Anomalous Floquet Phases. A resonance phenomena (2312.06778v2)
Abstract: Floquet topological phases emerge when systems are periodically driven out-of-equilibrium. They gained attention due to their external control, which allows to simulate a wide variety of static systems by just tuning the external field in the high frequency regime. However, it was soon clear that their relevance goes beyond that, as for lower frequencies, anomalous phases without a static counterpart are present and the bulk-to-boundary correspondence can fail. In this work we discuss the important role of resonances in Floquet phases. For that, we present a method to find analytical solutions when the frequency of the drive matches the band gap, extending the well-known high frequency analysis of Floquet systems. With this formalism, we show that the topology of Floquet phases with resonances can be accurately captured in analytical terms. We also find a bulk-to-boundary correspondence between the number of edge states in finite systems and a set of topological invariants in different frames of reference, which crucially do not explicitly involve the micromotion. To illustrate our results, we periodically drive a SSH chain and a $\pi$-flux lattice, showing that our findings remain valid in various two-band systems and in different dimensions. In addition, we notice that the competition between rotating and counter-rotating terms must be carefully treated when the undriven system is a semi-metal. To conclude, we discuss the implications to experimental setups, including the direct detection of anomalous topological phases and the measurement of their invariants.
- S. Sachdev, Quantum Phase Transitions, 2nd ed. (Cambridge University Press, 2011).
- A. Y. Kitaev, Physics-Uspekhi 44, 131 (2001).
- P. Delplace, J. B. Marston, and A. Venaille, Science 358, 1075 (2017).
- T. Oka and H. Aoki, Phys. Rev. B 79, 081406 (2009).
- N. H. Lindner, G. Refael, and V. Galitski, Nature Phys 7, 490 (2011).
- A. G. Grushin, A. Gómez-León, and T. Neupert, Physical Review Letters 112, 156801 (2014).
- A. Gómez-León and G. Platero, Physical Review Letters 110, 200403 (2013).
- A. Gómez-León, P. Delplace, and G. Platero, Phys. Rev. B 89, 205408 (2014).
- T. Bessho and M. Sato, Phys. Rev. Lett. 127, 196404 (2021), publisher: American Physical Society.
- F. Nathan and M. S. Rudner, New Journal of Physics 17, 125014 (2015).
- M. S. Rudner and N. H. Lindner, Nat Rev Phys 2, 229 (2020).
- I. I. Rabi, Phys. Rev. 51, 652 (1937).
- A. Gómez-León and G. Platero, Phys. Rev. B 84, 121310 (2011).
- A. Gómez-León and G. Platero, Phys. Rev. B 85, 245319 (2012).
- P. Delplace, A. Gómez-León, and G. Platero, Phys. Rev. B 88, 245422 (2013).
- M. Grifoni and P. Hänggi, Physics Reports 304, 229 (1998).
- S. J. Thomson, D. Magano, and M. Schirò, SciPost Phys. 11, 028 (2021).
- A. Eckardt and E. Anisimovas, New Journal of Physics 17, 093039 (2015).
- R. Peierls, Zeitschrift für Physik 80, 763 (1933).
- G. H. Wannier, Rev. Mod. Phys. 34, 645 (1962).
- Single-band models could also display resonant transitions, but only if the driving field is not spatially homogeneous and can couple states with different momentum.
- W. P. Su, J. R. Schrieffer, and A. J. Heeger, Phys. Rev. Lett. 42, 1698 (1979).
- V. Dal Lago, M. Atala, and L. E. F. Foa Torres, Phys. Rev. A 92, 023624 (2015).
- O. Balabanov and H. Johannesson, Phys. Rev. B 96, 035149 (2017), publisher: American Physical Society.
- J. K. Asbóth, B. Tarasinski, and P. Delplace, Phys. Rev. B 90, 125143 (2014).
- The springs could be phonons in some realizations, if their frequency is in the correct range of energies.
- A. Gómez-León and G. Platero, Physical Review Research 2, 033412 (2020).
- A. Gómez-León, Phys. Rev. A 106, 022609 (2022).
- Y. Aharonov and J. Anandan, Phys. Rev. Lett. 58, 1593 (1987).
- Although the first contribution to Eq. (38) is time-dependent, its evaluation turns out to be time-independent.
- Y.-X. Zhang, H.-M. Guo, and R. T. Scalettar, Phys. Rev. B 101, 205139 (2020).
- M. Rodriguez-Vega, A. Kumar, and B. Seradjeh, Phys. Rev. B 100, 085138 (2019).
- B. A. Bernevig and T. L. Hughes, Topological Insulators and Topological Superconductors (Princeton University Press, Princeton and Oxford, 2013).
- P. Delplace, D. Ullmo, and G. Montambaux, Phys. Rev. B 84, 195452 (2011).
- R. Roy and F. Harper, Physical Review B 96, 155118 (2017).
- We have checked that this simplified Hamiltonian perfectly reproduces the exact quasienergies of the full model, for the range of parameters of interest.
- Z. Lü and H. Zheng, Phys. Rev. A 86, 023831 (2012).
- T. Fukui, Y. Hatsugai, and H. Suzuki, Journal of the Physical Society of Japan 74, 1674 (2005), https://doi.org/10.1143/JPSJ.74.1674 .
Collections
Sign up for free to add this paper to one or more collections.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.