Majorana Zero Modes in Quasi-Two-Dimensional Systems: A New Approach via Chiral Hinge States ✛ ✎ ✦
Context
Majorana zero modes (MZMs) have long attracted attention as building blocks for topological quantum computers due to their non-Abelian statistics and robustness against decoherence. The concept was first proposed by Alexei Kitaev in a one-dimensional chain model with p-wave superconductivity, but realizing p-wave superconductivity in real materials remains a major challenge. As a result, hybrid systems are being actively developed, where conventional s-wave superconductivity is combined with materials with strong spin-orbit coupling to mimic p-wave pairing. This work offers an elegant route by exploiting a recently discovered class of materials—higher-order topological insulators (HOTIs)—which support chiral hinge states. This connection to fundamental quantum information makes MZMs a prime candidate for protected computation.
Methods
The researchers constructed a four-band model of a chiral HOTI on a cubic lattice, where an anisotropic mass term breaks time-reversal symmetry and opens a gap on the surfaces, leaving behind gapless hinge states. They then considered a sample that is thin along the x-axis and extended along y, with a finite length along z. To account for the superconducting proximity effect, the Bogoliubov–de Gennes Hamiltonian with s-wave pairing was used. The spectrum and wave functions were computed by exact diagonalization in real space via numerical simulations. Robustness against disorder was also tested by adding random potentials to the Hamiltonian.
Results
In the thin limit (just 2 lattice constants in thickness), the wave functions of opposite hinge states overlap, leading to their hybridization and splitting of the spectrum into two helical channels localized on opposite edges along y. By tuning the chemical potential into the gap of these channels, superconducting pairing opens a topological gap, and four entangled Majorana modes emerge at the channel ends—one at each corner in the y-z plane. Numerical calculations confirm the presence of these zero-energy modes, separated from excited states, as seen in the density-of-states peaks. The phase diagram in the (μ, Δ) plane shows a robust topological superconducting region that requires no fine-tuning of parameters. Moreover, the modes prove resilient to disorder: under moderate disorder, the superposition of states persists.
Implications
The proposed mechanism establishes a new class of platforms for creating Majorana corner states by leveraging finite-size effects and the intrinsic topology of HOTIs. This expands the toolkit for engineering topological superconductivity without resorting to nanowires or quantum anomalous Hall insulators. In the long run, such systems could serve as a foundation for quantum algorithms based on braiding Majorana modes, an idea first proposed by Frank Wilczek in the context of anyons.
Future development
Future work could extend this to other classes of higher-order topological phases, including magnetic and antiferromagnetic systems; combining them with other root states like Majorana loops and networks is also promising. Moreover, advances in quantum measurement techniques will enable detection of these states with high precision.
Impact
The results may spur experimental searches in known magnetic topological insulators, such as MnBi₂Te₄, where hinge states have already been observed, and advance the development of scalable qubits for topological quantum computing.
Next steps
Immediate next steps include simulating more realistic materials with full band structures and disorder effects, as well as designing detection schemes using scanning tunneling microscopy.
Key open problems
The work is directly tied to a major unsolved problem in condensed matter physics—the experimental realization of Majorana qubits—and to the fundamental challenge of classifying symmetry-protected topological phases. Robustness to quantum decoherence remains a central hurdle for practical computation.
The knowledge machine's view
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The paper proposes a four-zone model of a chiral higher-order topological insulator (HOTI) on a cubic lattice with an anisotropic mass term that opens a gap on the surfaces and leaves chiral hinge states. In the thin limit, the overlap of hinge states leads to hybridization and the formation of helical edge channels, and the superconducting proximity effect with s-wave pairing opens a topological gap, giving rise to four Majorana zero modes at the corners. Numerical diagonalization confirms the zero energy of the modes, their separation from excitations, and their robustness to moderate disorder.
Where its strength is
The work stands out for using the intrinsic topology of a chiral HOTI to localize Majorana modes at corners without external magnetic fields or nanowires, simplifying implementation and enhancing scalability. The demonstrated robustness to disorder and the absence of fine-tuning of parameters make the platform practical for further studies.
Where it could go next
- It might be interesting to see how the proposed corner Majorana modes interact with magnetic textures such as skyrmions, which in our archive are considered as a means to control topological states.based on: The Skyrmion Dance: How a Magnetic Vortex Conducts the Quantum Orchestra arXiv:2505.00266v1
- Nearby there is a work on superconductivity in systems without heavy atoms; perhaps their approach to interface engineering could help expand the class of materials for realizing the proposed mechanism.based on: Superconductivity Without Heavy Atoms arXiv:2605.01686
- Attention should be paid to the study of Majorana states in quantum wires; their detection and manipulation methods could be adapted for corner modes in HOTIs.based on: Knock, knock, who's there? Majorana arXiv:2607.23498
Worth trying
- Numerically test the effect of a skyrmion texture on the splitting of Majorana modes in the proposed geometry.
- Check whether the topological phase persists when moving to materials with light elements, using parameters from a neighboring work.
- Investigate nonlocal correlations between corner modes as a signature of their Majorana nature.
Why this may matter
If corner Majorana modes in chiral HOTIs can be realized experimentally, this would pave the way for scalable topological qubits robust to local perturbations and allow the study of non-Abelian statistics in two-dimensional systems without complex nanofabrication.
Nearby works in our archive
- Superconductivity Without Heavy Atomssimilarity 0.64
- Quantum Bricks at the Crystal's Edgesimilarity 0.63
- Quantum Dance in a Protective Cocoonsimilarity 0.62
- Math shuts the door on twin-particle quantum computerssimilarity 0.62
- Knock, knock, who's there? Majoranasimilarity 0.62
- The Skyrmion Dance: How a Magnetic Vortex Conducts the Quantum Orchestrasimilarity 0.62
The closest work in the archive sits at 0.64 by meaning — the usual level for our corpus.
Although Majorana fermions were predicted back in 1937, the hunt for them in condensed matter began only in the last two decades, and the idea of higher-order topological insulators emerged only in 2017.
Using Majorana fermions for quantum computing evokes the fictional 'anyons' of sci-fi novels, but here the physics is becoming reality.
Key numbers
- Number of Majorana zero modes: 4
- Sample thickness in the thin direction: 2 lattice constants
- Energy gap of the topological phase: on the order of 0.01 (in hopping units)
- Sample size in the y-z plane: 80×80 lattice constants
- Superconducting pairing amplitude Δ: 0.1 (in hopping units)