Floquet-spin-orbit compensation and flat- and quadratic-band contact in the α-T3 lattice
Abstract
We investigate Floquet--spin-orbit compensation in the three-band α-T3 system, which interpolates between graphene at α=0 and the dice lattice at α=1. By tuning the interplay between an off-resonant circularly polarized optical field and intrinsic spin--orbit coupling, we identify three distinct pairwise band-degeneracy conditions in the quasienergy spectrum: (i) valley--spin degeneracy, (ii) spin--band degeneracy, and (iii) flat--dispersive band degeneracy. The flat band is not an artifact of a two-band reduction but rather an exact property of the continuum Hamiltonian at this compensation point, where the complete three-band Hamiltonian supports a momentum-independent dark state. A winding-two low-energy Hamiltonian and a finite-momentum Berry-curvature maximum, whose radius scales as the square root of the detuning, emerge from detuning this contact. We further show that the intrinsic transverse thermoelectric response encodes these spectrum patterns. The flat- and quadratic-band degeneracy can be predicted for 0<α<1/2 because the two response scales linked to the linear contacts have a monotonic ratio independent of the common spin--orbit energy scale. This allows an inverse determination of α and of the common spectral scale. The analytical results are confirmed by full three-band Kubo calculations, which also define the regime in which this inverse characterization is still observable. These results connect an experimentally accessible, Berry-curvature-sensitive thermoelectric response to tunable Floquet--spin--orbit band geometry.
Related
- Nonreciprocal Floquet tunneling dynamics of spin-orbit-coupled bosonic atoms in a non-Hermitian double-well potential
- Simulating multi-node Weyl semimetals in a Mixed Floquet lattice
- Tan's Contact for Trapped Spin-Orbit-Coupled Fermi Gases at Finite Temperature
- Floquet Topological Spin-Valley-Layertronics on a Layered Dice Lattice
- Floquet engineering of competing antiferromagnetism and d-wave superconductivity on the square lattice
BibTeX
@misc{khan2026floquetspinorbit,
title = {{Floquet-spin-orbit compensation and flat- and quadratic-band contact in the $α$-$T_3$ lattice}},
author = {Imtiaz Khan and Muzamil Shah and Reza Asgari and Gao Xianlong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21586},
eprint = {2609.21586},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21586},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Floquet-spin-orbit compensation and flat- and quadratic-band contact in the α-T_3 lattice
AU - Imtiaz Khan
AU - Muzamil Shah
AU - Reza Asgari
AU - Gao Xianlong
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21586
UR - https://arxiv.org/abs/2609.21586
AB - We investigate Floquet--spin-orbit compensation in the three-band α-T_3 system, which interpolates between graphene at α=0 and the dice lattice at α=1. By tuning the interplay between an off-resonant circularly polarized optical field and intrinsic spin--orbit coupling, we identify three distinct pairwise band-degeneracy conditions in the quasienergy spectrum: (i) valley--spin degeneracy, (ii) spin--band degeneracy, and (iii) flat--dispersive band degeneracy. The flat band is not an artifact of a two-band reduction but rather an exact property of the continuum Hamiltonian at this compensation point, where the complete three-band Hamiltonian supports a momentum-independent dark state. A winding-two low-energy Hamiltonian and a finite-momentum Berry-curvature maximum, whose radius scales as the square root of the detuning, emerge from detuning this contact. We further show that the intrinsic transverse thermoelectric response encodes these spectrum patterns. The flat- and quadratic-band degeneracy can be predicted for 0<α<1/2 because the two response scales linked to the linear contacts have a monotonic ratio independent of the common spin--orbit energy scale. This allows an inverse determination of α and of the common spectral scale. The analytical results are confirmed by full three-band Kubo calculations, which also define the regime in which this inverse characterization is still observable. These results connect an experimentally accessible, Berry-curvature-sensitive thermoelectric response to tunable Floquet--spin--orbit band geometry.
ER -