Antichiral Transmission in Topological Systems

• Antichiral transmission is defined as the phenomenon where parallel boundary modes propagate in the same direction due to engineered band tilts and symmetry conditions.
• It is realized in models like the modified Haldane model and photonic gyromagnetic crystals, demonstrating high efficiency and robust unidirectional transport.
• Experimental observations include quantized conductance, high transmission efficiency under disorder, and diverse applications in topological photonics and spintronics.

Antichiral transmission refers to a class of wave propagation phenomena in which boundary modes (such as edge or hinge states) at parallel boundaries of a finite system propagate in the same direction, in marked contrast to conventional chiral transport where such modes propagate in opposite directions. Antichiral states require special symmetry conditions or engineered band structures leading to compensation via counterpropagating bulk modes. This paradigm has emerged as a robust feature across multiple platforms including electronic, photonic, and synthetic-dimension systems, with applications ranging from topological photonics to spintronics.

1. Fundamental Concepts and Model Hamiltonians

Antichiral modes arise in models where Dirac points or band extrema are shifted in energy in opposite directions, without opening a global bulk gap. A prototypical example is the modified Haldane model on a honeycomb lattice, where the phase of next-nearest-neighbor hopping is uniform rather than alternating, leading to an effective pseudoscalar term that shifts the two valleys oppositely in energy but does not gap them (Colomés et al., 2017, Mannaï et al., 2023). The corresponding low-energy Hamiltonian near Dirac points $\mathbf{K}$, $\mathbf{K}'$ is: $$H(\mathbf{q}) = \hbar v_F(\sigma_x\tau_z q_x + \sigma_y\tau_0 q_y) + t_2^a \sigma_0 \tau_z + t_2^b \sigma_0 \tau_0 + \Delta \sigma_z \tau_0$$ where $v_F$ is the Fermi velocity, $t_2^a$ shifts valleys, and $t_2^b$ shifts overall energies. In photonic gyromagnetic crystals, similar physics is accessed by implementing a "tilt" term via sublattice-biased magnetization, yielding copropagating edge states connecting shifted Dirac cones (Zhou et al., 2020).

Transfer-matrix analysis shows that edge mode dispersions $E_{\text{edge}}(k)$ bear identical group velocity signs at both parallel boundaries (Mizoguchi et al., 2020). In synthetic ladders with uniform gain/loss and gauge flux, antichiral edge currents appear due to non-Hermiticity (Ye et al., 2023).

2. Topological and Physical Origins

Unlike conventional chiral states described by a bulk Chern number, antichiral states often emerge in gapless topological semimetal phases or systems with valley-imbalanced band tilting. The topological characterization includes non-Abelian winding numbers, valley-Chern indices, or Wilson-loop invariants depending on context (Bao et al., 2022, Zhou et al., 2020, Wei et al., 21 Jun 2025, Ruiz et al., 12 Jun 2025):

• In honeycomb models, the valley-Chern number $C_v(K)-C_v(K')=1$ ensures one edge mode per valley, leading to antichiral transport when valley tilting makes group velocities agree (Zhou et al., 2020).
• In photonic/polaritonic systems, non-Abelian winding numbers distinguish edge states protected by Berry connections in gapless spectra (Bao et al., 2022).
• For Majorana modes in Rashba superconducting heterostructures, a $\mathbb{Z}_2$ Wilson-loop invariant signals the antichiral phase defined by the coexistence of Bogoliubov Fermi surfaces (Ruiz et al., 12 Jun 2025).

Physically, the net current at the boundaries is compensated by counter-propagating bulk or surface channels, preserving global current neutrality (Colomés et al., 2017, Wei et al., 21 Jun 2025).

3. Transmission Properties and Experimental Manifestations

Antichiral states yield copropagating edge or hinge channels on parallel boundaries, a feature verified across real and synthetic platforms:

• In gyromagnetic photonic crystals, antichiral edge modes circulate with robust propagation ($>$30 dB isolation), can traverse 60$^\circ$ bends without reflection, and scatter into bulk only at topologically incompatible corners (Zhou et al., 2020).
• Circuit analogs based on LC lattices directly measure edge group velocities; both boundaries show the same sign, confirmed by local probe coils tracking time-resolved pulses (Yang et al., 2020).
• In polariton honeycomb arrays, antichiral spin-polarized edge states carry distinct circular polarizations but propagate in the same direction, protected by topological invariants, with measured transmission efficiency $\sim$90% even around defects (Bao et al., 2022).
• 3D synthetic-dimension photonic systems implement tunable antichiral hinge states via controlled Hamiltonian tilt and programmable electro-optic modulation, detecting unidirectional signals at all four hinges by transmission spectroscopy (Wei et al., 21 Jun 2025).
• In non-Hermitian photonic ladders, balanced gain/loss and uniform flux produce edge currents of equal sign on both legs, linked to a nonzero spectral winding number and the non-Hermitian skin effect (Ye et al., 2023).
• In 2D proximity-induced superconductors, antichiral co-propagating Majorana edge states are identified by current-phase relation jumps and quantized zero-bias conductance plateaus (Ruiz et al., 12 Jun 2025).

4. Robustness, Fragility, and Disorder Effects

Robust antichiral transport is often argued to arise from spatial separation of edge versus bulk wavefunctions, suppressing overlap and backscattering (Colomés et al., 2017). Clean-limit conductance is quantized ($G_{\text{clean}} = 4 e^2/h$ for the modified Haldane ribbon) and survives strong disorder over macroscopic lengths (Colomés et al., 2017). However, detailed analysis shows that the absence of a bulk gap can render antichiral edge states fragile—characterized by rapid localization under moderate Anderson disorder, collapse of winding numbers, and finite inverse participation ratios above critical disorder strengths (Mannaï et al., 2023). In contrast, standard chiral edge states remain extended to much larger disorder amplitudes.

To enhance transmission efficiency, strategies include opening auxiliary bulk gaps via sublattice potentials or Floquet modulation, restoring net Chern number by stacking alternating layers, or embedding edge channels in disorder-protected environments (Mannaï et al., 2023, Cheng et al., 2021).

5. Extensions: Higher-Order Modes, Synthetic Dimensions, Non-Hermitian Dynamics

Antichiral transmission generalizes to higher-order boundary modes (hinge states) and synthetic-dimensional settings:

• Stacked Haldane models with alternating chirality across layers yield antichiral hinge states at diagonally opposite corners, tunable by relative hopping and robust up to strong disorder (Cheng et al., 2021, Wei et al., 21 Jun 2025).
• Photonic synthetic-dimension arrays utilize orbital angular momentum and frequency as synthetic spatial coordinates, with programmable transmission directions for each hinge via transversal modulation (Wei et al., 21 Jun 2025).
• Nonreciprocal or non-Hermitian hopping in bosonic ladders realizes flux-tunable transitions between chiral and antichiral regimes, with trap-skin dynamics appearing under the interplay of nonlinearity and disorder (Chen et al., 29 Oct 2024, Ye et al., 2023).
• Antichiral coplanar spin order in Mn$_3$Ge supports in-plane Goldstone modes with large group velocity and small damping—a scenario amenable to spintronic transmission applications (Chen et al., 2020).

6. Practical Applications and Prospective Directions

Antichiral transmission expands the scope of topological transport beyond conventional chirality, enabling new device concepts:

• Planar photonic circulators and frequency converters with same-direction edge ports (Zhou et al., 2020, Ye et al., 2023).
• Topologically protected spintronic channels in transition metal dichalcogenides and magnetic topological semimetals (Colomés et al., 2017, Chen et al., 2020).
• Programmable delay lines, robust couplers, and isolators in synthetic-dimension photonic chips (Wei et al., 21 Jun 2025).
• Exotic non-Hermitian devices exploiting skin effect and copropagating currents (Ye et al., 2023, Chen et al., 29 Oct 2024).
• Observation and control of Majorana edge transport in Josephson junctions with distinctive current-phase relations (Ruiz et al., 12 Jun 2025).

A plausible implication is that further development of antichiral transmission mechanisms—especially those accommodating disorder, nonlinearity, and synthetic gauge fields—will inform scalable implementations of topologically robust transport in both classical and quantum engineered platforms.