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Symmetry-Driven Floquet Engineering in Multivalley SnS

Sotirios Fragkos, Benshu Fan, Umberto De Giovannini, Dominique Descamps, Stéphane Petit, Hannes Hübener, Angel Rubio, Samuel Beaulieu

Abstract

Coherent interactions between time-periodic electromagnetic fields and materials offer a powerful platform for engineering light-matter hybrid Floquet states with tailored functionalities. In particular, the ability to manipulate the wavefunction symmetry of such Floquet states has recently emerged as a new frontier in the field of nonequilibrium control of quantum materials. Here, we investigate symmetry-driven Floquet engineering in bulk multivalley semiconductor tin sulfide (SnS) using time-, polarization-, and angle-resolved extreme ultraviolet photoemission spectroscopy, group-theory analysis, and time-dependent density functional theory. We demonstrate that the material's inherent symmetry gives rise to pronounced symmetry-driven photoemission selection rules for both equilibrium bands and light-induced Floquet states, which we probed through nonequilibrium linear dichroism in extreme ultraviolet photoemission. By leveraging the interplay between crystal and driving-light symmetry, we establish deterministic control over the parity of Floquet--Bloch states. Indeed, we show that the symmetry of Floquet--Bloch states can be fully controlled by the relative alignment between the drive polarization and the crystal axes, enabling selective parity inversion with respect to the equilibrium valence and conduction bands. Furthermore, we show that symmetry-driven parity engineering allows for polarization- and valley-selective band renormalization. These findings advance the understanding of guiding principles for wavefunction symmetry engineering, providing pathways for selectively controlling both the parity and renormalization of electronic states in quantum materials using tailored electromagnetic fields.

Symmetry-Driven Floquet Engineering in Multivalley SnS

Abstract

Coherent interactions between time-periodic electromagnetic fields and materials offer a powerful platform for engineering light-matter hybrid Floquet states with tailored functionalities. In particular, the ability to manipulate the wavefunction symmetry of such Floquet states has recently emerged as a new frontier in the field of nonequilibrium control of quantum materials. Here, we investigate symmetry-driven Floquet engineering in bulk multivalley semiconductor tin sulfide (SnS) using time-, polarization-, and angle-resolved extreme ultraviolet photoemission spectroscopy, group-theory analysis, and time-dependent density functional theory. We demonstrate that the material's inherent symmetry gives rise to pronounced symmetry-driven photoemission selection rules for both equilibrium bands and light-induced Floquet states, which we probed through nonequilibrium linear dichroism in extreme ultraviolet photoemission. By leveraging the interplay between crystal and driving-light symmetry, we establish deterministic control over the parity of Floquet--Bloch states. Indeed, we show that the symmetry of Floquet--Bloch states can be fully controlled by the relative alignment between the drive polarization and the crystal axes, enabling selective parity inversion with respect to the equilibrium valence and conduction bands. Furthermore, we show that symmetry-driven parity engineering allows for polarization- and valley-selective band renormalization. These findings advance the understanding of guiding principles for wavefunction symmetry engineering, providing pathways for selectively controlling both the parity and renormalization of electronic states in quantum materials using tailored electromagnetic fields.
Paper Structure (19 sections, 10 equations, 11 figures, 12 tables)

This paper contains 19 sections, 10 equations, 11 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Results
  3. Experimental and theoretical methodologies
  4. Symmetry of electronic valence and conduction bands
  5. Floquet--Bloch states symmetry engineering
  6. Polarization- and valley-selective Floquet-induced band renormalization
  7. Conclusions
  8. Methods
  9. Experimental setup
  10. First-principles calculation
  11. Symmetry analysis of bulk tin sulfide
  12. Symmetry analysis of monolayer tin sulfide
  13. Symmetry analysis of the photoemission spectroscopy
  14. The matrix element of ARPES
  15. The matrix element of trARPES
  16. ...and 4 more sections

Figures (11)

  • Figure 1: Experimental Setup and Static Band Mapping of SnS. (a) Polarization-tunable infrared pump (1.2 eV, 135 fs, 1.3 mJ/cm$^2$) and polarization-tunable XUV (21.6 eV) probe pulses are focused onto a bulk SnS sample, in the interaction chamber of a time-of-flight momentum microscope, at an incidence angle of 65$^{\circ}$, with the light incidence plane along the crystal mirror plane $\mathcal{M}_{y}$ (AC direction). (b) Concept of symmetry-driven Floquet engineering in multivalley SnS, where the parity of Floquet--Bloch states, and band renormalization can be controlled by the relative alignment of the drive polarization and the crystal axes. The square insets depict the real-space in-plane structure of SnS with pump polarization (red arrows) along ZZ or AC directions. (c) Static energy-momentum cuts measured along AC and ZZ directions, integrated over all XUV polarization angles, and associated constant energy contours (CEC) at different binding energies, highlighting the multivalley nature of SnS.
  • Figure 2: Valence and conduction band parity probed by TDDFT linear dichroism ARPES. (a) The calculated valence and conduction bands ARPES intensity maps along the $k_{\mathrm{AC}}$ direction summed for both AC ($p$-pol.) and ZZ ($s$-pol.) probe pulses polarizations. The inset depicts the real-space in-plane structure of $n$-doped monolayer SnS with polarization-tunable XUV probe pulse (purple arrows). (b) The corresponding LD-ARPES highlighting the VB and CB parity probed through photoemission selection rules.
  • Figure 3: Emergence of Floquet--Volkov sidebands under AC ($p$-pol.) pump. (a) Experimentally measured energy-momentum cuts along the $k_{\rm{AC}}$ direction at the pump-probe temporal overlap, using AC ($p$-pol.) pump and integrated for all XUV polarization angles, and (b) the associated LD-ARPES. The inset in (a) depicts the real-space in-plane structure of SnS with pump polarization along the AC direction (red arrow) and polarization-tunable probe (purple arrows). (c) Theoretically calculated energy-momentum cuts along the $k_{\rm{AC}}$ direction, using AC-polarized pump, obtained by TDDFT simulations by summing the spectra calculated for AC ($p$-pol.) and ZZ ($s$-pol.) probe pulses, and (d) the associated calculated LD-ARPES.
  • Figure 4: Parity switching of Floquet--Bloch states with ZZ ($s$-pol.) pump. (a) Experimentally measured energy-momentum cuts along the $k_{\rm{AC}}$ direction at the pump-probe temporal overlap, using ZZ ($s$-pol.) pump and integrated for all XUV polarization angles, and (b) the associated LD-ARPES. The inset in (a) depicts the real-space in-plane structure of SnS with IR pump polarization along the ZZ direction (red arrow) and polarization-tunable XUV probe (purple arrows). (c) Theoretically calculated energy-momentum cuts along the $k_{\rm{AC}}$ direction, using ZZ ($s$-pol.) pump, obtained by TDDFT simulations by summing the spectra calculated for AC ($p$-pol.) and ZZ ($s$-pol.) probe pulses, and (d) the associated calculated LD-ARPES.
  • Figure 5: Photoemission selection rules in light-driven SnS. (a) Symmetry-allowed (light green) and symmetry-forbidden (light red) photoemission matrix elements for the VB and CB at the Y$^\prime$ valleys under different XUV probe polarizations. (b) Symmetry-allowed (light green) and symmetry-forbidden photoemission matrix elements of the $n=1$ Floquet--Bloch states of the VB at the Y$^\prime$ valleys under different combinations of IR pump and XUV probe polarizations.
  • ...and 6 more figures