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Introduction
Torsional Force Microscopy (TFM) is a specialized atomic force microscopy (AFM) mode for detecting dynamic lateral forces at the nanoscale. It is particularly effective in visualizing moiré superlattices and atomic lattices in van der Waals (vdW) heterostructures such as bilayer graphene and graphene/hexagonal boron nitride (hBN) stacks, where even slight interlayer twist angle changes can dramatically modify electronic behavior. Unlike conventional AFM techniques, TFM does not require electrical connection to the sample or probe, making it ideal for electrically insulating or floating structures. Its operation under ambient conditions and ability to resolve surface and shallow subsurface features enable researchers to investigate two-dimensional (2D) materials on soft polymer substrates, even during intermediate fabrication stages.

Moiré superlattices arise from stacking two layers of graphene or other 2D materials at small twist angles. Although their unique physical properties have been widely explored, direct imaging under ambient conditions remains limited. Tiny twist angle variations — even hundredths of a degree — can drastically alter electronic characteristics. Existing imaging approaches often require complex instrumentation or extensive post-processing, and practical challenges such as inconsistent twist angles and poor spatial uniformity hinder reproducible fabrication and characterization. Thus, there is strong demand for a fast, accessible, and reliable imaging technique that works under ambient conditions, requires no electrical connections or surface modifications, and is compatible with partially assembled vdW stacks on polymer substrates. Park Systems has implemented TFM to meet these needs. This application note introduces TFM as a rapid, practical feedback solution and presents representative data acquired from 2D material samples using the Park FX40 AFM system, along with details of its hardware configuration optimized for TFM measurements.

Various SPM applications for imaging moiré superlattices
Several scanning probe microscopy techniques have been explored to visualize moiré patterns and atomic lattices in 2D materials. Conductive AFM (C-AFM) allows atomic resolution imaging but requires conductive samples and substrates. Amplitude-modulation AFM (AM-AFM), including tapping mode, often struggles to clearly resolve fine moiré contrasts, whereas contact mode typically provides better contrast. Scanning microwave impedance microscopy (sMIM) offers non-contact measurements but lacks atomic resolution. Among these, Lateral Force Microscopy (LFM) and Friction Force Microscopy (FFM) have been effective for visualizing both moiré and atomic-scale structures in materials such as hBN and graphite. However, their ability to detect subsurface structures remains unproven. TFM addresses this gap by utilizing torsional resonance modes, enabling high-sensitivity mapping of frictional contrast and thus offering clearer visualization of moiré structures across varying depths. Torsional resonances sensitive to dynamic friction at the AFM tip-sample interface were employed to achieve high-resolution maps comparable to previous techniques. This proved highly effective for clearly resolving moiré contrast or even atomic lattices.

Fundamentals of TFM
TFM operation involves two simultaneous control schemes. First, closed-loop feedback tracks the sample topography, maintaining a constant normal loading force. Concurrently, an open-loop excitation at the cantilever’s torsional resonance is applied to detect variations in lateral friction. This dual-mode configuration ensures high frictional contrast by combining sensitive torsional excitation with stable tip-sample contact control. To induce pure torsional motion without introducing vertical or flexural artifacts, a pair of bimorph actuators is driven 180° out of phase. This symmetric configuration ensures that vertical displacements are canceled out while generating a clean rotational torque at the cantilever base, thereby selectively exciting the torsional eigenmode with high efficiency. A single bimorph or asymmetrical drive would excite non-torsional modes and reduce signal clarity due to mechanical cross-talk and mode mixing. The lateral deflection resulting from this controlled torsional excitation is then measured to map nanoscale frictional variations. These signals, when analyzed at torsional resonances, provide high-resolution information about surface and subsurface structures without the need for electrical biasing.

TFM builds upon a two-mode control scheme that combines vertical feedback and lateral torsional excitation to detect nanoscale frictional variations with high spatial resolution. As illustrated in Fig. 1, the system simultaneously maintains topographic tracking through closed-loop control while driving the cantilever's torsional resonance via open-loop excitation. To ensure stable imaging conditions throughout the scan, the vertical Z-feedback maintains a constant normal force by adapting to the surface contours of the sample, following the principle used in conventional contact-mode AFM. Torsional excitation is achieved by applying 180° out-of-phase signals to a pair of piezo actuators integrated into the cantilever holder, generating a rotational drive around the cantilever’s long axis. The lateral deflection is detected by the photodetector’s side quadrant channel (the PSPD), and its amplitude near the torsional resonance frequency indicates local variations in friction. By scanning across the surface while maintaining this torsional excitation, TFM effectively maps nanoscale variations in friction linked to structural features such as moiré patterns or atomic lattices. Since the technique does not rely on electrical biasing or contact-based charge transfer, it avoids issues like electrostatic interference or sample charging. This makes TFM particularly well-suited for characterizing electrically insulating or floating samples, as well as fragile 2D materials or partially fabricated heterostructures. By combining vertical force stability with lateral resonance sensitivity, TFM provides a powerful and non-invasive method for revealing fine mechanical contrasts in complex nanoscale systems, supporting advanced surface and interface characterization.

High-resolution TFM Imaging of Moiré Patterns and Atomic Lattices
To demonstrate the capabilities of TFM, high-resolution imaging was performed under ambient conditions on a variety of van der Waals (vdW) heterostructures, including a cleaved (001) surface of muscovite mica, single-layer graphene on hexagonal boron nitride (Gr/hBN) and twisted bilayer graphene (tBG). The results demonstrate TFM’s ability to resolve both moiré patterns and atomic lattices with high spatial precision across multiple scales. TFM was also applied to a cleaved (001) mica surface to examine atomic-scale lattice contrast. As shown in Fig. 2, TFM clearly resolved periodic atomic-scale features, whereas LFM measurements at the same  location resulted in noisy images with less distinctive structure and frequent spike-like artifacts in specific directions. The superior sensitivity of TFM to lateral friction enabled clean visualization of atomic lattice contrast even at the small scan size of 5 × 5 nm². The TFM measurements matched the reported atomic lattice periodicity of 0.52 nm, confirming measurement accuracy.

Fig. 3 shows the TFM results obtained on a single graphene layer on hBN (Gr/hBN). The optical image and wide-area topography (40 × 40 μm²) confirm the multilayered structure. In the high-resolution small scans (100 × 100 nm²), TFM clearly resolved moiré contrast linked to the twist angle.

TFM was applied to a twisted bilayer graphene sample to visualize the resulting moiré patterns. As shown in Fig. 4, TFM clearly resolved the periodic features, whereas LFM measurements at the same location produced noisy images with poorly defined structures. The superior lateral friction sensitivity of TFM enabled clean and distinct visualization of the moiré pattern contrast.

Conclusion
Torsional Force Microscopy (TFM), as implemented on the Park AFM systems, provides a powerful and reliable method for high-resolution imaging of moiré superlattices and atomic lattices in 2D materials under ambient conditions. By detecting lateral frictional variations without the need for electrical contacts or sample conductivity, TFM enables direct and minimally invasive visualization of both surface and shallow subsurface structural features. This capability is particularly valuable for characterizing twisted heterostructures, where subtle differences in twist angle and interlayer coupling critically influence material properties.

The high spatial sensitivity, ability to operate in ambient conditions, and compatibility with soft or insulating substrates make TFM a practical and versatile tool for both research and process monitoring. As interest in 2D quantum and electronic materials continues to grow, TFM is expected to serve as a valuable technique for providing structural insight and supporting the development of next-generation devices.
 

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