Antiferromagnetic Superlattices in 2D Materials

• Antiferromagnetic superlattices (AFSL) are engineered 2D materials that impose periodic antiferromagnetic exchange, creating tunable spin–valley polarization and miniband structures.
• They produce valley-polarized minibands and anisotropic band dispersions that enable directional, supercollimated electron transport and controlled group velocity modulation.
• AFSLs form the basis for symmetry-protected spin–valley valves, offering electrically tunable platforms for advanced spintronics, valleytronics, and nano-electronic applications.

Antiferromagnetic superlattices (AFSL) are engineered structures where periodic antiferromagnetic exchange fields are imposed on a host material—often buckled hexagonal two-dimensional (2D) systems—through proximity effects, such as the periodic deposition of antiferromagnets. This approach leads to miniband formation, spin–valley polarization, and pronounced conduction anisotropy, all of which are tunable via electrical and structural parameters. AFSLs serve as a platform for realizing symmetry-protected spin–valley valves, providing an alternative pathway for the electric-field control of quantum degrees of freedom in 2D materials (Lu et al., 4 Sep 2025).

1. Fundamental Hamiltonian and Symmetry Principles

The low-energy electronic structure in AFSLs on buckled 2D hexagonal materials is governed by a generalized Dirac Hamiltonian: $$H_{(\eta,s)} = \hbar v_F (k_x \sigma_x - \eta k_y \sigma_y) + (\lambda_z + s\lambda_{\mathrm{AF}} - \eta s\lambda_{\mathrm{SO}}) \sigma_z + U$$ where

• $\eta = \pm1$ labels $K$ and $K'$ valleys,
• $s = \pm1$ denotes spin,
• $v_F$ is the Fermi velocity,
• $\lambda_z = \ell E_z$ is the sublattice-staggered potential due to a perpendicular electric field $E_z$ and buckling height $\ell$,
• $\lambda_{\mathrm{AF}}$ quantifies the AF proximity exchange,
• $\lambda_{\mathrm{SO}}$ is the intrinsic spin–orbit coupling (SOC),
• $U$ is an external, gate-controlled potential.

The term $$(\lambda_z + s\lambda_{\mathrm{AF}} - \eta s\lambda_{\mathrm{SO}})$$, denoted as $\Delta_{(\eta,s)}$, sets the local band gap at each valley and spin channel. This symmetry reduction, particularly under combined $\lambda_z$ and $\lambda_{\mathrm{AF}}$, lifts both spin and valley degeneracies and enables full manipulation of the system’s topological and transport character.

The symmetry of spin–valley polarization is analyzed through the combined effect of pseudospin rotations and spatial inversion. The AF configuration differs fundamentally from the FM case: while FM proximity lifts only spin degeneracy, AF proximity breaks valley symmetry as well, creating unbalanced populations in distinct $K$ and $K'$ channels.

2. Valley-Polarized and Spin–Valley-Polarized Minibands

AFSLs induce valley-polarized minibands even without external electric field $(\lambda_z = 0)$. The eigenvalues are: $$E_{(\eta,s)} = U \pm \sqrt{\Delta_{(\eta,s)}^2 + (\hbar v_F k_F)^2}$$ where $k_F$ is the Fermi wavevector. The band gap: $$\Delta_{(\eta, s)} = \lambda_z + s\lambda_{\mathrm{AF}} - \eta s\lambda_{\mathrm{SO}}$$ directly links valley and spin, so that the presence of $\lambda_{\mathrm{AF}}$ alone already yields conductance and spectral features that break valley symmetry for fixed spin. This is not obtainable in purely FM-proximitized systems.

Applying both $\lambda_z$ and $\lambda_{\mathrm{AF}}$ lifts all (spin and valley) degeneracies, allowing complete spin–valley polarization of both the miniband structure and the resulting conductance. The polarization is symmetry-protected: using appropriate pseudospin and inversion operations, the conductance in one spin–valley branch is suppressed when the others are open, providing functionality akin to a spin–valley filter.

Critical gap-closing conditions exist at: $$\lambda_z + s\lambda_{\mathrm{AF}} = 2\eta s\lambda_{\mathrm{SO}}$$ yielding topological transitions in band structure and transport, operationally controlled by field and gate tuning.

3. Anisotropic Band Dispersion and Group Velocity Control

A key consequence of AFSL structuring, in conjunction with SOC, is the emergence of highly anisotropic band dispersions. For an infinite AFSL, the group velocities along the in-plane directions are

$$v_x = \frac{\partial E_{(\eta,s)}}{\partial k_x}, \quad v_y = \frac{\partial E_{(\eta,s)}}{\partial k_y}$$

In this system, $v_y$ (perpendicular to the superlattice periodicity) remains unchanged, retaining the baseline $v_F$. In contrast, $v_x$ (parallel to the modulation) is strongly renormalized and can be made arbitrarily small by increasing $\lambda_{\mathrm{SO}}$ and $\lambda_{\mathrm{AF}}$ or tuning the external gates. This regime yields band flattening along $k_x$ and enables electronic supercollimation—a sharply directional, quasi-1D current propagation—which is fundamentally distinct from the anisotropy in, for example, monolayer graphene superlattices where $v_x$ is unperturbed.

By dynamically varying $\lambda_z$, $\lambda_{\mathrm{AF}}$, and $U$ (all achievable via gating and material engineering), one can also rotate or reshape the direction of maximum group velocity, providing an added design parameter for controlling electron optics in 2D systems.

4. Spin–Valley Valve Functionality and Device Implications

The complete lifting of spin and valley degeneracies in AFSLs under suitable $\lambda_z$, $\lambda_{\mathrm{AF}}$, and $\lambda_{\mathrm{SO}}$ creates the basis for a “spin–valley valve” (Editor's term): a transport device where only a desired spin–valley channel contributes to conduction, and where the “open” channel is selected by gate voltages. The operation principle is symmetry-protected (i.e., robust to weak disorder and symmetry-conserving perturbations), and can be switched or tuned entirely by electrical means.

In this configuration, miniband conduction is quantized according to channel selection rules—opening prospects for electrically tunable spintronics, valleytronics, and supercollimated electronic transport for information routing at the nanoscale.

5. Control via Antiferromagnetic Proximity and SOC

Achieving the requisite AF exchange field ($\lambda_{\mathrm{AF}}$) relies on the proximity effect—depositing periodic antiferromagnetic nanostructures on the target buckled 2D material. Unlike magnetic doping, this route avoids disorder and preserves carrier mobility while implementing strong time-reversal symmetry breaking in a way that is distinct from conventional FM cases.

The critical feature in buckled honeycomb materials (e.g., silicene, germanene) is their sizable and tunable intrinsic SOC, which entangles spin and valley degrees of freedom and responds directly to $\lambda_{\mathrm{AF}}$ and $\lambda_z$. This coupling is inseparable from the transport and spectral effects of AFSLs and remains a major source of flexibility in device design.

6. Perspectives and Engineering Opportunities

AFSLs, as demonstrated in (Lu et al., 4 Sep 2025), provide a versatile means to engineer the band topology, group velocity anisotropy, and spin–valley quantum numbers in 2D materials via structural and electrical control. These results establish clear design principles for the implementation of spin–valley valves whose operation hinges not on chemical modification but on the precise tuning of proximity-induced fields and gate voltages.

The fact that band flattening and group velocity engineering can be tuned for preferred directions without degradation of in-plane mobility opens promising avenues for supercollimated electronics, ballistic quantum wires, valleytronic logic gates, and other quantum information devices. The symmetry-protected switching mechanisms further enlarge the reliability and selectivity of such devices in practical architectures.

In summary, AFSLs represent a robust and highly tunable platform for the realization of symmetry-controlled, anisotropic, and spin–valley-polarized functionalities in 2D materials, and provide blueprints for next-generation devices at the intersection of spintronics, valleytronics, and nano-electronic engineering.