you see for testing these specific pairing symmetries in a lab setting?

Kai: I think the next step involves designing material systems that specifically exhibit this parallel spin-momentum locking and then trying to induce the s± and d+id components through external tuning.

Mira: And we need to be careful because the authors themselves flag that their analysis relies on certain parameter ranges, which means extending it beyond those limits might require new theoretical input.

Lev: That's where I see a lot of complexity; if you push the system outside those preferred regimes, we might lose the clean topological phase entirely and end up with something much harder to model for error correction purposes.

Kai: So, to summarize this paper, "Topological superconductivity in superconducting chiral topological semimetals with parallel spin-momentum locking" shows that chiral crystals allow Weyl nodes at TRIM points, which drives a Fermi surface texture that naturally favors zero-momentum intranode pairing.

Mira: This unique environment then supports the coexistence of s± and d+id pairings, leading to both first-order time-reversal invariant topological SC phases and second-order phases with chiral Majorana states depending on the specific pairing mixture.

Lev: If we translate this into hardware, I see the challenge being controlling that precise balance between the s± and d+id components needed to access those different topological regimes.

Kai: The real significance is showing that these intrinsic material properties can engineer a system with predictable, tunable topological superconducting phases based on symmetry constraints alone.

Mira: It opens up avenues for realizing superconductivity where the pairing mechanism isn't just imposed by external doping but is intrinsically dictated by the crystal lattice structure.

Lev: From an error correction standpoint, this means we have a new class of topological superconductors to consider, ones whose topology is defined by the specific spin texture rather than just a simple band structure.

Conclusion: Kai: So we've seen how these chiral materials set up a unique environment favoring zero-momentum pairing, but let's talk about what this paper actually means for the field and who put this together.

Mira: I think focusing on the title, "Topological superconductivity in superconducting chiral topological semimetals with parallel spin-momentum locking," highlights that it’s not just about finding *any* superconductor; it’s about a specific structural constraint dictating the phase.

Lev: From my end, if this is true, we're looking at a platform where the topology isn't just abstract math; it’s built into the fundamental spin texture of the crystal itself.

Kai: Exactly, and I want to emphasize that these authors didn't just find a theoretical possibility; they mapped out how this can happen in real cubic lattices.

Mira: That mapping is crucial because it shows how Weyl nodes precisely at TRIM points, combined with parallel spin-momentum locking, creates the necessary conditions for these distinct topological superconducting phases.

Lev: For error correction purposes, that means we're not just looking at generic topological states; we’re looking at states whose stability is protected by this specific symmetry enforced by the chiral structure.

Kai: And when you look at the authors, they've done a really thorough job connecting the microscopic spin-orbit coupling to these macroscopic superconducting outcomes.

Mira: I agree, their effective odd-parity model is well-justified because it systematically explores how different pairing symmetries like s± and d+id interact within this framework.

Lev: That systematic exploration helps us understand which configurations are even physically accessible, which is vital when we start designing actual physical realizations.

Kai: So the implication here is that we might be able to use material design to engineer specific topological superconducting phases rather than just hoping they emerge randomly in a system.

Mira: It’s about moving beyond simple band structures and showing how symmetry dictates the pairing itself, which is a major step forward for intrinsic superconductivity.

Lev: If this holds up experimentally, it suggests a path toward creating error-protected states where the topological protection comes from the inherent spin configuration of the material.

Kai: And that's what I find really compelling—it links fundamental crystal physics directly to cutting-edge quantum information science.

Mira: It definitely opens up new avenues for exploring novel superconducting states that aren't limited by conventional BCS theory assumptions.

Lev: We need to keep an eye on the limitations they mentioned regarding the effective model, because that’s where the real engineering challenge will lie when we try to build anything out of this.

School of Physics and Optoelectronic Engineering, Guangdong University of Technology · Guangdong Provincial Key Laboratory of Sensing Physics and System Integration Applications, Guangdong University of Technology

cond-mat.supr-con

Submitted: 2024-07-31

Updated: 2026-10-06

Comments: 12 pages, 5 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 71/100

The gist: Chiral topological semimetals present a fascinating platform for intrinsic unconventional superconductivity because their unique Fermi surface spin textures, characterized by parallel spin-momentum

Key concepts

Weyl Node Location: In chiral crystals, time-reversal symmetry forces the spin-orbit coupling term to be an odd function near a Time-Reversal Invariant Momentum (TRIM). This constraint dictates that Weyl nodes must reside exactly at these TRIM points, unlike achiral systems where nodes are typically constrained differently.
Parallel Spin-Momentum Locking: Chiral topological semimetals possess a unique Fermi surface spin texture where the electron's spin is locked parallel to its linear momentum. This specific configuration naturally favors spin-singlet pairing and enables a gapped zero-momentum intranode superconducting state.
First-Order TSC Phase: This topological superconducting phase occurs when an odd number of Fermi surfaces enclose a TRIM point with positive SC pairing, resulting in a winding number of ν=1. This phase can be realized either with closed or open nodal surfaces depending on the sign of the gap parameter $\Delta_0$.
Second-Order TSC Phase: This phase arises from the coexistence of s± and d+id-wave pairing symmetries, characterized by chiral Majorana hinge modes crossing at two momenta, yielding a winding number of ν=-2 for open Fermi surfaces.

Terminology

Chern Number — 7× in this paper · explained in 4 episodes
Hubbard Model — 3× in this paper · explained in 3 episodes
Bogoliubov-de Gennes — 2× in this paper
Adam — 1× in this paper · explained in 2 episodes
Core — 1× in this paper · explained in 2 episodes
Degeneracy — 1× in this paper · explained in 3 episodes
Entanglement — 1× in this paper · explained in 3 episodes
Phase Transitions — 1× in this paper · explained in 2 episodes
Symmetry Breaking — 1× in this paper · explained in 3 episodes
Time-Reversal Invariant Momentum — 1× in this paper

Summary

Chiral topological semimetals present a fascinating platform for intrinsic unconventional superconductivity because their unique Fermi surface spin textures, characterized by parallel spin-momentum locking, favor zero-momentum intranode superconductivity. This work investigates how these material properties lead to distinct topological superconducting phases, including first-order and second-order types.

The gist

Chiral topological semimetals in cubic lattices are fascinating platforms for exploring intrinsic unconventional superconductivity and topological superconductivity.

Weyl Node Location and Symmetry Constraints

The location of Weyl nodes is dictated by symmetry constraints, which differ significantly between chiral and achiral crystals. In chiral crystals, time-reversal symmetry enforces that the spin-orbit coupling term must be an odd function of momentum near a Time-Reversal Invariant Momentum (TRIM), allowing Weyl nodes to reside exactly at TRIM points. This contrasts with achiral crystals where the existence of mirror or roto-inversion operations forces constraints that typically lead to Kramers nodal lines or require higher-order terms to host Weyl nodes away from TRIM.

Fermi Surface Spin Texture and Pairing Favorability

The second critical distinction lies in the Fermi surface spin texture. Chiral topological semimetals exhibit a radial spin texture characterized by parallel spin-momentum locking, where the spin is isotropically locked parallel to the electron’s linear momentum. This specific configuration naturally favors spin-singlet pairing. This feature enables gapped zero-momentum intranode pairing (SC), which is absent in achiral Weyl semimetals.

Superconducting Pairing Symmetries

The analysis explores the coexistence of different superconducting pairings on a cubic lattice. The paper identifies that a cubic lattice system in general favors a mixture of spin-singlet s± and d + id-wave pairings. Specifically, an s±-wave pairing can lead to a first-order time-reversal invariant topological SC phase. Furthermore, the introduction of an additional pairing symmetry allows for the realization of a second-order topological superconductor with chiral Majorana states in the presence of a mixture of s±- and d+id-wave pairing.

Topological Superconductivity Phases

The study distinguishes between two main types of topological superconducting phases based on their Fermi surface configurations.

First-Order TSC: This phase is realized when an odd number of FSs enclosing TRIM with positive SC pairing leads to a TSC phase, which can result in a winding number of ν = 1. This is achieved through the nodal surface separating the FSs, which can be closed or open surfaces, depending on the sign of ∆0.
Second-Order TSC: This phase arises from s± + d + id-wave pairing and is characterized by chiral Majorana hinge modes crossing at two momenta for open Fermi surfaces, resulting in a winding number of ν = −2.

Effective Odd-Parity Model

The theoretical framework employs an effective odd-parity pairing model to analyze the system. The Hamiltonian is decoupled into two parts, H+ and H−, which are diagonalized based on the spin-orbit coupling strength and chemical potential. The superconducting order parameter is expressed as ∆(k) = ∆0 + ∆sηs(k) + ∆dηd(k), where ηs(k) and ηd(k) encode the momentum dependence of the pairing potentials. This model reveals that the dominance of s±-wave pairing in certain parameter ranges yields a first-order TSC, while the coexistence of s±- and d+id-wave pairings emerges in others.

Conclusion

The research demonstrates that both first- and second-order topological superconducting phases can emerge in a chiral topological semimetal. The unique protection afforded by chiral little group symmetry leads to Weyl nodes at TRIM points, which are surrounded by Fermi surfaces with parallel spin-momentum locking, favoring zero-momentum intranode spin-singlet superconducting pairing. This confirms that the zero-momentum intranode SC pairing can be generalized to chiral topological semimetal in cubic lattice with multiple band crossing. Furthermore, the study extends the topological superconductivity beyond Rashba spin-orbit coupling physics by exploring novel spin polarization behaviors.

How it works

Weyl nodes are located at TRIM points in chiral crystals because time-reversal symmetry enforces the SOC term to be odd near TRIM, unlike achiral crystals where constraints force nodes away from TRIM or into Kramers nodal lines.
The parallel spin-momentum locking on Fermi surfaces in chiral topological semimetals creates a unique environment that naturally favors spin-singlet pairing and enables gapped zero-momentum intranode pairing.
The system is modeled using a two-band Hamiltonian where the superconducting order parameter is decomposed into s± (s±-wave) and d+id (d+id-wave) components, allowing for the investigation of phase competition.

Improvements for AI systems

Based on the provided scientific paper, here are specific improvements for AI systems derived from its findings, along with what those improved systems could achieve:

) Improved AI Systems & Applications:

AI-driven Material Discovery and Design Platforms (Focusing on Topological Superconductivity):
Advanced Quantum Simulation and Predictive Modeling Engines (Focusing on Topological Phases):
Novel Spintronic Device Design Tools (Focusing on Spin-Momentum Locking).

) Specific Improvements & Capabilities:

AI-driven Material Discovery and Design Platforms:
The AI system can be trained on the complex phase diagrams (Fig. 2), mean-field calculations, and symmetry constraints derived from the paper (Section II and III).
It can predict the most stable superconducting pairing symmetry (e.g., favoring s±-wave vs. s±+d+id-wave) based on input lattice parameters, spin-orbit coupling strengths, and interaction potentials (U, W).
It can screen potential material candidates (like RhGe or AuBe mentioned in the conclusion) by predicting whether they possess the necessary chiral crystal structure and Fermi surface configurations required for realizing specific topological phases (First-Order TSC vs. Second-Order TSC).
It can suggest specific chemical doping strategies or strain profiles to tune the system into a desired topological regime, such as inducing an open Fermi surface configuration necessary for a first-order TSC phase.
Advanced Quantum Simulation and Predictive Modeling Engines:
This engine can utilize the derived Bogoliubov-de Gennes (BdG) Hamiltonians (Eqs. 6, 10, 11) and the topological invariants (Winding Number formula Eq. 13) to perform high-fidelity simulations of unconventional superconductivity in topological semimetals.
It can predict the existence and characteristics of Majorana zero modes at specific momentum points (e.g., predicting the location of Majorana cones in Fig. 4).
It can simulate the transition between different topological phases (e.g., from a trivial state to a first-order TSC state) by varying external parameters like chemical potential or spin-orbit coupling strength, allowing for rapid exploration of the phase diagram shown in Fig. 2.
Novel Spintronic Device Design Tools:
The system can leverage the parallel spin-momentum locking property (Section II, Part ii) to design novel spintronic devices where electron spin is intrinsically locked to its momentum direction in chiral materials.
It can predict the resulting topological properties, such as the Chern number and helicoid-arc surface states mentioned in Section I, which are crucial for designing spintronic components like topological insulators or quantum Hall effect devices.
It can optimize device architectures based on the predicted spin textures to maximize spin-polarized currents or generate specific topological responses (e.g., helicoid-arc surface states) in optoelectronic applications (Section I).