Quantum Twisting Microscope (QTM)

• Quantum Twisting Microscope is a scanning probe platform that uses adjustable twist angles between vdW layers to achieve momentum-resolved spectroscopy.
• It combines in-situ twistronics with coherent tunneling to probe electronic, phononic, and superconducting properties in 2D and moiré materials.
• QTM delivers local momentum information with spatial resolutions of ~100 nm and angular precision down to 0.001°, enabling detailed band and interaction studies.

The Quantum Twisting Microscope (QTM) is a scanning probe platform that performs local quantum interference experiments at its tip and uses a continuously tunable twist angle between a van der Waals (vdW) tip and sample to probe electrons in momentum space (Inbar et al., 2022). In its original formulation, it combines two orthogonal capabilities: in-situ twistronics, in which the tip’s active vdW layer is brought into direct contact with the sample’s active layer to form a twistable 2D interface whose transport can be measured continuously as $\theta$ is scanned, and momentum-resolved tunneling, in which a thin vdW tunnel barrier decouples the wavefunctions while preserving coherent tunneling, so that scanning $\theta$ locally selects momentum components of the sample’s electronic states (Inbar et al., 2022). Subsequent experimental and theoretical work has expanded QTM from a band-imaging microscope for graphene-based junctions into a broader momentum-resolved spectroscopic platform for phonons, magnetism, plasmons, superconductivity, and interaction-driven flat-band phenomena in moiré materials (Birkbeck et al., 2024, Xiao et al., 25 Jun 2025, Waschitz et al., 15 Oct 2025).

1. Definition, scope, and relation to other probes

QTM differs fundamentally from conventional STM/STS and from momentum-space probes such as ARPES. STM/STS probe the local density of states in real space through a single atomic-scale tunneling junction, whereas QTM forms an extended, pristine 2D tip–sample junction with many coherent tunneling trajectories, turning the tip into a phase-sensitive interferometer (Inbar et al., 2022). With twist, QTM scans an arc in $k$-space of the sample in a manner analogous to how STM scans in real space, thereby providing local momentum-resolved spectroscopy. In the foundational experiments, this was demonstrated at room temperature and under tunable pressure and gating (Inbar et al., 2022).

Relative to ARPES, QTM is local, with spatial resolution set by the tip plateau size, reported as approximately $100\,\mathrm{nm}$ to $1\,\mu\mathrm{m}$ in the foundational work and as approximately $100\,\mathrm{nm}$ in the comparison statements that emphasize device compatibility (Inbar et al., 2022). It is compatible with device environments, local gates, buried interfaces, magnetic field, and pressure, and it can access occupied and unoccupied states through bias-dependent tunneling rather than photoemission (Inbar et al., 2022, Wei et al., 2024). The measured momentum resolution in graphene, approximately $0.004$ of the Brillouin zone from an angular peak of full width at half maximum of about $0.2^\circ$ at $V_b=40\,\mathrm{mV}$, was explicitly stated to be comparable to state-of-the-art ARPES for graphene (Inbar et al., 2022).

Later work sharpened the conceptual scope of the method. Theoretical studies cast QTM as a momentum-resolved tunneling spectrometer built from vdW materials, in which a monolayer graphene tip with linear Dirac dispersion serves as a sharply momentum-selective probe whose Dirac point traces symmetry-related arcs through the sample Brillouin zone as $\theta$ is varied (Wei et al., 2024). In this formulation, QTM is not merely a twist-dependent transport tool but a general platform for measuring single-particle spectral functions and, in inelastic configurations, collective response functions such as the dynamical spin structure factor and bosonic spectral functions (Pichler et al., 2024, Wei et al., 5 Jun 2025).

2. Device architecture and operating modes

The canonical QTM tip is a vdW heterostructure assembled on a focused-ion-beam-deposited platinum pyramid near the edge of an AFM cantilever. In the original implementation, the pyramid was approximately $\theta$0–$\theta$1 tall, while the later construction paper reported a base of about $\theta$2 and an optimized height of $\theta$3–$\theta$4, with failure modes outside that window: above $\theta$5 the membrane does not form a smooth tent structure, and below $\theta$6 the cantilever apex can contact the sample first (Inbar et al., 2022, Biswas et al., 3 Apr 2026). Graphite and hBN are transferred first, followed by the active layer, such as monolayer graphene. The resulting vdW stack forms a tent with folds converging at the pyramid apex, where a flat plateau spontaneously forms. Its lateral size can be tuned from approximately $\theta$7 to $\theta$8 by geometry and layer thickness (Inbar et al., 2022).

The self-aligned, atomically flat plateau is central to QTM operation. Upon contact, it becomes parallel to the sample and creates a pristine 2D interface without lithographic edges or dangling bonds. Graphite screens substrate disorder; hBN acts as a spacer; buried graphite gates can tune density and displacement fields. In a practical AFM-based build, a commercial Nanosurf Easyscan 2 AFM was adapted with an open geometry beneath the scan head, a custom stack of translation and rotation stages, an $\theta$9 wedge to reduce effective cantilever tilt, and adjustable AFM legs for final tilt tuning (Inbar et al., 2022, Biswas et al., 3 Apr 2026).

Two measurement modalities are standard. In direct contact, the active layer on the tip is placed directly on the active sample layer; strong hybridization probes interface transport versus $k$0. In tunnel-junction mode, a thin barrier such as few-layer WSe$k$1, $k$2–$k$3 layers of WSe$k$4, or hBN is inserted between tip and sample, suppressing hybridization while keeping tunneling coherent (Inbar et al., 2022, Lee et al., 3 Jul 2025). The foundational room-temperature momentum-resolved experiments used WSe$k$5 barriers, whereas later room-temperature high-bias graphene spectroscopy replaced WSe$k$6 by ultrathin hBN, reporting measured thicknesses of $k$7 for bilayer hBN and $k$8 for four-layer hBN, and extending usable bias to $k$9 (Lee et al., 3 Jul 2025).

Twist control is likewise an essential subsystem. The original room-temperature microscope used a piezoelectric rotator with X/Y nanopositioners and reported $100\,\mathrm{nm}$0 angular resolution while maintaining continuous contact at constant force (Inbar et al., 2022). The 2026 construction paper described a two-tier XY-stage arrangement, with bottom stages used to align the rotation axis under the tip and top Xeryon XLS stages mounted above a Xeryon XRT-U rotation stage to position the flat sample relative to the curved tip sample. In validation measurements, continuous rotation was performed at $100\,\mathrm{nm}$1, and lateral centering of the rotation axis within approximately $100\,\mathrm{nm}$2 of the scan center was achieved by iterative scan superposition (Biswas et al., 3 Apr 2026).

3. Twist-controlled momentum selection and theoretical framework

Because the tip–sample junction is extended, an electron can tunnel coherently at many locations across the interface. The total tunneling amplitude is a coherent sum over paths,

$100\,\mathrm{nm}$3

where the phases are set by twist-induced momentum shifts $100\,\mathrm{nm}$4 associated with the moiré geometry (Inbar et al., 2022). In twisted graphene systems, these $100\,\mathrm{nm}$5 connect Dirac points of opposing layers. For small angles, the relative rotation shifts the Dirac points by

$100\,\mathrm{nm}$6

while the moiré period is

$100\,\mathrm{nm}$7

Scanning $100\,\mathrm{nm}$8 therefore scans a momentum arc through the sample Brillouin zone (Inbar et al., 2022).

In momentum-resolved tunneling mode, the current is formulated in terms of sample and tip spectral functions and a momentum-selective matrix element,

$100\,\mathrm{nm}$9

For a sharp tip spectral feature, the differential conductance is sensitive to the sample spectral function at the selected momentum,

$1\,\mu\mathrm{m}$0

Electrostatics is nontrivial because the quantum and geometric capacitances are comparable, so the applied bias partitions according to

$1\,\mu\mathrm{m}$1

with $1\,\mu\mathrm{m}$2, $1\,\mu\mathrm{m}$3, and $1\,\mu\mathrm{m}$4 determined self-consistently (Inbar et al., 2022).

For monolayer graphene with Dirac dispersion $1\,\mu\mathrm{m}$5, the original work derived analytic alignment conditions. The momentum-resolved onset obeys

$1\,\mu\mathrm{m}$6

while additional curved loci correspond to nesting, where a macroscopically large set of states satisfies energy–momentum conservation (Inbar et al., 2022). The later room-temperature graphene interaction study retained this onset/nesting language but replaced the strictly linear dispersion by

$1\,\mu\mathrm{m}$7

so that interaction-induced deviations from linearity split the single Dirac nesting line into distinct “Nesting I” and “Nesting II” branches (Lee et al., 3 Jul 2025).

Theoretical developments after the original demonstration generalized the same twist-to-momentum map to several spectroscopies. In Dirac-point spectroscopy, the singular density of states of a graphene tip at its Dirac points generates sharp features in $1\,\mu\mathrm{m}$8 when the tip Dirac energy matches a sample band, producing a direct map of the sample dispersion along the scanned arcs (Wei et al., 2024). In proposed inelastic modes, the second derivative of the tunneling current can directly access bosonic response functions. For magnetic excitations, one obtains

$1\,\mu\mathrm{m}$9

so that twist selects the probed momentum of the dynamical spin structure factor (Pichler et al., 2024). For superconducting states, the superconducting spectral function

$100\,\mathrm{nm}$0

implies that the relative intensities of positive- and negative-bias quasiparticle peaks encode the Bogoliubov coherence factors $100\,\mathrm{nm}$1 and $100\,\mathrm{nm}$2, and hence the momentum dependence of $100\,\mathrm{nm}$3 along the QTM trajectories (Waschitz et al., 15 Oct 2025).

4. Foundational experiments and benchmark performance

The original experimental paper established several benchmarks at $100\,\mathrm{nm}$4 (Inbar et al., 2022). In monolayer-graphene–monolayer-graphene momentum-resolved tunneling through WSe$100\,\mathrm{nm}$5, the measured $100\,\mathrm{nm}$6 and $100\,\mathrm{nm}$7 maps displayed the predicted straight-X and curved-X features in the $100\,\mathrm{nm}$8 plane. Fitting the straight-X yielded

$100\,\mathrm{nm}$9

and the narrow angular peak at $0.004$0 had $0.004$1, implying momentum resolution of approximately $0.004$2 of the Brillouin zone (Inbar et al., 2022). Modeling included lifetime broadening $0.004$3 with fitted $0.004$4 and $0.004$5, from which the inferred low-energy coherence length was approximately $0.004$6, comparable to the tip plateau size (Inbar et al., 2022).

In direct-contact in-situ twist experiments on monolayer graphene, the conductance $0.004$7 at $0.004$8 was mirror-symmetric about $0.004$9, minimal near $0.2^\circ$0, and exhibited sharp commensurate peaks at $0.2^\circ$1 and $0.2^\circ$2, corresponding to the $0.2^\circ$3 supercell (Inbar et al., 2022). The 2026 construction paper independently validated the instrument on graphite–graphite junctions, again finding clear $0.2^\circ$4 periodicity and enhanced conductance near $0.2^\circ$5 and $0.2^\circ$6, with stable conditioned junction conductance of a few $0.2^\circ$7 (Biswas et al., 3 Apr 2026). That validation is significant because it anchors practical angle calibration through the $0.2^\circ$8 symmetry of the lattice and through the recurrence of the commensurate peaks.

QTM also directly imaged the bands of twisted bilayer graphene with $0.2^\circ$9. In monolayer-graphene–WSe$V_b=40\,\mathrm{mV}$0–TBG junctions, $V_b=40\,\mathrm{mV}$1 simultaneously showed the TBG flat bands near zero energy, remote bands at higher energy, and two displaced copies of the monolayer graphene Dirac bands separated by $V_b=40\,\mathrm{mV}$2 (Inbar et al., 2022). Using the imaged monolayer-graphene Dirac features as an internal energy calibrant, the flat-band dispersion $V_b=40\,\mathrm{mV}$3 was extracted and found to agree broadly with Bistritzer–MacDonald trends while exhibiting a measurable electron–hole asymmetry of approximately $V_b=40\,\mathrm{mV}$4 along $V_b=40\,\mathrm{mV}$5–$V_b=40\,\mathrm{mV}$6–$V_b=40\,\mathrm{mV}$7 and approximately $V_b=40\,\mathrm{mV}$8 near $V_b=40\,\mathrm{mV}$9–$\theta$0 (Inbar et al., 2022). The same experiment showed sensitivity to layer polarization: features were stronger when the probe aligned with the top TBG layer than when aligned with the bottom layer, and the tunneling amplitude along the flat-band features tracked the calculated layer polarization versus momentum (Inbar et al., 2022).

A further benchmark was local pressure tuning. Using AFM force control, the original paper applied $\theta$1-scale forces over a small junction area, generating GPa-scale pressures. At $\theta$2, $\theta$3, and $\theta$4, the flat bands moved toward $\theta$5 while remote bands moved away, consistent with pressure-enhanced interlayer tunneling and band anticrossing (Inbar et al., 2022). The flat-band width at $\theta$6 decreased linearly with pressure and was reduced by approximately $\theta$7 at $\theta$8; the paper noted that theory predicted approximately $\theta$9–$\theta$00 and that linear extrapolation suggested full band flattening near $\theta$01 for $\theta$02 TBG (Inbar et al., 2022).

5. QTM as a probe of interaction-driven flat bands and many-body renormalization

Subsequent experimental work used QTM to resolve interaction effects beyond the original room-temperature demonstrations. In a room-temperature monolayer-graphene/hBN/monolayer-graphene device, high-bias tunneling maps displayed two features not reproduced by nearest-neighbor or next-nearest-neighbor single-particle models: the splitting of the nesting line into “nesting I” and “nesting II” and a deviation of the onset from linearity (Lee et al., 3 Jul 2025). Fitting the full maps with the logarithmically corrected dispersion yielded $\theta$03, $\theta$04, cutoff $\theta$05, and junction areal capacitance $\theta$06, while the low-bias apparent velocity remained approximately $\theta$07 (Lee et al., 3 Jul 2025). This showed that QTM can resolve subtle electron–electron interaction corrections in symmetric, nonordered graphene states even at room temperature.

At cryogenic temperature, QTM was then applied to magic-angle twisted bilayer graphene. In the 2025 study of interacting MATBG bands, a monolayer graphene tip tunneled through a bilayer WSe$\theta$08 barrier into TBG at $\theta$09, with the probe–sample angle continuously tunable with millidegree precision and with momentum and energy resolutions reported as $\theta$10 and $\theta$11 (Xiao et al., 25 Jun 2025). Away from the magic angle, at $\theta$12, the measured bands along the QTM trajectory followed single-particle Bistritzer–MacDonald theory, showing Dirac points at $\theta$13 and $\theta$14, a flat-band bandwidth of about $\theta$15 near the $\theta$16 points, gaps of approximately $\theta$17 and $\theta$18 to the remote conduction and valence bands, and remote-band van Hove singularities at $\theta$19 and $\theta$20 (Xiao et al., 25 Jun 2025).

Near the magic angle, at $\theta$21, the measured bands were qualitatively reshaped by interactions. Across most of the measured trajectory, two extremely flat bands were observed, separated by an energy gap of approximately $\theta$22 and flat to within approximately $\theta$23, whereas near the $\theta$24 point the bands remained dispersive and gapless (Xiao et al., 25 Jun 2025). Upon doping from $\theta$25 to $\theta$26 and $\theta$27, the heavy flat bands exhibited Mott-like cascades at momenta such as $\theta$28, while the light Dirac-like sector near $\theta$29 underwent Hartree-driven stretching with total shifts of approximately $\theta$30 at $\theta$31 and approximately $\theta$32 at $\theta$33 (Xiao et al., 25 Jun 2025). The momentum dependence of the QTM intensity revealed a filling-dependent partition between a heavy sector dominant over most of the mini-Brillouin zone and a light sector confined near $\theta$34, with the normalized radius of the light region growing to approximately $\theta$35 at $\theta$36 (Xiao et al., 25 Jun 2025). The same study extracted $\theta$37 from momentum-dependent peak intensities, smaller than the commonly used $\theta$38, and identified a persistent filling-independent excitation at $\theta$39 relative to $\theta$40 that was present only in the heavy regions of momentum space (Xiao et al., 25 Jun 2025).

These experiments significantly broadened the interpretation of QTM data. In the original TBG imaging study, deviations from the Bistritzer–MacDonald model were recorded mainly as electron–hole asymmetry and layer-polarization effects at $\theta$41 (Inbar et al., 2022). By contrast, in magic-angle devices QTM directly resolved momentum-dependent coexistence of heavy and light sectors within the same topological flat bands and followed their distinct doping evolutions at fixed momentum (Xiao et al., 25 Jun 2025). A plausible implication is that QTM is particularly powerful when the decisive physics is strongly $\theta$42-dependent but not easily separable in real-space probes.

6. Collective excitations, superconductivity, limitations, and outlook

QTM has been generalized beyond elastic band imaging to inelastic spectroscopy of neutral collective modes. A cryogenic QTM implementation at $\theta$43 demonstrated phonon spectroscopy in twisted bilayer graphene by exploiting the fact that, at large twist angles, elastic tunneling is suppressed and inelastic tunneling can proceed only by emitting a phonon with momentum

$\theta$44

which bridges the twist-induced momentum mismatch (Birkbeck et al., 2024). In that work, $\theta$45 peaks traced acoustic and optical phonon branches, and the inelastic step height obeyed

$\theta$46

The measured optical coupling yielded $\theta$47–$\theta$48, while the acoustic gauge branch displayed a coupling that increased strongly as twist angle decreased and was attributed to a layer-antisymmetric phason mode of the moiré system (Birkbeck et al., 2024). A companion theory paper formalized the perturbative distinction between first-order interlayer and second-order intralayer phonon-assisted processes and the mode-dependent dominance of the two channels (Xiao et al., 2024).

Comparable theoretical extensions were proposed for magnetic and plasmonic excitations. For moiré TMD heterostructures, QTM was proposed as a probe of both the single-particle spectral function and the dynamical spin structure factor, with predicted signatures that distinguish ferromagnetic and antiferromagnetic generalized Wigner crystals and track the softening of a roton-like collective mode at the transition between a chiral spin liquid and a $\theta$49 ordered state (Pichler et al., 2024). For quantum spin liquids, a graphene–QSL–graphene planar junction was proposed in which exchange-mediated inelastic tunneling gives

$\theta$50

so that twist and bias directly image the barrier’s dynamical spin structure factor (Peri et al., 2023). For plasmons in TBG, a 2025 theory developed a multiband inelastic tunneling formalism in which features in $\theta$51 and $\theta$52 track the plasmon dispersion and the electron–plasmon coupling strength, with strong dependence on screening environment and local-field effects (Wei et al., 5 Jun 2025).

Superconductivity is another major proposed application. One theoretical framework showed that, because QTM preserves in-plane momentum, the relative intensities of electron-like and hole-like Bogoliubov peaks at the same momentum encode the coherence-factor ratio

$\theta$53

allowing direct extraction of $\theta$54 along the QTM trajectory from the peak separation and intensity ratio (Waschitz et al., 15 Oct 2025). A related theory formulated the zero-temperature conductance singularities of a normal monolayer-graphene tip tunneling into a superconducting graphene sample and proposed protocols for mapping gap anisotropy, locating nodes by triangulation in $\theta$55 space, and reconstructing Bogoliubov equal-energy contours (Wei et al., 26 Sep 2025). These studies remain theoretical, but they place superconducting order-parameter tomography within the established QTM kinematic framework.

Several limitations recur across the literature. QTM requires pristine, flat vdW interfaces and can be affected by tip-induced electrostatics, local strain, drift during long twist scans, finite junction-size broadening of momentum resolution, and barrier breakdown at high bias (Inbar et al., 2022). In practical construction, stable operation depends on vibration isolation, careful tilt control, compact mechanical layout, and clean membrane transfer; at low conductance, below $\theta$56 in the graphite validation experiments, angle-dependent signals become noisy and irreproducible (Biswas et al., 3 Apr 2026). In cryogenic phonon spectroscopy, small-angle elastic tunneling can overwhelm the inelastic signal below approximately $\theta$57 (Birkbeck et al., 2024). More generally, the accessible momentum manifold is a one-dimensional arc rather than the full two-dimensional Brillouin zone, and matrix-element effects must be modeled to interpret intensity variations (Wei et al., 2024, Xiao et al., 25 Jun 2025).

Even with those constraints, the combined experimental and theoretical record defines QTM as a local, gate-tunable, twist-controlled momentum spectrometer for vdW materials. Established experiments have shown room-temperature coherence, direct band imaging, layer-polarization sensitivity, pressure tuning, cryogenic phonon spectroscopy, and interaction-resolved flat-band measurements (Inbar et al., 2022, Birkbeck et al., 2024, Xiao et al., 25 Jun 2025). The broader literature suggests a unified outlook in which the same twist-selected momentum conservation principle can be used to interrogate spectral functions, bosonic modes, and symmetry-breaking order parameters across graphene, moiré systems, transition-metal dichalcogenides, complex oxides, and chiral materials (Biswas et al., 3 Apr 2026, Pichler et al., 2024, Waschitz et al., 15 Oct 2025).