Giant Berry-phase-driven X-ray beam translations in strain-engineered semiconductors

The manipulation of visible/infrared light through its interactions with artificially structured media is a cornerstone of modern photonics. The rescaling of this concept to the X-ray realm, however, is extremely challenging, due to the inherent difficulty of realizing photonic structures with the sub-nanometric resolution dictated by X-ray wavelengths.

A promising approach to X-ray photonics may be based on the so-called Berry-phase translation effect, a geometric phase phenomenon that reflects how quantum states evolve along a path in parameter space. At a fundamental level, this effect originates from the simultaneous presence of Berry curvatures in real and reciprocal space, which modify the semiclassical trajectory of the X-ray wave packet. As a result, X-rays transmitted through a deformed crystal undergo large lateral translations, of interest for applications in X-ray photonics and interferometry.

In this work, the crystal deformations required to trigger the Berry-phase effect are achieved by selectively introducing hydrogen into GaAsN/GaAs epilayers, locally modifying their lattice structure in a controlled and reproducible way. Through a series of X-ray transmission experiments, carried out at the XRD1 beamline of Elettra on these strain-engineered samples, we consistently measured beam translations in excess of 100 μm (see Fig. 1), while also revealing a clear dependence of the observed translations on the deterministically altered lattice deformation profile.

Figure 1: (a) Sketch of the experimental configuration employed to measure the X-rays transmitted by selectively hydrogenated GaAsN samples. For θ ~ θ_B [where θ_B is the Bragg angle corresponding to the (004) direction of GaAs], the Berry-phase translation effect can be observed, with the appearance of two or more transmission branches corresponding to the interaction of the propagating X-rays with different regions of the deformed sample. (b) False-color image of the intensity profile of the transmitted X-ray photons — measured along the vertical axis of the detector, see (a) — plotted as a function of θ - θ_B. The figure refers to a GaAsN:H sample patterned with dots spaced by a = 1 µm and with diameter w = 1 µm. (c) False-color plots of the distribution of Δ_Berry, the deviation of the X-ray group velocity computed at each point of the sample (see origial paper). The beam deviations associated with points located within the substrate and in the untreated/hydrogenated regions of the epilayer are displayed in green, blue, and red, respectively. (All panels are adapted from M. Felici et al., Adv. Mater. 38, e13259 (2026), published under a Creative Commons Attribution License).

The experimental results were compared with an extensive numerical analysis of the X.ray beam propagation in the fabricated samples, based on the direct computation (via Finite-Elements calculations) of the deformation landscape within the crystal. Through this comparison, the individual translation branches observed in X-ray transmission (see Fig. 1b) can be traced back to specific deformation features present within the samples (see Fig. 1c), establishing a predictive framework for the control of X-ray propagation via Berry-curvature engineering.

These results open new, enticing prospects for the realization of tailor-made, compact X-ray optical components, with potential applications in photonics and interferometry. Future work may further explore how different deformation patterns influence beam propagation, as well as extend this concept to other material systems, such as flexible two-dimensional crystals and/or dynamically deformed materials, e.g., via surface acoustic waves.

Marco Felici¹, Giorgio Pettinari², Michela Fratini^3,4, Luisa Barba⁵, Simone Birindelli¹, Gaetano Campi⁶, Silvia Rubini⁷, Tobias Schülli⁸, Mario Capizzi¹ and Antonio Polimeni^1
1 Physics Department, Sapienza Univ. of Rome, Rome, Italy
² Institute for Photonics and Nanotechnologies (CNR-IFN), National Research Council, Rome, Italy
³ Institute of Nanotechnology (CNR-Nanotec), National Research Council, c/o Physics Dept., Sapienza Univ. of Rome, Rome, Italy
⁴ Santa Lucia Foundation, Rome, Italy
⁵ Institute of Crystallography (CNR-IC), National Research Council, Basovizza (Trieste), Italy
⁶ Institute of Crystallography (CNR-IC), National Research Council, Monterotondo (Rome), Italy
⁷ Istituto Officina dei Materiali, (CNR-IOM), National Research Council, Basovizza (Trieste), Italy
⁸ ESRF - The European Synchrotron, Grenoble, France

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