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        <dc:title>Probing topological phase transitions using high-harmonic generation</dc:title>
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        <bibo:abstract>The prediction and realization of topological insulators have sparked great interest in experimental approaches to the classification of materials1,2,3. The phase transition between non-trivial and trivial topological states is important, not only for basic materials science but also for next-generation technology, such as dissipation-free electronics4. It is therefore crucial to develop advanced probes that are suitable for a wide range of samples and environments. Here we demonstrate that circularly polarized laser-field-driven high-harmonic generation is distinctly sensitive to the non-trivial and trivial topological phases in the prototypical three-dimensional topological insulator bismuth selenide5. The phase transition is chemically initiated by reducing the spin–orbit interaction strength through the substitution of bismuth with indium atoms6,7. We find strikingly different high-harmonic responses of trivial and non-trivial topological surface states that manifest themselves as a conversion efficiency and elliptical dichroism that depend both on the driving laser ellipticity and the crystal orientation. The origins of the anomalous high-harmonic response are corroborated by calculations using the semiconductor optical Bloch equations with pairs of surface and bulk bands. As a purely optical approach, this method offers sensitivity to the electronic structure of the material, including its nonlinear response, and is compatible with a wide range of samples and sample environments.</bibo:abstract>
        <bibo:volume>16</bibo:volume>
        <bibo:issue>9</bibo:issue>
        <bibo:startPage>620-624</bibo:startPage>
        <bibo:endPage>620-624</bibo:endPage>
        <dc:publisher>Springer Nature</dc:publisher>
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