---
title: Quantum Twisting Microscope (QTM)
url: https://www.emergentmind.com/topics/quantum-twisting-microscope-qtm
type: topic
---

# Quantum Twisting Microscope (QTM)

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 [2208.05492]. 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 [2208.05492]. 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 [2407.13404] [2506.20738] [2510.13641].

## 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 [2208.05492]. 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 [2208.05492].

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 [2208.05492]. 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 [2208.05492] [2410.08383]. 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 [2208.05492].

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 [2410.08383]. 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 [2402.04311] [2506.05485].

## 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 $1.2$–$1.6\,\mu\mathrm{m}$ tall, while the later construction paper reported a base of about $2\times2\,\mu\mathrm{m}$ and an optimized height of $1.5$–$2.0\,\mu\mathrm{m}$, with failure modes outside that window: above $2.5\,\mu\mathrm{m}$ the membrane does not form a smooth tent structure, and below $1.5\,\mu\mathrm{m}$ the cantilever apex can contact the sample first [2208.05492] [2604.03483]. 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 $50\,\mathrm{nm}$ to $1\,\mu\mathrm{m}$ by geometry and layer thickness [2208.05492].

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 $8^\circ$ wedge to reduce effective cantilever tilt, and adjustable AFM legs for final tilt tuning [2208.05492] [2604.03483].

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 $\theta$. In **tunnel-junction mode**, a thin barrier such as few-layer WSe$_2$, $2$–$3$ layers of WSe$_2$, or hBN is inserted between tip and sample, suppressing hybridization while keeping tunneling coherent [2208.05492] [2507.03189]. The foundational room-temperature momentum-resolved experiments used WSe$_2$ barriers, whereas later room-temperature high-bias graphene spectroscopy replaced WSe$_2$ by ultrathin hBN, reporting measured thicknesses of $0.633\,\mathrm{nm}$ for bilayer hBN and $1.39\,\mathrm{nm}$ for four-layer hBN, and extending usable bias to $V_b=\pm2.5\,\mathrm{V}$ [2507.03189].

Twist control is likewise an essential subsystem. The original room-temperature microscope used a piezoelectric rotator with X/Y nanopositioners and reported $0.001^\circ$ angular resolution while maintaining continuous contact at constant force [2208.05492]. 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 $2^\circ/\mathrm{min}$, and lateral centering of the rotation axis within approximately $100\,\mathrm{nm}$ of the scan center was achieved by iterative scan superposition [2604.03483].

## 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,
$$
M(\mathbf{k}, \theta) \approx \sum_j t_j\, e^{i \phi_j(\mathbf{k}, \theta)},
$$
where the phases are set by twist-induced momentum shifts $\mathbf{q}_j(\theta)$ associated with the moiré geometry [2208.05492]. In twisted graphene systems, these $\mathbf{q}_j$ connect Dirac points of opposing layers. For small angles, the relative rotation shifts the Dirac points by
$$
k_\theta \approx 2 K_D \sin(\theta/2) \simeq K_D\, \theta,
$$
while the moiré period is
$$
L(\theta) \approx \frac{a}{2 \sin(\theta/2)}.
$$
Scanning $\theta$ therefore scans a momentum arc through the sample Brillouin zone [2208.05492].

In momentum-resolved tunneling mode, the current is formulated in terms of sample and tip spectral functions and a momentum-selective matrix element,
$$
I(V_b, \theta) \propto \int d\omega \sum_{\mathbf{k}} |M(\mathbf{k}, \theta)|^2\, A_s(\mathbf{k}, \omega)\, A_t(\mathbf{k}, \omega + e V_b)\, [f(\omega) - f(\omega + e V_b)].
$$
For a sharp tip spectral feature, the differential conductance is sensitive to the sample spectral function at the selected momentum,
$$
\frac{dI}{dV}(V_b, \theta) \propto \sum_{\mathbf{k}} |M(\mathbf{k}, \theta)|^2\, A_s(\mathbf{k}, \omega = e V_b).
$$
Electrostatics is nontrivial because the quantum and geometric capacitances are comparable, so the applied bias partitions according to
$$
V_b = \phi + \mu_B - \mu_T,
$$
with $\phi$, $\mu_T$, and $\mu_B$ determined self-consistently [2208.05492].

For monolayer graphene with Dirac dispersion $E=\pm \hbar v_F |\mathbf{k}|$, the original work derived analytic alignment conditions. The momentum-resolved onset obeys
$$
V_b = \hbar v_F K_D\, \theta,
$$
while additional curved loci correspond to nesting, where a macroscopically large set of states satisfies energy–momentum conservation [2208.05492]. The later room-temperature graphene interaction study retained this onset/nesting language but replaced the strictly linear dispersion by
$$
E(k)=\pm \hbar v_0\,k\left[\,1+\alpha\,\ln\!\left(\frac{\Lambda}{k}\right)\right],
$$
so that interaction-induced deviations from linearity split the single Dirac nesting line into distinct “Nesting I” and “Nesting II” branches [2507.03189].

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 $d^2I/dV^2$ when the tip Dirac energy matches a sample band, producing a direct map of the sample dispersion along the scanned arcs [2410.08383]. In proposed inelastic modes, the second derivative of the tunneling current can directly access bosonic response functions. For magnetic excitations, one obtains
$$
\frac{\partial^2 I^{(2)}}{\partial \phi^2} = \gamma \sum_{n=0}^2 S(\Delta K_n(\theta), \phi),
$$
so that twist selects the probed momentum of the dynamical spin structure factor [2402.04311]. For superconducting states, the superconducting spectral function
$$
A_s(k, \omega) = u_k^2 \delta(\omega - E_k) + v_k^2 \delta(\omega + E_k)
$$
implies that the relative intensities of positive- and negative-bias quasiparticle peaks encode the Bogoliubov coherence factors $u_k^2$ and $v_k^2$, and hence the momentum dependence of $|\Delta_k|$ along the QTM trajectories [2510.13641].

## 4. Foundational experiments and benchmark performance

The original experimental paper established several benchmarks at $T=300\,\mathrm{K}$ [2208.05492]. In monolayer-graphene–monolayer-graphene momentum-resolved tunneling through WSe$_2$, the measured $dI/dV$ and $d^2I/dV^2$ maps displayed the predicted straight-X and curved-X features in the $(\theta,V_b)$ plane. Fitting the straight-X yielded
$$
v_F = 1.05 \pm 0.02 \times 10^6\,\mathrm{m/s},
$$
and the narrow angular peak at $V_b=40\,\mathrm{mV}$ had $\mathrm{FWHM}\approx 0.2^\circ$, implying momentum resolution of approximately $0.004$ of the Brillouin zone [2208.05492]. Modeling included lifetime broadening $\Gamma(\epsilon)=\Gamma_0+\Gamma_1|\epsilon-\mu|$ with fitted $\Gamma_0\approx4\,\mathrm{meV}$ and $\Gamma_1\approx0.035$, from which the inferred low-energy coherence length was approximately $150\,\mathrm{nm}$, comparable to the tip plateau size [2208.05492].

In direct-contact in-situ twist experiments on monolayer graphene, the conductance $dI/dV(\theta)$ at $300\,\mathrm{K}$ was mirror-symmetric about $30^\circ$, minimal near $30^\circ$, and exhibited sharp commensurate peaks at $\theta=21.8^\circ$ and $38.2^\circ$, corresponding to the $\sqrt7\times\sqrt7$ supercell [2208.05492]. The 2026 construction paper independently validated the instrument on graphite–graphite junctions, again finding clear $60^\circ$ periodicity and enhanced conductance near $21.8^\circ$ and $38.2^\circ$, with stable conditioned junction conductance of a few $\mu\mathrm{S}$ [2604.03483]. That validation is significant because it anchors practical angle calibration through the $C_6$ symmetry of the lattice and through the recurrence of the commensurate peaks.

QTM also directly imaged the bands of twisted bilayer graphene with $\theta_{\mathrm{TBG}}\approx2.7^\circ$. In monolayer-graphene–WSe$_2$–TBG junctions, $d^2I/dV^2$ 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 $\Delta\theta=2.7^\circ$ [2208.05492]. Using the imaged monolayer-graphene Dirac features as an internal energy calibrant, the flat-band dispersion $E(k)$ was extracted and found to agree broadly with Bistritzer–MacDonald trends while exhibiting a measurable electron–hole asymmetry of approximately $12\%$ along $K_{\mathrm{bot}}$–$M$–$K_{\mathrm{top}}$ and approximately $20\%$ near $K_{\mathrm{top}}$–$M$ [2208.05492]. 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 [2208.05492].

A further benchmark was local pressure tuning. Using AFM force control, the original paper applied $\mu\mathrm{N}$-scale forces over a small junction area, generating GPa-scale pressures. At $P=0.01$, $0.40$, and $0.68\,\mathrm{GPa}$, the flat bands moved toward $V_b=0$ while remote bands moved away, consistent with pressure-enhanced interlayer tunneling and band anticrossing [2208.05492]. The flat-band width at $M$ decreased linearly with pressure and was reduced by approximately $17\%$ at $0.68\,\mathrm{GPa}$; the paper noted that theory predicted approximately $6$–$14\%$ and that linear extrapolation suggested full band flattening near $P\sim4\,\mathrm{GPa}$ for $2.7^\circ$ TBG [2208.05492].

## 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 [2507.03189]. Fitting the full maps with the logarithmically corrected dispersion yielded
$\alpha=0.32\pm0.01$, $\epsilon_\parallel=8.3\pm0.3$, cutoff $A=3.3\,\mathrm{eV}$, and junction areal capacitance $\epsilon_1/d=2.4\,\epsilon_0/\mathrm{nm}$, while the low-bias apparent velocity remained approximately $1.04\times10^6\,\mathrm{m/s}$ [2507.03189]. 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$_2$ barrier into TBG at $T=4\,\mathrm{K}$, with the probe–sample angle continuously tunable with millidegree precision and with momentum and energy resolutions reported as $\Delta k\sim3\times10^{-3}\,\mathrm{\AA}^{-1}$ and $\Delta E\le10\,\mathrm{meV}$ [2506.20738]. Away from the magic angle, at $\theta_{\mathrm{TBG}}=1.2^\circ$, the measured bands along the QTM trajectory followed single-particle Bistritzer–MacDonald theory, showing Dirac points at $K_T$ and $K_B$, a flat-band bandwidth of about $70\,\mathrm{meV}$ near the $I$ points, gaps of approximately $50\,\mathrm{meV}$ and $40\,\mathrm{meV}$ to the remote conduction and valence bands, and remote-band van Hove singularities at $+174\,\mathrm{meV}$ and $-171\,\mathrm{meV}$ [2506.20738].

Near the magic angle, at $\theta_{\mathrm{TBG}}=1.1^\circ$, 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 $35\,\mathrm{meV}$ and flat to within approximately $4\,\mathrm{meV}$, whereas near the $I$ point the bands remained dispersive and gapless [2506.20738]. Upon doping from $v=-4$ to $v=+4$ and $v=4.6$, the heavy flat bands exhibited Mott-like cascades at momenta such as $K_T$, while the light Dirac-like sector near $I$ underwent Hartree-driven stretching with total shifts of approximately $42\,\mathrm{meV}$ at $v=+4$ and approximately $54\,\mathrm{meV}$ at $v=-4$ [2506.20738]. 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 $I$, with the normalized radius of the light region growing to approximately $0.45$ at $v=4$ [2506.20738]. The same study extracted $W_0/W_1=0.6$ from momentum-dependent peak intensities, smaller than the commonly used $0.8$, and identified a persistent filling-independent excitation at $\pm15\,\mathrm{meV}$ relative to $E_F$ that was present only in the heavy regions of momentum space [2506.20738].

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 $2.7^\circ$ [2208.05492]. 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 [2506.20738]. A plausible implication is that QTM is particularly powerful when the decisive physics is strongly $k$-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 $T=4\,\mathrm{K}$ 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
$$
q_M(\theta)=2K_D\sin(\theta/2),
$$
which bridges the twist-induced momentum mismatch [2407.13404]. In that work, $d^2I/dV_b^2$ peaks traced acoustic and optical phonon branches, and the inelastic step height obeyed
$$
\Delta G_\nu(\theta)=B A_{\mathrm{tip}} V_T V_B \left[ |g_{\mathrm{inter-layer},\nu}(q_M)|^2 + \alpha^2 N_{\mathrm{layer}} |g_{\mathrm{in-layer},\nu}(q_M)|^2 \right].
$$
The measured optical coupling yielded $g_{\mathrm{TO}}\approx300$–$350\,\mathrm{meV}$, 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 [2407.13404]. 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 [2407.12092].

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 $120^\circ$ ordered state [2402.04311]. For quantum spin liquids, a graphene–QSL–graphene planar junction was proposed in which exchange-mediated inelastic tunneling gives
$$
\frac{d^2 I^{(2)}}{dV_{tb}^2}(V_{tb},\theta)\propto \sum_{n=0}^2 S(\Delta\mathbf{K}_n,\omega=eV_{tb}),
$$
so that twist and bias directly image the barrier’s dynamical spin structure factor [2308.15533]. For plasmons in TBG, a 2025 theory developed a multiband inelastic tunneling formalism in which features in $G(V,\theta)$ and $d^2I/dV^2$ track the plasmon dispersion and the electron–plasmon coupling strength, with strong dependence on screening environment and local-field effects [2506.05485].

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
$$
R(k)=\frac{I_+(\theta)}{I_-(\theta)}=\frac{u_k^2}{v_k^2},
$$
allowing direct extraction of $|\Delta_k|$ along the QTM trajectory from the peak separation and intensity ratio [2510.13641]. 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 $(\theta,\mu_t)$ space, and reconstructing Bogoliubov equal-energy contours [2509.22902]. 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 [2208.05492]. In practical construction, stable operation depends on vibration isolation, careful tilt control, compact mechanical layout, and clean membrane transfer; at low conductance, below $1\,\mu\mathrm{S}$ in the graphite validation experiments, angle-dependent signals become noisy and irreproducible [2604.03483]. In cryogenic phonon spectroscopy, small-angle elastic tunneling can overwhelm the inelastic signal below approximately $6^\circ$ [2407.13404]. 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 [2410.08383] [2506.20738].

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 [2208.05492] [2407.13404] [2506.20738]. 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 [2604.03483] [2402.04311] [2510.13641].

Source: https://www.emergentmind.com/topics/quantum-twisting-microscope-qtm