Irregular Bloch Zener oscillations in two-dimensional flat-band Dirac materials (2402.14243v2)
Abstract: When a static electrical field is applied to a two-dimensional (2D) Dirac material, Landau-Zener transition (LZT) and Bloch-Zener oscillations can occur. Employing alpha-T3 lattices as a paradigm for a broad class of 2D Dirac materials, we uncover two phenomena. First, due to the arbitrarily small energy gaps near a Dirac point that make it more likely for LZTs to occur than in other regions of the Brillouin zone, the distribution of differential LZT probability in the momentum space can form a complicated morphological pattern. Second, a change in the LZT morphology as induced by a mutual switching of the two distinct Dirac points can lead to irregular Bloch-Zener oscillations characterized by a non-smooth behavior in the time evolution of the electrical current density associated with the oscillation. These phenomena are due to mixed interference of quantum states in multiple bands modulated by the geometric and dynamic phases. We demonstrate that the adiabatic-impulse model describing Landau-Zener-Stuckelberg interferometry can be exploited to calculate the phases, due to the equivalence between the alpha-T3 lattice subject to a constant electrical field and strongly periodically driven two- or three-level systems. The degree of irregularity of Bloch-Zener oscillations can be harnessed by selecting the morphology pattern, which is potentially experimentally realizable.
- L. Landau, On the theory of transfer of energy at collisions II, Phys. Z. Sowjetunion 2, 118 (1932).
- C. Zener, Non-adiabatic crossing of energy levels, Proc. R. Soc. London Ser. A 137, 696 (1932).
- S. N. Shevchenko, S. Ashhab, and F. Nori, Landau–zener–stückelberg interferometry, Phys. Rep. 492, 1 (2010).
- B. Damski and W. H. Zurek, Adiabatic-impulse approximation for avoided level crossings: From phase-transition dynamics to Landau-Zener evolutions and back again, Phys. Rev. A 73, 063405 (2006).
- C. Carroll and F. Hioe, Generalisation of the Landau-Zener calculation to three levels, J. Phys. A Math. Gen. 19, 1151 (1986).
- R. Khomeriki and S. Flach, Landau-Zener Bloch oscillations with perturbed flat bands, Phys. Rev. Lett. 116, 245301 (2016).
- J. R. Parkavi, V. Chandrasekar, and M. Lakshmanan, Stable Bloch oscillations and Landau-Zener tunneling in a non-hermitian PT-symmetric flat-band lattice, Phys. Rev. A 103, 023721 (2021).
- F. Bloch, Quantum mechanics of electrons in crystal lattices, Z. Phys 52, 555 (1928).
- C. Zener, A theory of the electrical breakdown of solid dielectrics, Proc. R. Soc. London Ser. A 145, 523 (1934).
- L.-K. Lim, J.-N. Fuchs, and G. Montambaux, Bloch-Zener oscillations across a merging transition of dirac points, Phys. Rev. Lett. 108, 175303 (2012).
- B. Breid, D. Witthaut, and H. Korsch, Bloch–Zener oscillations, New J. Phys. 8, 110 (2006).
- B. Breid, D. Witthaut, and H. Korsch, Manipulation of matter waves using Bloch and Bloch–Zener oscillations, New J. Phys. 9, 62 (2007).
- L.-K. Lim, J.-N. Fuchs, and G. Montambaux, Geometry of Bloch states probed by Stückelberg interferometry, Phys. Rev. A 92, 063627 (2015).
- A. R. Kolovsky and E. N. Bulgakov, Wannier-Stark states and Bloch oscillations in the honeycomb lattice, Phys. Rev. A 87, 033602 (2013).
- E. Illes, J. Carbotte, and E. Nicol, Hall quantization and optical conductivity evolution with variable Berry phase in the α𝛼\alphaitalic_α-T3subscript𝑇3T_{3}italic_T start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT model, Phys. Rev. B 92, 245410 (2015).
- C. Kittel and P. McEuen, Kittel’s Introduction to Solid State Physics (John Wiley & Sons, 2018).
- B. Dóra and R. Moessner, Nonlinear electric transport in graphene: quantum quench dynamics and the schwinger mechanism, Phys. Rev. B 81, 165431 (2010).
- N. Vitanov and B. Garraway, Landau-Zener model: Effects of finite coupling duration, Phys. Rev. A 53, 4288 (1996).
- Y. Abranyos, G. Gumbs, and O. Berman, Superfluidity of dipolar excitons in a double layer of alpha-t3 with a mass term, in APS March Meeting Abstracts, Vol. 2021 (2021) pp. U71–063.
- A. Trabesinger, Quantum simulation, Nat. Phys. 8, 263 (2012).
- I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86, 153 (2014).