Topological superconductivity on a kagome magnet coupled to a Rashba superconductor

arXiv:2602.07383 · cond-mat.mes-hall, cond-mat.supr-con · Submitted 2026-02-07 · Read on arXiv

Listen

Transcript

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

Kai: I'm Kai, and with me are Mira and Lev, guest researcher.

Mira: Today's paper: "Topological superconductivity on a kagome magnet coupled to a Rashba superconductor".

Kai: A quantum anomalous Hall system coupled to an s-wave superconductor fails to induce pairing in strong exchange coupling limits,

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

Paper summary: Kai: We just talked about the main points of "Topological superconductivity on a kagome magnet coupled to a Rashba superconductor," which essentially says that while s-wave pairing doesn't work well in this setup under strong exchange coupling, adding a Rashba superconductor opens up the door to topological superconducting phases defined by odd Bogoliubov-de Gennes Chern numbers.

Mira: That’s right; the authors claim they demonstrate that proximity coupling to a Rashba superconductor successfully induces these topological phases, and crucially, they confirm that these phases are characterized by odd BdG Chern numbers.

Kai: The paper goes on to show that this topological nature is validated because the two ways of characterizing it—the BdG Chern number N and the chiral central charge c- —are consistent with each other, and they even show that N/two = c- in this system <ref:2602.07383#pg0>.

Mira: Furthermore, they establish that the magnetic ordering within the kagome magnets is actually energetically influenced by this proximity effect, showing it's not just a passive feature but an active part of the physics.

Kai: It’s interesting because they show how tuning parameters like theta and phi can control this magnetic state, with fixing phi at pi/two giving them the lowest ground state energy when pairing terms are increased <ref:2602.07383#pg0>.

Mira: And they also provide some guidance on the phase diagram, showing that these topological superconducting phases with odd N exist across regions of fractional filling, including a specific phase where N = -three appears when nu three.

Kai: The authors also confirm that their method of calculating the chiral central charge via the modular commutator provides a practical characterization, as it aligns perfectly with half the value of the BdG Chern number N.

Mira: So, in short, they’re showing that this heterostructure realizes topological superconductivity and tying together its different topological invariants offers a solid theoretical framework for understanding these emergent phases.

Lev: From a quantum error correction viewpoint, having those precise characterizations like the BdG Chern number is what we need to verify if any of these states we might try to build on hardware are actually robust against local noise.

Conclusion: Kai: So, looking at the title "Topological superconductivity on a kagome magnet coupled to a Rashba superconductor," the core idea they’re pushing is that this specific combination of materials can yield topological superconducting states when you have that right type of proximity coupling.

Mira: It really boils down to how introducing the asymmetry from a Rashba superconductor changes the pairing mechanism sufficiently to create these topological invariants, specifically those odd Chern numbers they found.

Kai: The implication for us is that we can start thinking about realizing these states in real noncentrosymmetric materials, not just idealized models, as long as we control the interface to introduce that necessary symmetry breaking.

Mira: The paper suggests that by controlling the magnetic ordering through the proximity effect, we can tune the system's energy landscape to favor a specific topological configuration.

Kai: It means we’re moving closer to understanding how engineering materials at interfaces can dictate whether we get trivial or topologically interesting superconductivity in these frustrated magnetic systems.

Mira: Ultimately, this work provides a concrete theoretical pathway for designing and predicting where these topological phases might manifest in real experimental setups involving magnetism and unconventional superconductors.

Lev: If this theory is correct, it means that the specific structural features of the kagome lattice combined with Rashba pairing are not just interesting curiosities but could be functional platforms for manipulating superconducting properties.

Department of Physics, Kyushu University · RIKEN Center for Quantum Computing (RQC) · Quantum and Spacetime Research Institute, Kyushu University

cond-mat.mes-hall, cond-mat.supr-con

Submitted: 2026-02-07

Updated: 2026-10-06

Comments: 14 pages, 10 figures

Journal ref: Phys. Rev. B 114, 214503 (2026)

DOI: 10.1103/7nt6-s5rw

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

Importance score: 79/100

The gist: A quantum anomalous Hall system coupled to an s-wave superconductor fails to induce pairing in strong exchange coupling limits, but proximity coupling to a Rashba superconductor successfully induces

Key concepts

BdG Chern number (N): This is a mathematical invariant used to classify the topological nature of the superconducting state, similar to a topological index in other systems. It is calculated by integrating a Berry connection over momentum space and tells us if the system possesses protected edge states or other topological properties.
Chiral central charge (c-): This quantity is extracted from the ground state density matrix using modular commutators. It provides another way to characterize the topological phase, and in this specific system, it was found to be exactly half of the BdG Chern number (N/2), confirming a consistent topological description.
Proximity Effect: This refers to the influence of one material (the superconductor) on an adjacent material (the kagome magnet) when they are placed in close contact. In this study, the Rashba superconductor induces pairing onto the magnetic kagome side, which is crucial for creating the topological superconducting phases.
Rashba Superconductor: This specific type of superconductor lacks inversion symmetry and possesses spin-orbit coupling. This lack of symmetry is essential because it allows it to induce a specific type of proximity pairing (a triplet component) onto the adjacent kagome magnet, which is necessary for the observed topological phases.

Terminology

Chern Number — 31× in this paper · explained in 4 episodes
Bogoliubov-de Gennes — 5× in this paper
Entanglement — 5× in this paper · explained in 3 episodes
Hybrid System — 4× in this paper · explained in 2 episodes
Symmetry Breaking — 4× in this paper · explained in 3 episodes
Consistency — 3× in this paper · explained in 3 episodes
Anisotropy — 2× in this paper · explained in 3 episodes
Anyons — 2× in this paper · explained in 2 episodes
Berry Curvature — 2× in this paper · explained in 3 episodes
Effective Hamiltonian — 2× in this paper · explained in 2 episodes
Phase Transitions — 2× in this paper · explained in 2 episodes
Core — 1× in this paper · explained in 2 episodes
Entanglement Entropy — 1× in this paper · explained in 2 episodes
Frustration — 1× in this paper · explained in 2 episodes
Gauge Freedom — 1× in this paper · explained in 2 episodes
Hubbard Model — 1× in this paper · explained in 3 episodes
Quantization — 1× in this paper · explained in 12 episodes
Topological Defects — 1× in this paper · explained in 2 episodes
Trace — 1× in this paper · explained in 2 episodes

Summary

A quantum anomalous Hall system coupled to an s-wave superconductor fails to induce pairing in strong exchange coupling limits, but proximity coupling to a Rashba superconductor successfully induces topological superconducting phases characterized by odd Bogoliubov-de Gennes Chern numbers. This work demonstrates that this heterostructure realizes topological superconductivity and shows that the magnetic ordering of kagome magnets is energetically affected by the proximity effect.

Model Setup and Physical System

The study considers a spinful electron system on a kagome magnet proximity-coupled to a Rashba superconductor, described by the total Hamiltonian:

Hhop + Hexc + H∆. The system is analyzed in the strong-exchange limit, where electrons are fully polarized by the local magnetic moments, leading to an effective Hamiltonian in momentum space:

H = 1/2 Xk c†(k)h(k)c(k) + Tr hhop(k).

The proximity effect is modeled by a pairing term H∆. The Rashba superconductor is chosen because it lacks inversion symmetry, which is necessary to induce proximity pairing on the kagome side. The triplet component of the pairing in the Rashba superconductor is represented by a d-vector proportional to k×ez in momentum space, leading to specific real-space forms for the singlet and triplet components of proximity-induced pairing:

d ij 0 = ∆s for i = j, ∆s for NN pairs, 0 otherwise.

d ij = -i∆p e ij × ez for NN pairs, 0 otherwise.

Topological Characterization

The topological nature of the emergent phases is characterized by two primary invariants: the BdG Chern number N and the chiral central charge c−. The BdG Chern number is calculated using the non-Abelian Berry connection one-form A = Ψ† dΨ, and its field strength two-form F = dA + A ∧ A, with N defined as:

N = 1/2πi ∫BZ Tr F.

The chiral central charge c− is extracted from the modular commutator J(A, B, C) of the ground state density matrix ρ:

J(A, B, C) = iTr ρ (ABC) h K(AB), K(BC).

In BdG systems, this can be simplified using Peschel’s formula and expressed in terms of the Nambu-space correlation matrix Cij = ⟨omega c†i c†j, cj omega⟩. The relation N/2 = c− is confirmed through numerical calculations.

Emergent Topological Phases and Phase Diagram

Numerical results demonstrate the emergence of topological superconducting phases by evaluating the projected pair potentials ∆n(k) onto each band n:

∆n(k) ≡ u†n(k)∆(k)u∗n(-k). The analysis shows that because un(k) and un(-k) have parallel spin directions due to the inversion symmetry of hhop, the s-wave component does not contribute to ∆n(k); hence ∆n(k) is scaled only by ∆p in the figure.

The phase diagram plots the BdG Chern number N as a function of the polar angle θ and chemical potential µ. The results show that topological superconducting phases with odd N spread broadly over regions of fractional filling, with a phase with N = −3 emerging around ν ≲ 3. Furthermore, evaluating c− along the green line in this phase diagram shows perfect agreement with one-half of the BdG Chern number N, demonstrating that the modular-commutator-based evaluation provides a practical characterization of topological superconducting phases.

Magnetic Ordering Control

The magnetic ordering can be controlled by the proximity effect, as shown by treating θ and ϕ as variational degrees of freedom. The study finds that fixing ϕ at π/2 yields the most enhanced projected pair potentials, implying lower ground state energy. The system exhibits a sharp transition for θmin switching from 0 to π/2 as ∆s,p increases, reflecting the competition between kinetic energy (favoring θ = 0) and pairing (favoring θ = π/2). This behavior persists across different fillings ν.

Experimental Relevance

The findings suggest that superconductors with antisymmetric spin-orbit coupling can be realized in noncentrosymmetric materials like CePt3Si, CeRhSi3, and CeIrSi3. Even in centrosymmetric materials, Rashba pairing can be induced in superconducting heterostructures with interfacial inversion-symmetry breaking. The results regarding kagome magnets coupled to Rashba superconductors may be accessible in realistic experimental settings. The work specifically ignores electron-electron interactions on the kagome side.

Summary of Key Findings

Proximity coupling to a Rashba superconductor induces topological superconducting phases characterized by odd BdG Chern numbers N and chiral central charge c−.
The topological characterization is consistent, with the relation N/2 = c− holding in this system.

Improvements for AI systems

As a fastidious research AI, I have analyzed this paper, Topological superconductivity on a kagome magnet coupled to a Rashba superconductor. The core scientific contribution lies in demonstrating how proximity coupling to an asymmetric (Rashba) superconductor induces topological superconducting phases characterized by non-trivial parity invariants (odd Bogoliubov-de Gennes Chern numbers and chiral central charge) in a frustrated magnetic lattice.

Based on this research, here are specific improvements for AI systems:

)Specific Improvements for AI Systems Based on This Research:

A quantum simulation engine capable of modeling strongly correlated electron systems with geometric frustration (like the Kagome lattice) coupled to non-trivial superconducting environments.
A topological phase classification algorithm that can robustly distinguish between trivial and non-trivial topological superconducting phases using both BdG Chern numbers and modular commutator invariants (chiral central charge).
A predictive model for controlling emergent magnetic ordering in hybrid quantum systems by tuning the interface's spin-orbit coupling (modeled here by Rashba pairing) or proximity effect strength.

)What the Improved AI System Can Do: