Orthogonally-Twisted vdW Heterostructures

• Orthogonally-twisted vdW heterostructures are engineered 2D materials stacked with a 90° twist to form large moiré superlattices with distinct interlayer interactions.
• They enable controlled tuning of electronic, topological, magnetic, and superconducting properties through symmetry breaking and momentum-selective tunneling.
• Advanced techniques like 4D STEM and deterministic stacking reveal strain solitons and domain formations, paving the way for novel spintronic and quantum devices.

Orthogonally-twisted van der Waals (vdW) heterostructures are artificial materials formed by stacking atomically thin layers with a deliberate in-plane rotation, typically 90°, between adjacent crystals. This structural motif leverages the intrinsic symmetry, lattice mismatch, and chemical diversity of layered solids—such as graphene, transition metal dichalcogenides (TMDs), magnetic semiconductors, superconductors, or metal–organic frameworks—to generate new quantum phenomena through moiré superlattices, control of interlayer tunneling, anisotropic transport, topological defect engineering, and manipulation of collective states. The properties of these systems arise from a complex interplay between the symmetry breaking induced by the orthogonal twist, momentum-selective tunneling, emergent interfacial interactions, and tunable band structures. Below, a comprehensive overview is provided, spanning topological, electronic, magnetic, superconducting, optical, mechanical, and device-oriented dimensions of these heterostructures, as elucidated by contemporary experimental and theoretical studies.

1. Structural Motifs, Moiré Patterns, and Twist-Angle Control

Orthogonally-twisted vdW heterostructures are realized by stacking two or more 2D layers with a relative rotation angle θ ≈ 90°. This orthogonal alignment breaks the symmetry present in commensurate or small-angle twisted structures and frequently leads to the formation of a large moiré superlattice. The superlattice periodicity is governed by both the twist angle and the inherent lattice constants, as described by:

$$L = \frac{a}{2\sin\left(\frac{\theta_{\rm twist}}{2}\right)},$$

where $a$ is the relevant lattice constant and $\theta_{\rm twist}$ is the twist angle (Maßmeyer et al., 8 Feb 2024).

Epitaxial relationships can be controlled via bottom-up growth (as in WS$_2$/graphene by MOCVD) or by deterministic mechanical stacking, with the twist angle defined locally by the orientations $\varphi$ of the respective layers:

$$\theta_{\mathrm{twist}} = |\varphi_{\rm WS_2} - \varphi_{\rm Gr}|.$$

Local twist-angle variation is influenced by grain boundaries (GBs), which serve as templates determining nucleation and produce domains with distinct moiré periodicities and spatially varying stacking registries (Maßmeyer et al., 8 Feb 2024). State-of-the-art 4D STEM and scanning nanobeam diffraction enable direct visualization and quantification of moiré patterns, grain orientations, and stacking-induced modulation.

At a larger scale, the formation of long-wavelength moiré patterns in orthogonally-twisted structures produces spatially modulated electronic and topological properties. Structural relaxation, dislocation network formation, and symmetry breaking due to the misalignment and elasticity mismatch are captured quantitatively by bicrystallography-informed Frenkel–Kontorova models, which relate moiré periodicity and strain solitons to twist angle and lattice mismatch (Ahmed et al., 2023).

2. Topological and Electronic Properties

The orthogonal twist introduces a profound modulation of the local potential landscape, often transforming topologically trivial states into nontrivial phases. In buckled honeycomb materials (germanene, stanene, silicene) supported on h‑BN, the rotation relieves lattice mismatch and generates spatially varying staggered potentials. This gives rise to massive Dirac systems whose Hamiltonian near the $K/K'$ valleys can be written as:

$$H_{\rm eff} = v_F (\tau_z k_x \sigma_x - k_y \sigma_y) + [t_{\rm so} \tau_z s_z + U_{h{\text–}BN} + U_{EF}] \, \sigma_z,$$

with $v_F$ the Fermi velocity, $\tau_z$ the valley index, $s_z$ the spin index, $t_{\rm so}$ the intrinsic spin–orbit coupling, $U_{h{\text–}BN}$ the substrate-induced staggered potential, and $U_{EF}$ an external field (Wang et al., 2016).

The spatial modulation of the mass term $M(\tau_z, s_z)$ results in patterned regions of differing Chern number and $Z_2$ index, enabling the appearance of topological domain walls with protected, valley-polarized helical modes. The analytic form of their topological charge jump,

$$C^{\rm DW}(\tau_z, s_z) = \frac{\tau_z}{2} [\text{sgn}(M^L) - \text{sgn}(M^R)],$$

captures the emergence of Jackiw–Rebbi modes at mass inversion boundaries.

In incommensurate TMD heterobilayers with periodic moiré superlattices, periodic modulation of local band topology further produces a mosaic pattern of topological insulator (TI) and normal insulator (NI) domains, with robust helical edge channels at their interface. These can be programmed electrically via interlayer bias, enabling switchable and reconfigurable topological nano-dot or nano-stripe networks (Tong et al., 2016).

Analogously, twisted bilayer graphene offers a general theoretical backdrop: orthogonal twists (90°) generate complex moiré interference patterns that renormalize the Fermi velocity, lead to new van Hove singularities, and tailor the optical conductivity and plasmonic response. These concepts, formalized via generalized umklapp conditions and continuum models,

$$v_{F}^{*}(\theta)/v_{F} = 1-\frac{9\alpha^2}{4\sin^2(\theta/2)},$$

translate directly to other orthogonally-twisted heterostructures (Catarina et al., 2019).

3. Magnetic Anisotropy, Exchange Bias, and Programmable Magnetism

Orthogonally-twisted magnets, particularly those based on CrSBr, Fe$_3$GeTe$_2$ (FGT), and other 2D magnetic semiconductors, exemplify the power of anisotropy engineering via stacking. In 90°-twisted CrSBr bilayers, strong in-plane easy-axis anisotropy along mutually orthogonal axes creates a scenario where each monolayer’s magnetization is energetically pinned along a different direction (Boix-Constant et al., 2023, Healey et al., 24 Oct 2024). This allows for competition between abrupt spin-flip and gradual spin-reorientation mechanisms, producing multistep magnetization switching, programmable magnetic hysteresis, and the ability to toggle between volatile and non-volatile magnetic memory states (Boix-Constant et al., 28 Oct 2024). The effective Hamiltonian including exchange, anisotropy, Zeeman, and dipolar terms,

$$H = -\sum_{ij} J_{ij} (\mathbf{S}_i \cdot \mathbf{S}_j) + \sum_{ij} \mathbf{D}_{ij} \cdot (\mathbf{S}_i \times \mathbf{S}_j) - K(\mathbf{S} \cdot \mathbf{\hat{a}})^2 - 2\mu_s (\mathbf{S} \cdot \mathbf{B}) + H_{\rm dipole},$$

captures the competition leading to canted and non-collinear magnetic textures.

In antiferromagnet/ferromagnet heterostructures (CrSBr/FGT), orthogonal magnetic anisotropies (out-of-plane in FGT, in-plane in CrSBr) induce interfacial exchange bias and asymmetric magnetization reversal. Switchable and robust exchange bias—quantified by an offset in the coercive field,

$H_{e_b} = (H_C^+ + H_C^-)/2,$

is mediated by correlated stripe-like domain formation and persists up to the $T_N$ of CrSBr (132 K). Off-axis electron holography reveals stabilization of three-dimensional flux-closure domains in FGT, induced by interfacial exchange from CrSBr, and the maintenance of the bulk antiferromagnetic order with a secondary c-axis canting (Kumar et al., 31 Jul 2025).

These results articulate a general principle: orthogonal twists can be exploited to program domain wall structure, coupling strength, and switching fields, enriching the portfolio of operations for spintronic, magnonic, and memory devices.

4. Superconducting and Quantum-Coherent States

Orthogonally-twisted Josephson junctions formed by cuprate (BSCCO) or NbSe$_2$ van der Waals heterostructures provide a powerful handle over interlayer tunneling and the nature of the induced superconducting gap. Cryogenic dry transfer combined with inert encapsulation preserves pristine d-wave order at the interface, maintaining bulk-like critical current densities at zero twist, but yielding a dramatic suppression (by up to two orders of magnitude in $I_c$) for twist angles near 45°, in accordance with the relation

$I_c R_N \propto \cos 2\theta,$

where $\theta$ is the twist angle and $R_N$ the normal-state resistance (Martini et al., 2023, Lee et al., 2022). The mismatch in the d-wave order parameter symmetry effectively suppresses first-order Cooper pair tunneling and allows for the emergence of a second harmonic (sin(2φ)) current-phase relation and fractional Josephson effects.

This principle underpins novel quantum device designs, such as the “flowermon” qubit, whose Hamiltonian includes both first and second harmonics:

$$H = 4E_C(\hat{n}-n_g)^2 - E_J^\theta \cos\hat\phi + E_\kappa\cos(2\hat\phi),$$

where $E_J^\theta = E_J\cos 2\theta$ is suppressed near 45°, rendering two-Cooper-pair tunneling ($E_\kappa$) dominant. The resulting qubit enjoys inherent charge parity protection and exponential suppression of both charge and quasiparticle decoherence channels, owing to the symmetry-induced selection rules (Brosco et al., 2023).

Further, materials with strong spin–orbit coupling (TMDs, NbSe$_2$) arranged with controlled twist enable proximity-induced Ising superconductivity, odd-frequency pairing, and spatially programmable topological transitions, including conditions conducive to the stabilization of high-temperature Majorana zero modes (Rossi et al., 2019, Doan et al., 25 Sep 2024). Device schemes encompass tunnel transistors, field-effect superconducting switches, and hybrid quantum processors, leveraging tunable interlayer coupling and SOC anisotropy controlled by the twist.

Cryogenic dry-exfoliation and transfer techniques (Patil et al., 30 May 2024) and hBN encapsulation (Lee et al., 2022) facilitate the construction of such high-quality, inert interfaces even in chemically reactive materials.

5. Optical Anisotropy, Excitons, and One-Dimensional vdW Heterostructures

Optical properties in orthogonally-twisted vdW heterostructures reflect the interplay between underlying electronic structure, twist-imposed symmetry breaking, and interlayer hybridization. In highly anisotropic 2D coordination polymers ([FeX(pzX)(bpy)]), strong differences in optical response (birefringence, photoluminescence) along orthogonal axes can be “switched off” in orthogonally-twisted stacks, as manifested in the vanishing of polarization-dependent contrast in the twisted overlap region (Mazarakioti et al., 25 Aug 2025). The effect is robust to chemical substitution (Cl versus F), with DFT calculations tracing the underlying mechanism to ligand-controlled tuning of band dispersions and direct/indirect gap character.

In TMD heterobilayers, twist engineering controls both exciton localization and interlayer charge transfer rates: in orthogonally-twisted (misaligned) cases, momentum mismatch severely impedes ultrafast interlayer charge transfer, suppressing exciton recombination and affecting photoluminescence and photovoltaic response (Gogoi et al., 2019). Only when the valleys are directly aligned (0° or 60°) is the charge transfer maximized (lifetime $\sim$ 5 fs), suggesting a route to rational control over optoelectronic dynamics via the twist angle.

6. Mechanics, Tribology, and Rotational Superstructures

The mechanical response of orthogonally-twisted vdW heterostructures, including friction, energy dissipation, and rotational dynamics, is governed not only by the interlayer corrugation (which can be superlubric in translation), but also by twist-induced variation in structural potential energy. Experiments on MoS$_2$/graphite interfaces demonstrate that, while translational friction can approach the superlubric regime, the rotational resistance is dominated by a twist-dependent torque,

$\tau_{\rm intrinsic} = -\frac{dE}{d\theta},$

with $E(\theta)$ the twist-angle–dependent energy per unit area (Liao et al., 20 Oct 2024). Periodic valleys in the rotational friction force with 60° periodicity arise from the modulation of the moiré superstructure and the evolving strain landscape, providing an additional pathway for energy dissipation (distinct from sliding) in twisted devices.

7. Design Principles, Device Applications, and Outlook

Orthogonally-twisted vdW heterostructures present a robust and versatile platform for exploring and utilizing emergent quantum phenomena:

• Topological Electronics and Valleytronics: Domain-wall and edge-state engineering via spatially modulated potential (through patterning, gating, or twist) enables creation of dissipationless, valley-polarized channels and tunable QSH states (Wang et al., 2016, Tong et al., 2016).
• Spintronics and Twistronics: Precise programming of magnetic hysteresis, domain-wall formation, and interlayer exchange by selecting twist angle, layer number, and stacking order offers functionality for memory, logic, and logic-in-memory devices (Boix-Constant et al., 2023, Kumar et al., 31 Jul 2025, Boix-Constant et al., 28 Oct 2024).
• Quantum Circuits and Qubits: Ultraclean, twist-controlled Josephson junctions with d-wave or Ising pairing symmetry facilitate design of high-coherence qubits (providing on–off coupling or parity protection) and may support non-Abelian excitations (Martini et al., 2023, Brosco et al., 2023, Doan et al., 25 Sep 2024).
• Optoelectronic Modulation: Polarization “switch-off” in highly anisotropic layered organics, together with twist-controlled exciton and charge-transfer lifetimes in TMDs, enables active modulation of photonic and excitonic devices (Mazarakioti et al., 25 Aug 2025, Gogoi et al., 2019).
• Mechanics and Metamaterials: Acoustic analogs of twisted bilayer systems demonstrate that twist-mediated local mode confinement and interaction enhancement can be engineered in classical media, bridging quantum and metamaterial design principles (Gardezi et al., 2020).

Scalable, dry, cryogenic exfoliation and encapsulation techniques now allow assembly of heterostructures with atomically sharp, twist-controlled interfaces—preserving stability even for highly reactive compounds such as BSCCO (Patil et al., 30 May 2024). Emerging methodologies, such as four-dimensional STEM, holography, and low-temperature spatial imaging, enable mapping of local structural, magnetic, and electronic textures at nanometer scales.

Future directions include integration of orthogonally-twisted stacks with external fields (electric, magnetic, strain), interface functionalization, exploration of higher-order stacking and moiré patterns, and the design of hybrid quantum materials combining topological, magnetic, and superconducting order. Orthogonally-twisted vdW heterostructures stand at the forefront of atomically engineered quantum materials and device heterointegration, offering tuning modalities that are both conceptually and technologically unmatched among naturally occurring compounds.