Chiral Andreev Edge States

• Chiral Andreev edge states are unidirectional Bogoliubov modes localized at interfaces between chiral electronic systems and superconductors, characterized by electron–hole mixing via Andreev reflection.
• They are modeled through diverse microscopic Hamiltonians in systems like QAHI/s-wave and quantum Hall–superconductor hybrids, revealing distinct Majorana and hybrid electron–hole features.
• Experimental signatures include quantized Andreev reflection, zero-bias peaks, and oscillatory interferometry, which provide insights into topological invariants and transport phenomena.

Searching arXiv for recent and foundational papers on chiral Andreev edge states. Chiral Andreev edge states are unidirectional Bogoliubov edge modes localized at the boundary between a chiral electronic medium and a superconductor. In a quantum anomalous Hall insulator proximitized by an $s$-wave superconductor, they are the “one-way, charge-conjugation–symmetric edge modes” that emerge when a chiral fermionic edge channel is split into co-propagating Majorana components; in quantum Hall and topological-insulator hybrids they appear as hybridized electron and hole edge modes generated by Andreev reflection in a magnetic field (Shen et al., 2018, Zhao et al., 2019, Tiwari et al., 2013). Across these settings, their defining features are chirality, electron–hole coherence, interface localization, and transport responses governed by Andreev conversion rather than by purely electronic edge propagation.

1. Conceptual definition and physical content

The term denotes edge excitations whose propagation direction is fixed by a broken time-reversal symmetry and whose Nambu structure mixes electron and hole amplitudes. In the quantum anomalous Hall context, they are described as “half” of a usual chiral fermion, because each chiral edge channel of the quantum anomalous Hall insulator splits into two co-propagating Majorana modes when superconductivity is induced (Shen et al., 2018). In integer quantum Hall–superconductor interfaces, the corresponding modes are hybridized electron and hole states similar to chiral Majorana fermions, but are commonly discussed as chiral Andreev edge states because their observable consequences are organized around Andreev reflection, crossed Andreev reflection, and electron–hole interference (Zhao et al., 2019).

A minimal one-dimensional description repeatedly appears in the literature. For a single spin-polarized chiral edge at filling $\nu=1$, one starts from

$$H_0=\int dx\,\psi^\dagger(x)\bigl[-i\hbar v_F\partial_x-\mu\bigr]\psi(x),$$

introduces the Nambu spinor $\Psi(x)=(\psi(x),\psi^\dagger(x))^T$, and adds an induced pairing term

$$H_{\rm pair}=\int dx\,\bigl[\Delta(x)\psi^\dagger(x)\psi^\dagger(x)+{\rm h.c.}\bigr].$$

The corresponding BdG Hamiltonian is

$$H_{\rm BdG}=\frac12\int dx\,\Psi^\dagger(x)\bigl[(-i\hbar v_F\partial_x-\mu)\tau_z+{\rm Re}\,\Delta(x)\tau_x-{\rm Im}\,\Delta(x)\tau_y\bigr]\Psi(x),$$

which is the standard effective description of a chiral edge proximitized by an $s$-wave superconductor (Galambos et al., 2022). Closely related one-dimensional edge Hamiltonians also underlie analyses of quantum Hall weak links and interference devices (Alavirad et al., 2018).

The physical interpretation depends on platform. In a QAHI/$s$-wave heterostructure, the modes are topological edge excitations of a two-dimensional class-D superconductor. In QH/$s$-wave devices, they are coherent interface channels formed by repeated Andreev processes along a magnetic edge, with transport controlled by phase accumulation and interface coupling. In Dirac NS junctions under perpendicular field, they arise within each Landau level from the hybridization of electron-like and hole-like Landau levels (Tiwari et al., 2013). This suggests that “chiral Andreev edge state” is a unifying interface concept rather than the name of a single microscopic phase.

2. Microscopic Hamiltonians and interface formation mechanisms

Several microscopic realizations appear in the literature, all formulated in BdG language but differing in how the superconducting correlations are induced.

In magnetic topological-insulator thin films realizing the quantum anomalous Hall effect, the normal-state Hamiltonian is built from top and bottom surface Dirac cones with exchange splitting and hybridization. In the basis

$$\Psi_k=(c_{t,\uparrow},c_{t,\downarrow},c_{b,\uparrow},c_{b,\downarrow})^T,$$

the normal-state block is

$\nu=1$0

with $\nu=1$1. Adding pairing only on the top surface, $\nu=1$2, $\nu=1$3, yields the BdG Hamiltonian

$\nu=1$4

where $\nu=1$5 (Shen et al., 2018). In this platform the proximitized edge supports chiral Majorana edge modes, experimentally probed by Andreev-reflection spectroscopy.

In a quantum Hall bar with a superconducting finger, the proximitized edge is instead generated by nonlocal pairing between spatially separated chiral edges on opposite sides of the finger. The induced pairing amplitude is attributed to crossed Andreev reflection and is weighted by the Meissner-generated in-plane field: $\nu=1$6 Here the Meissner effect distorts the perpendicular magnetic field close to the QH–SC boundary and produces an in-plane component that cants the edge spins, enabling singlet pairing without invoking spin–orbit coupling or nontrivial magnetic textures (Galambos et al., 2022).

A complementary microscopic derivation integrates out a superconductor that has both Rashba spin–orbit coupling and a Meissner screening current. Starting from an $\nu=1$7-wave SC Hamiltonian with orbital coupling, surface Rashba SOC, and gap $\nu=1$8, coupled by tunneling to a $\nu=1$9 QH edge, one obtains

$$H_0=\int dx\,\psi^\dagger(x)\bigl[-i\hbar v_F\partial_x-\mu\bigr]\psi(x),$$0

with leading odd-parity pairing

$$H_0=\int dx\,\psi^\dagger(x)\bigl[-i\hbar v_F\partial_x-\mu\bigr]\psi(x),$$1

In this formulation both Rashba SOC and the Meissner supercurrent are essential, because the former provides spin mixing and the latter shifts the Cooper-pair momentum by $$H_0=\int dx\,\psi^\dagger(x)\bigl[-i\hbar v_F\partial_x-\mu\bigr]\psi(x),$$2, enabling momentum-conserving Andreev processes between $$H_0=\int dx\,\psi^\dagger(x)\bigl[-i\hbar v_F\partial_x-\mu\bigr]\psi(x),$$3 and $$H_0=\int dx\,\psi^\dagger(x)\bigl[-i\hbar v_F\partial_x-\mu\bigr]\psi(x),$$4 sectors of the chiral edge (Michelsen et al., 2022).

For a two-dimensional electron gas proximitized by an $$H_0=\int dx\,\psi^\dagger(x)\bigl[-i\hbar v_F\partial_x-\mu\bigr]\psi(x),$$5-wave superconductor, a continuum BdG Hamiltonian with London screening and interface transparency takes the form

$$H_0=\int dx\,\psi^\dagger(x)\bigl[-i\hbar v_F\partial_x-\mu\bigr]\psi(x),$$6

which exposes the class-C structure relevant for spin transport (Parfenov et al., 7 May 2026). A later spinful treatment adds Zeeman and Rashba terms explicitly,

$$H_0=\int dx\,\psi^\dagger(x)\bigl[-i\hbar v_F\partial_x-\mu\bigr]\psi(x),$$7

and emphasizes orbital and spin mixing of chiral Andreev bands at higher filling factors (Maji et al., 18 May 2026).

In weak-field Rashba 2DEGs, the same interface physics can be viewed semiclassically. The proximitized boundary supports skipping orbits with alternating electron–hole character and helicity-dependent cyclotron radii $$H_0=\int dx\,\psi^\dagger(x)\bigl[-i\hbar v_F\partial_x-\mu\bigr]\psi(x),$$8, which makes the Andreev edge dynamics directly imageable in magnetic focusing setups (Gavensky et al., 2021).

3. Topological classification and edge spectra

The topological content depends on the Altland–Zirnbauer class and on whether the proximitized phase is a bulk topological superconductor or an interface channel embedded in an otherwise normal system.

For QAHI/$$H_0=\int dx\,\psi^\dagger(x)\bigl[-i\hbar v_F\partial_x-\mu\bigr]\psi(x),$$9-wave structures, the relevant symmetry class is class D, with Chern number

$\Psi(x)=(\psi(x),\psi^\dagger(x))^T$0

The standard phase sequence is $\Psi(x)=(\psi(x),\psi^\dagger(x))^T$1, then $\Psi(x)=(\psi(x),\psi^\dagger(x))^T$2, then $\Psi(x)=(\psi(x),\psi^\dagger(x))^T$3 as the exchange gap is tuned through successive bulk gap closings (Shen et al., 2018). In a lattice QAHS+$\Psi(x)=(\psi(x),\psi^\dagger(x))^T$4-wave model, the bulk gap closes at $\Psi(x)=(\psi(x),\psi^\dagger(x))^T$5, yielding

$\Psi(x)=(\psi(x),\psi^\dagger(x))^T$6

The integer $\Psi(x)=(\psi(x),\psi^\dagger(x))^T$7 counts the net number of chiral Majorana edge modes (Ii et al., 2011).

The dispersions reflect this topology. In the $\Psi(x)=(\psi(x),\psi^\dagger(x))^T$8 phase, there is exactly one mode crossing zero energy,

$\Psi(x)=(\psi(x),\psi^\dagger(x))^T$9

where $$H_{\rm pair}=\int dx\,\bigl[\Delta(x)\psi^\dagger(x)\psi^\dagger(x)+{\rm h.c.}\bigr].$$0. In the $$H_{\rm pair}=\int dx\,\bigl[\Delta(x)\psi^\dagger(x)\psi^\dagger(x)+{\rm h.c.}\bigr].$$1 phase, two branches exist, approximately

$$H_{\rm pair}=\int dx\,\bigl[\Delta(x)\psi^\dagger(x)\psi^\dagger(x)+{\rm h.c.}\bigr].$$2

described as two copropagating Majorana modes (Shen et al., 2018). The corresponding edge-local density of states develops zero-bias weight in the topological sectors and is fully gapped in the trivial phase (Ii et al., 2011).

At a quantum Hall–superconductor interface, one commonly speaks of chiral Andreev edge states even when the bulk topology is not phrased in terms of a class-D Chern number. A finite superconducting segment hybridizes the electron and hole edge modes into two chiral interface modes whose outgoing electron and hole content oscillates with their phase difference. In the simplest spinless treatment, the zero-energy interface eigenstates are

$$H_{\rm pair}=\int dx\,\bigl[\Delta(x)\psi^\dagger(x)\psi^\dagger(x)+{\rm h.c.}\bigr].$$3

and their interference produces Andreev conversion with probability determined by the wave-vector difference $$H_{\rm pair}=\int dx\,\bigl[\Delta(x)\psi^\dagger(x)\psi^\dagger(x)+{\rm h.c.}\bigr].$$4 (Maji et al., 18 May 2026). The same two-mode picture underlies the scattering theory of interference devices (Zhao et al., 2019).

In Dirac NS junctions on a 3D topological-insulator surface, the interface supports a dispersive family $$H_{\rm pair}=\int dx\,\bigl[\Delta(x)\psi^\dagger(x)\psi^\dagger(x)+{\rm h.c.}\bigr].$$5 within each Landau-level gap, satisfying

$$H_{\rm pair}=\int dx\,\bigl[\Delta(x)\psi^\dagger(x)\psi^\dagger(x)+{\rm h.c.}\bigr].$$6

For $$H_{\rm pair}=\int dx\,\bigl[\Delta(x)\psi^\dagger(x)\psi^\dagger(x)+{\rm h.c.}\bigr].$$7, one recovers the zero-energy Majorana mode at $$H_{\rm pair}=\int dx\,\bigl[\Delta(x)\psi^\dagger(x)\psi^\dagger(x)+{\rm h.c.}\bigr].$$8. When the superconducting chemical potential exceeds $$H_{\rm pair}=\int dx\,\bigl[\Delta(x)\psi^\dagger(x)\psi^\dagger(x)+{\rm h.c.}\bigr].$$9, the $$H_{\rm BdG}=\frac12\int dx\,\Psi^\dagger(x)\bigl[(-i\hbar v_F\partial_x-\mu)\tau_z+{\rm Re}\,\Delta(x)\tau_x-{\rm Im}\,\Delta(x)\tau_y\bigr]\Psi(x),$$0 and $$H_{\rm BdG}=\frac12\int dx\,\Psi^\dagger(x)\bigl[(-i\hbar v_F\partial_x-\mu)\tau_z+{\rm Re}\,\Delta(x)\tau_x-{\rm Im}\,\Delta(x)\tau_y\bigr]\Psi(x),$$1 branches anticross at finite $$H_{\rm BdG}=\frac12\int dx\,\Psi^\dagger(x)\bigl[(-i\hbar v_F\partial_x-\mu)\tau_z+{\rm Re}\,\Delta(x)\tau_x-{\rm Im}\,\Delta(x)\tau_y\bigr]\Psi(x),$$2, and the effective Nambu charge

$$H_{\rm BdG}=\frac12\int dx\,\Psi^\dagger(x)\bigl[(-i\hbar v_F\partial_x-\mu)\tau_z+{\rm Re}\,\Delta(x)\tau_x-{\rm Im}\,\Delta(x)\tau_y\bigr]\Psi(x),$$3

can vanish at finite guiding-center coordinate. The resulting charge-neutral propagating modes are a distinct subtype of chiral Andreev edge state (Tiwari et al., 2013).

For 2DEG–superconductor hybrids without Zeeman splitting, the symmetry class is class C rather than class D. The two-dimensional bulk then has a $$H_{\rm BdG}=\frac12\int dx\,\Psi^\dagger(x)\bigl[(-i\hbar v_F\partial_x-\mu)\tau_z+{\rm Re}\,\Delta(x)\tau_x-{\rm Im}\,\Delta(x)\tau_y\bigr]\Psi(x),$$4 topological invariant, and the protected edge content is most sharply expressed through spin transport: the even-integer invariant guarantees $$H_{\rm BdG}=\frac12\int dx\,\Psi^\dagger(x)\bigl[(-i\hbar v_F\partial_x-\mu)\tau_z+{\rm Re}\,\Delta(x)\tau_x-{\rm Im}\,\Delta(x)\tau_y\bigr]\Psi(x),$$5 chiral edge modes and a quantized transverse spin response rather than a quantized charge conductance (Parfenov et al., 7 May 2026).

4. Andreev processes, chirality, and gap generation

The central microscopic process is Andreev conversion constrained by chirality. At a conventional NS boundary, an incoming electron can be retroreflected into a hole on the same side. At a chiral boundary this process is modified because backscattering is restricted or absent.

In QH–SC systems with a superconducting finger, an incident wave on the left edge can emerge on the opposite edge as a hole with crossed Andreev reflection amplitude $$H_{\rm BdG}=\frac12\int dx\,\Psi^\dagger(x)\bigl[(-i\hbar v_F\partial_x-\mu)\tau_z+{\rm Re}\,\Delta(x)\tau_x-{\rm Im}\,\Delta(x)\tau_y\bigr]\Psi(x),$$6, or as an electron with co-tunneling amplitude $$H_{\rm BdG}=\frac12\int dx\,\Psi^\dagger(x)\bigl[(-i\hbar v_F\partial_x-\mu)\tau_z+{\rm Re}\,\Delta(x)\tau_x-{\rm Im}\,\Delta(x)\tau_y\bigr]\Psi(x),$$7, with chirality and unitarity implying $$H_{\rm BdG}=\frac12\int dx\,\Psi^\dagger(x)\bigl[(-i\hbar v_F\partial_x-\mu)\tau_z+{\rm Re}\,\Delta(x)\tau_x-{\rm Im}\,\Delta(x)\tau_y\bigr]\Psi(x),$$8 (Galambos et al., 2022). The effective CAR amplitude opens a spectral gap,

$$H_{\rm BdG}=\frac12\int dx\,\Psi^\dagger(x)\bigl[(-i\hbar v_F\partial_x-\mu)\tau_z+{\rm Re}\,\Delta(x)\tau_x-{\rm Im}\,\Delta(x)\tau_y\bigr]\Psi(x),$$9

In the weak-coupling regime,

$s$0

so that

$s$1

The dependence on $s$2, $s$3, and $s$4 identifies the gap as a nonlocal pairing effect set by finger geometry and spin canting (Galambos et al., 2022).

A different microscopic route reaches a formally $s$5-wave effective edge Hamiltonian by integrating out a Rashba-coupled superconductor carrying a screening current. Linearizing about the Fermi point yields

$s$6

with $s$7. This is explicitly odd in momentum through $s$8, and the paper identifies it with the Kitaev $s$9-wave chain at $s$0, so that domain walls in the induced pairing can bind Majorana zero modes (Michelsen et al., 2022).

In weak-field focusing geometries, the same chirality is described in terms of skipping orbits. For a transparent interface and $s$1,

$s$2

while $s$3 vanishes. Each Andreev bounce flips charge and spin simultaneously,

$s$4

or on the other helicity branch,

$s$5

and backscattering is forbidden because the motion is unidirectional (Gavensky et al., 2021). This formulation emphasizes that chiral Andreev edge states may be gap-opening interface bands in one regime and coherent alternating electron–hole skipping trajectories in another.

For quantum Hall weak links carrying Josephson current, chirality imposes an additional restriction: a single edge alone cannot mediate supercurrent. The exact Green’s-function analysis shows that only a pair of counter-propagating edges can transfer a Cooper pair across the device, establishing the strict sense in which the supercurrent is “chiral” (Alavirad et al., 2018). This suggests that chirality constrains not only the existence of Andreev edge states but also which nonlocal superconducting processes remain kinematically allowed.

5. Transport, spectroscopy, and interference signatures

The most direct observables are differential conductance, nonlocal resistance, local density of states, and Josephson interferometry.

In QAHI/$s$6-wave heterostructures, the zero-temperature Andreev-reflection conductance for a single normal lead coupled to the edge is

$s$7

With one chiral Majorana mode,

$s$8

which appears as a quantized plateau $s$9 for $s$0. In the $s$1 phase, two Majorana amplitudes cancel at zero bias to lowest order, giving

$s$2

namely a zero-bias dip flanked by peaks (Shen et al., 2018). Experimentally, field sweeps through magnetization reversal produce the sequence “dip + peaks $s$3 plateau $s$4 zero $s$5 plateau $s$6 dip + peaks,” mapping onto $s$7 (Shen et al., 2018).

In three-terminal QH–SC devices, nonlocal transport is controlled by the competition between normal transmission and Andreev conversion. For the superconducting-finger geometry at $s$8,

$s$9

with $$\Psi_k=(c_{t,\uparrow},c_{t,\downarrow},c_{b,\uparrow},c_{b,\downarrow})^T,$$0, $$\Psi_k=(c_{t,\uparrow},c_{t,\downarrow},c_{b,\uparrow},c_{b,\downarrow})^T,$$1, and $$\Psi_k=(c_{t,\uparrow},c_{t,\downarrow},c_{b,\uparrow},c_{b,\downarrow})^T,$$2. A negative downstream resistance requires $$\Psi_k=(c_{t,\uparrow},c_{t,\downarrow},c_{b,\uparrow},c_{b,\downarrow})^T,$$3, and numerical transport shows $$\Psi_k=(c_{t,\uparrow},c_{t,\downarrow},c_{b,\uparrow},c_{b,\downarrow})^T,$$4 dips approaching $$\Psi_k=(c_{t,\uparrow},c_{t,\downarrow},c_{b,\uparrow},c_{b,\downarrow})^T,$$5 when crossed Andreev reflection is strong (Galambos et al., 2022). In the supercurrent-enabled edge theory, a related generalized Landauer–Büttiker argument gives

$$\Psi_k=(c_{t,\uparrow},c_{t,\downarrow},c_{b,\uparrow},c_{b,\downarrow})^T,$$6

so the downstream resistance becomes negative once the particle-to-hole transmission probability exceeds $$\Psi_k=(c_{t,\uparrow},c_{t,\downarrow},c_{b,\uparrow},c_{b,\downarrow})^T,$$7 (Michelsen et al., 2022).

Interference of the two chiral Andreev interface modes generates gate-, field-, and bias-dependent oscillations. For a superconducting segment of length $$\Psi_k=(c_{t,\uparrow},c_{t,\downarrow},c_{b,\uparrow},c_{b,\downarrow})^T,$$8, the scattering matrix can be written in terms of the accumulated phase $$\Psi_k=(c_{t,\uparrow},c_{t,\downarrow},c_{b,\uparrow},c_{b,\downarrow})^T,$$9 as

$\nu=1$00

so that the outgoing hole probability is

$\nu=1$01

The downstream resistance therefore oscillates with $\nu=1$02, directly revealing coherent electron–hole conversion over the interface (Zhao et al., 2019).

Local spectroscopy provides an additional diagnostic. For a finite superconducting finger, the retarded Green’s function yields

$\nu=1$03

Numerically, a robust zero-bias peak appears at the tip of the finger when $\nu=1$04, and disorder in $\nu=1$05 up to several $\nu=1$06 barely shifts the zero mode. The result is described as compatible with the emergence of a Majorana bound state (Galambos et al., 2022).

In Josephson weak links, the supercurrent itself is a probe of chiral Andreev transport. The current–phase relation derived for a chiral QH weak link has period $\nu=1$07, and the critical current oscillates with external flux with doubled period relative to conventional junctions (Alavirad et al., 2018). A conceptually similar $\nu=1$08 periodicity also appears in phase-sensitive Josephson interferometry on Al/Ni multilayers, where period-doubled $\nu=1$09, an upward offset, and edge-localized reconstructed $\nu=1$10 profiles are interpreted as evidence for chiral Andreev edge transport mediated by opposite-edge electron and hole propagation (Belogolovskii et al., 28 Jul 2025).

6. Spin structure, disorder, and extensions

Spin structure is platform-dependent and strongly affects what is protected. In the $\nu=1$11 superconducting-finger proposal, the edge is initially spin-polarized, and pairing is enabled by Meissner-induced spin canting rather than by intrinsic spin–orbit coupling (Galambos et al., 2022). In the many-body derivation with Rashba SOC and Meissner supercurrent, both ingredients are essential: without SOC the spin-polarized edge cannot inherit singlet pairing, and without the supercurrent the momentum mismatch blocks the relevant Andreev channel (Michelsen et al., 2022).

At $\nu=1$12, two co-propagating edge channels allow both singlet and triplet superconducting correlations. Diagonalizing the normal edge Hamiltonian with Zeeman and Rashba terms yields an inter-edge singlet amplitude

$\nu=1$13

and an intra-edge triplet amplitude

$\nu=1$14

The resulting low-energy BdG Hamiltonian contains both $\nu=1$15 and $\nu=1$16, so the chiral Andreev states can interpolate between pure inter-edge singlet physics and emergent $\nu=1$17-wave-like intra-edge pairing (Arrachea et al., 2023). The non-linear conductance and zero-frequency noise distinguish these regimes: a purely singlet edge yields constant $\nu=1$18, while the triplet component produces a $\nu=1$19-dependence and suppresses the zero-bias slope of the noise (Arrachea et al., 2023).

Disorder and multimode mixing do not affect all observables equally. In class-C 2DEG–S hybrids, the charge conductance of the chiral Andreev edge states is described as non-integer-quantized and disorder sensitive, but the transverse spin conductance is exactly quantized. Each BdG edge branch contributes

$\nu=1$20

and the total spin conductance is

$\nu=1$21

with the quantization enforced by the Wess–Zumino term of the class-C nonlinear $\nu=1$22-model even in the presence of strong Andreev disorder (Parfenov et al., 7 May 2026). This reinterprets “topological protection” as protection in the spin channel rather than in charge transport.

A spinful multimode BdG treatment of QH–SC interfaces shows that Andreev reflection can mix orbital edge modes at higher filling factors, even though such mixing is prohibited in clean purely electronic QH systems. With only perpendicular Zeeman splitting, the chiral Andreev bands separate into orthogonal spin sectors $\nu=1$23 and $\nu=1$24, but the combination of Rashba SOC and an in-plane field hybridizes all four bands and produces multiple conductance frequencies. The same analysis derives exact equalities among transmission probabilities from unitarity and particle–hole symmetry of the scattering matrix (Maji et al., 18 May 2026).

The concept also extends beyond canonical QH/QAH platforms. In a superconductor–topological-insulator NS junction, Andreev coupling between Landau levels produces neutral propagating edge modes that carry heat but no net charge (Tiwari et al., 2013). In chiral superconductors such as a $\nu=1$25 state, rough surfaces broaden and shift the surface Andreev bound-state band, opening a sub-gap $\nu=1$26 through second-order repulsion between bound states and propagating Bogoliubov quasiparticles (Nagato et al., 2011). In Kagome chiral-flux-phase topological superconductors, ribbon spectra can display mixed-chirality edge branches even when the net chirality remains fixed by the BdG Chern number, and two-terminal transport exhibits plateau values in $\nu=1$27 associated with the edge-mode content (Zeng et al., 2023). In artificially engineered Al/Ni multilayers, phase-sensitive Josephson interferometry has been interpreted as possible evidence for edge-localized one-way chiral Andreev channels despite the absence of strong spin–orbit coupling or intrinsic topological band structure (Belogolovskii et al., 28 Jul 2025).

A common misconception is that all chiral Andreev edge states are identical to isolated Majorana modes. The literature distinguishes several cases: true chiral Majorana edge modes in class-D QAHI/$\nu=1$28-wave superconductors (Shen et al., 2018, Ii et al., 2011), hybridized electron–hole QH interface modes whose interference mimics Majorana phenomenology without necessarily constituting a bulk topological superconductor (Zhao et al., 2019), neutral finite-$\nu=1$29 modes generated by Landau-level anticrossing (Tiwari et al., 2013), and class-C Andreev edges whose robust quantization appears in spin rather than charge transport (Parfenov et al., 7 May 2026). The shared structure is chirality plus Andreev-induced electron–hole coherence; the topological invariant, protected observable, and microscopic pairing mechanism vary across platforms.