Microscopy Reveals Hidden States in Graphene Layers

Researchers are increasingly focused on utilising light to control the electronic properties of materials, a field known as Floquet engineering. Nils Jacobsen, from the Institute for Theoretical Physics and Bremen Center for Computational Materials Science at the University of Bremen, Michael Schüler of the PSI Center for Scientific Computing, Theory and Data at the Paul Scherrer Institute, and Angel Rubio from the Max Planck Institute for the Structure and Dynamics of Matter, alongside Martin Wolf, Melanie Müller and Michael A. Sentef working with colleagues at the Fritz Haber Institute of the Max Planck Society and the University of Bremen, demonstrate a novel approach to probing these light-induced states. Their work introduces ultrafast terahertz scanning tunneling microscopy (THz-STM) as a real-space, energy-resolved technique for investigating Floquet physics in graphene. This method offers the potential for direct, local detection of key features like Floquet gaps and edge states, representing a significant advancement beyond existing spectroscopic techniques and providing a pathway to reconstruct band structures and examine chiral edge state properties.

THz-STM offers unprecedented insight into manipulating the behaviour of electrons in materials. This breakthrough allows for real-time observation of quantum effects within graphene, potentially paving the way for more efficient electronic devices. The method visualises how light can be used to engineer new properties in two-dimensional materials.

This research introduces ultrafast terahertz scanning tunneling microscopy (THz-STM) as a means to probe light-induced topological states in materials, offering a real-space, energy-resolved view of Floquet physics. This technique overcomes limitations inherent in existing methods such as ultrafast transport measurements and time-resolved photoemission spectroscopy.

The study derives a theoretical framework, based on nonequilibrium Green’s functions, that extends standard STM theory to account for time-dependent tunneling currents, providing a clear interpretation of the observed signals. This framework is crucial for understanding the rectified ultrafast currents measured by THz-STM, which depend on driving field strength and photon energy.

The research focuses on applying this approach to graphene and graphene nanoribbons. Results demonstrate that THz-STM can spectroscopically access Floquet-induced gap openings in bulk graphene, allowing for comparison between pulsed and continuous-wave light illumination. For graphene nanoribbons, the technique reveals time- and space-resolved imaging of Floquet-induced topological edge states, pinpointing the ribbon width at which these protected states cease to exist.

Furthermore, the team shows how the band structure of graphene nanoribbons and the chiral edge modes can be reconstructed through Floquet quasiparticle interference. Circularly-dichroic Floquet local density of states renormalization around chiral impurities identifies edge mode chirality, offering a direct probe of the spin-polarized nature of these edge states.

By enabling the visualization of these subtle effects at the nanoscale, this research paves the way for a deeper understanding of light-matter interactions and the potential for controlling topological properties in quantum materials, opening possibilities for novel electronic devices and quantum technologies. The ability to map Floquet topology with atomic precision addresses a critical need in the field, particularly in materials where inherent inhomogeneity can significantly alter the induced topological properties.

Terahertz Spectroscopy Reveals Floquet Band Modifications and Topological Edge States in Graphene

Simulations employing a field strength of 350kV cm−1 and a photon energy of 0.4 eV reveal hybridization gaps appearing at the edges of the Floquet Brillouin zone at an energy of ħΩ/2, alongside a Haldane gap opening at the Dirac point. These gaps signify direct spectroscopic access to Floquet-induced band modifications within bulk graphene. Continuous-wave measurements, contrasted with pulsed pump-probe protocols, demonstrate the ability to discern these Floquet-induced features in the steady-state limit.

For finite graphene nanoribbons, the research details time- and space-resolved imaging of Floquet-induced edge states, providing a localized view of these topological phenomena. Analysis establishes a ribbon-width scale below which the protection of these edge states breaks down, influencing the robustness of the edge state confinement. Band structures of graphene nanoribbons and Floquet chiral edge modes are reconstructed via Floquet quasiparticle interference, offering a detailed map of the electronic structure under driven conditions. This reconstruction relies on the interference patterns arising from scattered electronic wave functions, providing insights into the topological characteristics of the system.

Rectified charge measurement via time-dependent terahertz scanning tunneling microscopy

Ultrafast terahertz scanning tunneling microscopy (THz-STM) serves as the central technique in this work, providing a real-space, energy-resolved probe of Floquet physics. Building upon conventional scanning tunneling microscopy, THz-STM introduces a time-dependent element by illuminating the STM tip with a single-cycle terahertz laser pulse, generating a time-dependent bias voltage, VTHz(t).

While the full temporal evolution of the tunneling current remains beyond the bandwidth of current STM electronics, the rectified charge, Qrect, accumulated over time is measured. This rectified charge arises even when the time-dependent bias integrates to zero, due to a non-linear and temporally non-local current-bias relationship within the tunneling junction.

The non-linearity is fundamentally determined by the local density of states (LDOS) of the sample. Crucially, the study acknowledges that the standard adiabatic interpretation of THz-STM is insufficient, necessitating accounting for the non-equilibrium nature of the tunneling process and the resulting temporal non-locality. To theoretically underpin the experimental approach, a nonequilibrium Green’s function formalism was derived for time-dependent tunneling, extending standard STM theory and offering an intuitive understanding of the rectified ultrafast currents. The method was then applied to both bulk graphene and graphene nanoribbons of varying widths, allowing for direct spectroscopic access to Floquet-induced gap openings in the bulk material and time- and space-resolved imaging of Floquet-induced edge states in the finite ribbons, identifying the point at which edge state protection diminishes with decreasing ribbon width.

Visualising transient quantum states with ultrafast terahertz scanning tunnelling microscopy

For decades, ultrafast spectroscopy has been the primary tool for observing and manipulating light-induced quantum states in materials, relying on indirect measurements of how materials respond to brief pulses of light. While powerful, these techniques often struggle to pinpoint exactly where these changes occur at the nanoscale, and disentangle bulk effects from those happening at edges or surfaces.

This work proposes a significant refinement: ultrafast terahertz scanning tunneling microscopy, offering the potential to ‘see’ these fleeting quantum states in both space and energy. What distinguishes this development isn’t simply a technological advance, but a shift in how we probe these phenomena. By extending standard scanning tunneling microscopy theory to account for time-dependent tunneling currents, the researchers create a framework for directly imaging the gaps and edge states induced by Floquet physics.

The demonstration on graphene and nanoribbons is compelling, showing how the technique could map band structures and even detect chiral edge states, potentially revealing subtle asymmetries in the material. Achieving the necessary temporal and spatial resolution remains a considerable hurdle, and interpreting the complex tunneling signals will require careful modelling and validation.

Looking ahead, this technique could be combined with other spectroscopic methods to provide a more complete picture of light-matter interactions. The real promise lies in extending this approach to more complex materials, potentially unlocking new functionalities and paving the way for designer quantum materials with tailored optical properties.