Quantum Twisting Microscope with 3-Channel Spectroscopy Resolves Momentum-Dependent Superconducting Pairing

Superconductivity, the ability of certain materials to conduct electricity with zero resistance, remains a profoundly important and intensely studied phenomenon, and understanding its microscopic origins requires increasingly sophisticated techniques. Yuval Waschitz, Ady Stern, and Yuval Oreg, all from the Weizmann Institute of Science, now present a theoretical framework for directly probing superconductivity with unprecedented momentum resolution using a novel instrument called the quantum twisting microscope. Their work establishes this microscope as a powerful tool for mapping the superconducting state, revealing crucial details about how electrons pair up and how this pairing depends on their momentum within the material. By directly measuring the superconducting spectral function, the team’s approach allows for the detection of subtle symmetry breaking and the identification of key features in the superconducting order parameter, offering new insights into the fundamental mechanisms driving superconductivity in two-dimensional materials.

Momentum conservation allows the Quasiparticle Tunneling Microscopy (QTM) to directly measure the superconducting spectral function along well-defined trajectories in momentum space. This technique reveals how electrons pair up to form superconducting currents and provides insights into the material’s superconducting properties. The relative intensities of electron and hole excitations encode information about the pairing strength, revealing how this strength varies with momentum. Threefold rotational symmetry breaking and the presence of nodal points, where superconductivity may be suppressed, can also be directly detected. By applying this framework to models of complex materials, the team establishes the QTM as a powerful tool for investigating unconventional superconducting systems.

STM Mapping Reveals Superconducting Gap Symmetry

This work focuses on understanding and detecting the pairing symmetry in magic-angle twisted bilayer graphene (MATBG), a material exhibiting unconventional superconductivity. The researchers propose a novel experimental technique using a Scanning Tunneling Microscope (STM) to map the superconducting gap, a crucial energy range for superconductivity, and identify potential nodes where the gap closes. This goes beyond simply observing superconductivity and aims to determine how it arises in this complex material. The technique relies on understanding that MATBG, with its specific twist angle, creates unique electronic properties that enhance electron interactions and promote superconductivity.

The research explores key concepts including the magic-angle twist, which creates a flat electronic band structure, and pairing symmetry, which dictates the material’s superconducting properties. Nodes in the superconducting gap, points where superconductivity is suppressed, are also central to the investigation. The STM is used to probe the superconducting gap by measuring the differential conductance, a measure of current change with voltage, which is directly related to the material’s electronic structure. Understanding the density of states and the Fermi surface are also crucial to interpreting the results.

The team performs detailed band structure calculations to model the electronic properties of MATBG and calculates the superconducting gap’s dependence on momentum. The proposed experimental method involves measuring the differential conductance at zero bias voltage, sensitive to the superconducting gap, and tuning the chemical potential of the STM tip to scan momentum space. A key innovation is detecting sharp features in the measurements, indicating the presence of nodes in the superconducting gap, and using geometric triangulation to pinpoint their location. The researchers predict that py-wave pairing will exhibit these sharp features, while s-wave pairing will not.

The team’s analysis confirms that the proposed method accurately locates nodal points and confirms the pairing symmetry in MATBG. This work addresses a fundamental question in unconventional superconductivity, aiming to understand the pairing mechanism in MATBG. The novel experimental technique and data analysis methods could also be used to study other unconventional superconductors, potentially leading to the development of new materials with improved superconducting properties.

Twisting Microscope Maps Superconducting Excitation Spectrum

The quantum twisting microscope (QTM) directly probes the superconducting spectral function along defined trajectories in momentum space, revealing crucial information about pairing symmetry and the microscopic origin of superconductivity in two-dimensional materials. This technique utilizes a graphene tip rotated relative to the sample, enabling selective measurement of the sample’s spectral function due to in-plane momentum conservation. The team analytically evaluated the differential conductance, demonstrating that the Bogoliubov excitation spectrum, which describes the energy of excited electrons, can be mapped along the tip’s trajectory by varying the bias voltage and rotation angle. Experiments using models of materials demonstrate the QTM’s capability to trace the energies of Bogoliubov excitations, revealing the pairing magnitude.

For s-wave pairing, the QTM traces identical spectra along all measured trajectories, while px and py pairings exhibit broken symmetry, resulting in splitting of the traces and the appearance of distinct gaps. Measurements confirm that the QTM extracts the same gap magnitude as conventional STM, but at a specific momentum. Detailed analysis of the differential conductance at various twist angles reveals coherence peaks whose intensities are proportional to the Bogoliubov coherence factors. The team extracted quasiparticle dispersions and pairing magnitudes, demonstrating a variation in pairing magnitude along the measured trajectory for py-wave pairing. These results establish the QTM as a powerful tool for directly probing the pairing symmetry and microscopic origin of superconductivity in two-dimensional materials, providing insights into the behavior of electrons in these complex systems.

Quantum Twisting Reveals Superconducting Pairing Symmetry

This work establishes a theoretical framework for utilizing the quantum twisting microscope (QTM) to probe superconductivity with momentum resolution. The QTM, a device where a graphene tip rotates relative to a two-dimensional sample, directly measures the superconducting spectral function along defined trajectories in momentum space, revealing information about the pairing of electrons. By analyzing the relative intensities of electron and hole excitations, the method determines the magnitude of the pairing amplitude and identifies potential symmetry breaking or nodal points within the superconducting order parameter. The researchers demonstrate that the QTM can be applied to models of materials, offering insights into superconductivity in various two-dimensional materials, including moiré superconductors.

The technique allows for the measurement of pairing potential and characterization of unconventional superconductivity, and can be combined with normal-state measurements to calibrate tunneling matrix elements and understand the material’s normal state properties. Looking ahead, the team suggests extending the technique to stronger tunneling regimes to enable phase-sensitive spectroscopy and incorporating spin and valley selectivity to explore the internal structure of the superconducting pairing. These advancements promise a more comprehensive understanding of superconductivity in two-dimensional materials and moiré systems, solidifying the QTM as a powerful platform for investigating these complex phenomena.