Researchers have, for the first time, visualized Landau-Zener-Majorana (LZM) tunnelling, described as “notoriously elusive”, within graphene using attosecond-precision subcycle band-structure videography. The work demonstrates a coherent displacement and distortion of momentum distribution at the Brillouin zone edge, capturing the process across the entire first Brillouin zone. This new technique expands upon previous capabilities limited to small electron momenta, providing a comprehensive view of electron behavior within the material. The team’s panoramic view of strong-field-driven electron motion lays the foundation for understanding light-driven phenomena in condensed matter physics.
Attosecond-Precision Subcycle Band-Structure Videography in Graphene
Attosecond-precision subcycle band-structure videography now extends observation of electron behavior to the entire first Brillouin zone, a significant expansion beyond previous techniques limited to smaller momentum ranges. This advancement allows for a comprehensive view of carrier dynamics within the material, essential for understanding how coherent field-driven phenomena and scattering events interact. Researchers at the University of Regensburg and Philipps-Universität Marburg achieved this by developing a method to track electron movement throughout momentum space.
This step is important for investigating light-matter interactions in quantum materials. The ability to visualize these processes across the entire Brillouin zone is vital because lightwave-driven elementary processes often occur throughout momentum space.
Simultaneously, the visualizations capture how specific scattering events influence and potentially limit the fully coherent evolution of the system, providing insight into the factors governing electron behavior under strong light fields. The team’s approach builds upon recent developments in time-resolved angle-resolved photoemission spectroscopy, but overcomes the previous limitation of one-dimensional momentum access. The implications of this work extend beyond fundamental physics, potentially resolving key questions in condensed matter physics and informing the development of ultrafast information technologies.
“Following the same principle, our comprehensive subcycle band-structure videography may soon resolve a plethora of other key open questions of modern condensed matter physics and upcoming ultrafast information technologies,” the researchers state. The method’s ability to visualize electron motion with attosecond precision, coupled with its broad momentum space coverage, provides a powerful tool for investigating a wide range of lightwave-driven phenomena in quantum materials, promising a deeper understanding of these complex interactions and clearing the way for future advancements in the field.
Lightwave-Driven Landau-Zener-Majorana Transitions Visualized
Researchers achieved this by employing attosecond-precision subcycle band-structure videography, enabling observation of quantum processes not as averaged results but as they unfold in real time. This capability is important for understanding how strong light fields manipulate electron trajectories and engineer material properties. The team directly observed Landau-Zener-Majorana (LZM) tunnelling, described as a “notoriously elusive” process, within the two-dimensional momentum space of graphene. This wasn’t simply detection of tunnelling, but visualization of a specific type of non-adiabatic transition where electrons move between energy bands under the influence of both light and material properties.
The videography reveals how the carrier distribution is initially displaced along the ky direction, then elongated into an ellipse due to the LZM transitions, a process occurring on a timescale of femtoseconds. For later delays, the electron distribution broadens along kx, indicating the influence of scattering events.
Analysis of the electron distribution’s centre of mass shows its displacement, providing a direct measure of the lightwave-driven electron motion. The researchers noted that, for vanishing fields, the electron distribution relaxes back to its original shape, completing the cycle. This detailed observation of LZM transitions is particularly important because these events often occur throughout momentum space, and understanding their behavior is essential for controlling light-induced phenomena in quantum materials.
The implications of this technique extend beyond graphene, offering a pathway to investigate similar strong-field phenomena in other materials. The ability to visualize these transitions with such precision and across a broad momentum range promises to accelerate the development of lightwave-driven technologies.
Graphene as an Ideal Testbed for LZM Transitions
Graphene’s unique properties now allow for observation of coherent electron dynamics throughout its entire band structure, a feat previously restricted by limitations in both momentum microscopy and subcycle angle-resolved photoemission spectroscopy (ARPES). The new platform increases the accessible momentum area with subcycle resolution by over two orders of magnitude, and peak field strengths by one order of magnitude, enabling visualization of complex electron behavior. Exploiting few-cycle mid-infrared field transients with large peak amplitudes, scientists are driving these coherent electron dynamics within the material.
This advancement allows for the simultaneous observation of displacement and distortion of the light-driven electron distribution, revealing the interplay between intra- and interband dynamics that underpin Landau-Zener-Majorana (LZM) transitions in graphene. The material’s quasi-relativistic electron dispersion and robustness under intense light irradiation have established it as a prime test ground for lightwave electronics, including demonstrations of electronic logic gates and the observation of Floquet-Bloch states.
The ability to directly observe these foundational quantum effects in momentum space had remained elusive until now. The technique overcomes previous restrictions by using the unique characteristics of graphene, making it an ideal testbed for observing LZM transitions. “Graphene’s unique optical, electronic, and chemical properties represent the ideal testbed for observing LZM transitions,” the researchers state in their published work. This approach allows for a detailed understanding of how electrons respond to strong light fields, potentially clearing the way for new optoelectronic devices and a deeper understanding of light-matter interactions at the quantum level.
Expanding Momentum Access with Subcycle Temporal Resolution
This wider field of view allows for a more complete understanding of electron behavior within graphene under intense light, moving beyond one-dimensional momentum access. Graphene’s unique properties facilitated observation of Landau-Zener-Majorana (LZM) interferometry, a phenomenon where electrons undergo ballistic acceleration and potentially tunnel between energy bands. Intense, phase-stable mid-infrared (MIR) pulses at 30 THz drove electrons within an epitaxially-grown graphene monolayer on a silicon carbide substrate.
Subsequent ultrashort extreme ultraviolet (XUV) pulses, with a central photon energy of 21. 7 eV, then photoemitted the electrons, allowing researchers to observe the induced dynamics with subcycle temporal resolution. The interplay of these processes dictates strong-field light-matter interaction. Optical selection rules within graphene favor transitions perpendicular to the electric field’s polarization, influencing the direction of electron movement. The experimental setup involved a s-polarized MIR pulse driving the graphene, followed by a p-polarized XUV probe pulse with a variable time delay.
This configuration enabled snapshots of the induced dynamics at subcycle resolution, revealing how electrons respond to the applied field. The researchers write, detailing the method used to initiate the observed effects. The resulting data provides a complete view of carrier dynamics across the entire first Brillouin zone, important for tracking both coherent field-driven phenomena and scattering-induced momentum redistribution.
Coherent Displacement of Momentum Distribution at Brillouin Zone Edge
This isn’t merely a shift in position. But a reshaping of how electrons distribute themselves within graphene’s energy bands under intense light, a phenomenon previously predicted but never directly visualized with this level of detail. Researchers were able to disentangle competing scattering processes and assess their impact on coherent electronic control through electron redistribution and thermalization. Simulations predict distinctive momentum fingerprints for electron-electron and electron-optical phonon scattering processes, allowing for identification of their signatures within the 2D mapping.
Neglecting all forms of scattering results in a broadening, up to 0. 053 Å-1, and displacement, approximately 0. 107 Å-1, of the carrier distribution along the direction of the driving field, with the distribution remaining elliptical at the end of the mid-infrared pulse. The theory also qualitatively reproduces the rise in carrier density in the conduction band, further validating the experimental findings and demonstrating the accuracy of the model in capturing the complex dynamics of light-driven electrons in graphene.
Non-Thermal Electron Distributions Reveal Scattering Processes
This level of detail wasn’t previously accessible, as the technique allows researchers to observe how these processes affect lightwave electronic dynamics. The work moves beyond simply observing electron behavior to understanding the mechanisms governing it, revealing how different scattering events influence the movement of electrons within the material. Observations of the carrier distribution showed a clear evolution over time, directly linked to the applied field and the influence of Landau-Zener-Majorana (LZM) transitions.
MIR Field Transients Drive Coherent Electron Dynamics
This advance moves beyond simply tracking electron movement to visualizing the forces that govern it, offering a new window into quantum material dynamics. Researchers observed an apparent shift in the overall band structure, a phenomenon caused by the streaking of photoemitted electrons in the incident mid-infrared field while in vacuum. This effect, however, proved useful; it allowed for direct retrieval of the mid-infrared waveform at the sample surface, and subsequent compensation for the shift, isolating the subcycle field-driven electron dynamics occurring within graphene’s electronic band structure.
A femtosecond snapshot of the occupied band structure, captured at a time of -13. 6 fs, revealed a highly nonthermal electron distribution driven by the lightwave. Simultaneously, electrons undergo ballistic acceleration by the electric field and interband Landau-Zener-Majorana transitions on subcycle timescales, tunneling from the valence band to the conduction band, resulting in an elongated electron distribution in the conduction band, weighted in the direction parallel to the field.
Bloch Acceleration and LZM Transitions in Dirac Fermions
These equations model both intraband acceleration and interband Landau-Zener-Majorana (LZM) coupling, providing a comprehensive framework for understanding the observed dynamics. The observed LZM transitions, occurring in the band structure of a solid for the first time, are not isolated events but are coupled with the field-driven acceleration of quasi-relativistic fermions along the Dirac cone. A systematic switch-off analysis further clarifies how coherent strong-field light-matter interaction manifests in the observed dynamics, pinpointing the contributions of various physical processes.
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