Quantum Twisting Microscopy

• Quantum Twisting Microscopy is a momentum-selective tunneling platform that uses a rotated 2D graphene tip to probe energy bands and collective excitations in 2D materials.
• It leverages twist-angle control to enforce momentum conservation, converting local tunneling currents into detailed momentum- and energy-resolved spectroscopic signals.
• Experimental implementations demonstrate high resolution and room-temperature operation, enabling studies of superconductivity, spin excitations, phonons, and plasmons.

Searching arXiv for recent and foundational papers on Quantum Twisting Microscopy and adjacent meanings of the term. {"query":"Quantum Twisting Microscope arXiv (Inbar et al., 2022, Pichler et al., 2024, Xiao et al., 2024, Wei et al., 2024, Wei et al., 5 Jun 2025, Lee et al., 3 Jul 2025, Waschitz et al., 15 Oct 2025, Biswas et al., 3 Apr 2026)", "max_results": 10} Quantum Twisting Microscopy (QTM) is a scanning-probe and planar tunneling technique in which a crystalline, atomically thin tip—typically monolayer graphene—is rotated relative to a two-dimensional sample so that the junction is controlled by lateral position, vertical separation, bias, and twist angle $\theta$. In the tunneling regime, the extended 2D–2D interface enforces approximate in-plane momentum conservation, so the twist angle acts as a momentum knob and the measured current becomes momentum- and energy-resolved rather than purely local in real space. In direct-contact mode, the same platform functions as an in-situ twistronic device in which the interface itself is the system under study (Inbar et al., 2022).

1. Definition and scope

In the condensed-matter literature, QTM denotes a momentum-selective tunneling platform in which a crystalline 2D tip is twisted relative to a 2D sample to form a planar junction. The central control variable is the relative crystallographic angle, and the principal observables are $I(\theta,V)$, $dI/dV$, and $d^2I/dV^2$, measured while the tip Dirac point or Fermi contour is swept through the sample Brillouin zone by changing $\theta$ and bias (Inbar et al., 2022).

This usage is distinct from optical quantum imaging with twisted photons. Work on “quantum imaging exploiting twisted photon pairs” develops a Hong–Ou–Mandel-based imaging protocol with orbital-angular-momentum modes and tunable spatial correlations, but that is an optical correlation-imaging architecture rather than the planar tunneling microscope defined above (Cui et al., 2022). Likewise, the review “Quantum light microscopy” does not define “quantum twisting microscopy” and does not use the language of twisting, orbital angular momentum, or Laguerre–Gaussian modes (Bowen et al., 2023). A common misconception is therefore to treat all “twisting” usages as equivalent; in published practice, QTM most specifically denotes the twist-controlled vdW tunneling microscope of graphene-based condensed-matter spectroscopy.

2. Device architecture and operating principle

A QTM device consists of a 2D crystalline tip, a 2D sample, a planar tunneling barrier, and electrostatic control of both subsystems. In the superconductivity formulation, the electrochemical potentials satisfy

$-eV_b = \mu_T - \mu_S + \phi,$

where $V_b$ is the bias, $\mu_T$ and $\mu_S$ are tip and sample chemical potentials, and $\phi$ is the electrostatic potential difference across the junction (Waschitz et al., 15 Oct 2025).

The defining kinematic constraint is in-plane momentum conservation up to reciprocal lattice vectors: $I(\theta,V)$0 For incommensurate twist angles there is at most one pair $I(\theta,V)$1 for a given $I(\theta,V)$2, so different Umklapp channels do not interfere (Waschitz et al., 15 Oct 2025). Because the graphene tip has a sharp Dirac dispersion and a small Fermi surface, the tunneling current is dominated by states near the tip Dirac point, and as $I(\theta,V)$3 is varied the Dirac point traces a trajectory through the sample’s extended moiré Brillouin zone (Waschitz et al., 15 Oct 2025).

This is the core distinction from STM. In STM, a point contact does not conserve in-plane momentum and $I(\theta,V)$4 measures the local density of states after integrating over momentum. In QTM, the crystalline, twisted planar junction converts the tunneling current into a momentum- and energy-resolved probe (Waschitz et al., 15 Oct 2025). The original QTM work further emphasized that the tip is itself a vdW device with a mesoscopic 2D interface, so electrons tunnel through many spatially distinct paths that remain quantum coherent and therefore interfere (Inbar et al., 2022).

3. Tunneling formalism and Dirac-point spectroscopy

The general weak-tunneling current can be written as

$I(\theta,V)$5

with $I(\theta,V)$6 and $I(\theta,V)$7 the tip and sample spectral functions (Waschitz et al., 15 Oct 2025). In the elastic-QTM formulation used for moiré magnetism, the same structure appears as

$I(\theta,V)$8

so the twist angle enters through the momentum shift of the graphene Brillouin zone and the current samples the single-particle spectral function $I(\theta,V)$9 of the bottom layer (Pichler et al., 2024).

A particularly sharp regime is “Dirac-point spectroscopy,” where features associated with the tip Dirac points provide a more immediate and precise map of the sample band structure than Fermi-edge singularities (Wei et al., 2024). For a flat sample band relative to the tip, zero temperature, infinite lifetime, and $dI/dV$0, the second derivative of the current localizes onto the superconducting spectral function: $dI/dV$1 In the nonsuperconducting case, the same kinematic logic underlies the use of $dI/dV$2 as a map of band dispersions along the trajectories $dI/dV$3 set by the twist (Waschitz et al., 15 Oct 2025).

The formalism is also wavefunction-sensitive. For MATBG, the tunneling matrix elements depend on the top-layer amplitudes $dI/dV$4 and $dI/dV$5, so QTM does not only trace dispersions; it also probes layer polarization and sublattice-interference effects (Wei et al., 2024).

4. Spectroscopic modalities

QTM has been developed well beyond elastic band mapping. In moiré magnets, elastic QTM measures the single-particle spectral function, while an inelastic three-layer geometry measures the dynamical spin structure factor. In the spin-channel formulation,

$dI/dV$6

so the second derivative of the inelastic current directly measures the spin structure factor at momenta set by the twist angle (Pichler et al., 2024). A closely related tunneling proposal for quantum spin liquids arrives at

$dI/dV$7

thereby turning QTM into an atomically thin analogue of momentum-resolved spin spectroscopy for fractionalized excitations (Peri et al., 2023).

For phonons, the large-twist regime is especially important: while elastic tunneling dominates at small twist angles, the momentum mismatch between the $dI/dV$8-points of tip and sample at large twist angles can only be bridged by inelastic scattering, allowing phonon dispersions to be probed along certain lines in reciprocal space by measuring tunneling current as a function of twist angle and bias voltage (Xiao et al., 2024). For plasmons, the dependence of the differential conductance on twist angle and bias reveals both the plasmon spectrum and the strength of plasmon-electron interactions; the formalism was worked out microscopically for TBG close to the magic angle (Wei et al., 5 Jun 2025).

Superconductivity provides another extension. In the weak-tunneling limit, QTM resolves the superconducting spectral function along twist-selected trajectories and the relative intensities of the positive- and negative-bias peaks encode the Bogoliubov coherence factors. The ratio

$dI/dV$9

allows extraction of $d^2I/dV^2$0, so QTM becomes a direct probe of pairing symmetry, nodal structure, and the microscopic origin of superconductivity in two-dimensional materials (Waschitz et al., 15 Oct 2025).

5. Experimental implementations and performance

The initial QTM demonstrations established the microscope as a practical room-temperature platform. The 2022 work reported room temperature quantum coherence at the tip, direct imaging of the energy bands of monolayer and twisted bilayer graphene, and the ability to apply large local pressures while visualizing the evolution of the flat energy bands of the latter (Inbar et al., 2022). In an MLG/WSe$d^2I/dV^2$1/MLG junction, the current $d^2I/dV^2$2 at small bias exhibited an extremely narrow peak with full width at half maximum of about $d^2I/dV^2$3, corresponding to $d^2I/dV^2$4, which the same work identified as comparable to state-of-the-art ARPES momentum resolution (Inbar et al., 2022).

A later implementation detailed how to build QTM on a commercial AFM. That instrument used a Nanosurf Easyscan 2 platform, an $d^2I/dV^2$5 wedge to compensate cantilever tilt, a focused-ion-beam Pt pyramid of height $d^2I/dV^2$6, a graphite membrane $d^2I/dV^2$7 thick transferred over the pyramid, and continuous rotation at about $d^2I/dV^2$8 during conductance measurements (Biswas et al., 3 Apr 2026). Validation on graphite–graphite junctions showed clear $d^2I/dV^2$9 periodicity and conductance enhancements near the commensurate twist angles of $\theta$0 and $\theta$1, consistent with the hexagonal lattice symmetry and with resonant interlayer tunneling at commensurate angles (Biswas et al., 3 Apr 2026).

Instrumental performance has also improved spectroscopically. Replacing WSe$\theta$2 with hBN as tunneling dielectric extended the accessible bias range to $\theta$3 V and enabled resolution of high-energy features in graphene–graphene tunneling. In that configuration, QTM resolved a logarithmic correction to the Dirac dispersion consistent with electron–electron interactions and extracted a fine-structure constant $\theta$4, notably at room temperature (Lee et al., 3 Jul 2025).

6. Applications, comparison with other probes, and outlook

QTM is particularly valuable where momentum structure matters but standard probes are incomplete. For superconductors, it accesses both occupied and unoccupied Bogoliubov branches and directly encodes coherence factors, unlike ARPES, which observes only occupied states at low temperature (Waschitz et al., 15 Oct 2025). For moiré magnets, it can distinguish ferromagnetic and antiferromagnetic generalized Wigner crystals through their single-particle spectra and their magnon or collective-mode structure factors, and it can track quantum phase transitions such as the proposed transition between a chiral spin liquid and a $\theta$5 ordered state (Pichler et al., 2024). For quantum spin liquids, it provides a route to $\theta$6 in systems too thin for neutron scattering (Peri et al., 2023).

The phonon and plasmon theories further show that QTM is not limited to quasiparticle bands. It can operate as a momentum-resolved inelastic tunneling spectrometer of collective electronic and lattice modes, with the twist angle selecting the relevant $\theta$7-vector and the bias selecting the excitation energy (Xiao et al., 2024). In TBG close to the magic angle, this establishes a concrete route to spectroscopic extraction of plasmon dispersions and plasmon-electron couplings under different screening environments (Wei et al., 5 Jun 2025).

A further practical implication is that QTM is both local and reconfigurable. Standard twistronics relies on globally twisted bilayers with fixed $\theta$8; QTM varies $\theta$9 continuously in a single device and at a single spatial location (Biswas et al., 3 Apr 2026). This suggests direct studies of domains, inhomogeneity, and pressure-tuned band engineering within the same sample region. A plausible implication is that QTM will continue to occupy the niche between STM and ARPES: more momentum-resolved than STM, more local and device-compatible than ARPES, and uniquely adaptable to vdW heterostructures whose most important degrees of freedom are twist, moiré momentum, and interlayer coherence.