Implementation and characterization of the dice lattice in the electron quantum simulator
Abstract: Materials featuring touching points, localized states, and flat bands are of great interest in condensed matter and artificial systems due to their implications in topology, quantum geometry, superconductivity, and interactions. In this theoretical study, we propose the experimental realization of the dice lattice with adjustable parameters by arranging carbon monoxide molecules on a two-dimensional electron system at a (111) copper surface. First, we develop a theoretical framework to obtain the spectral properties within a nearly free electron approximation and then compare them with tight-binding calculations. Our investigation reveals that the high mobility of Shockley state electrons enables an accurate theoretical description of the artificial lattice using a next-nearest-neighbor tight-binding model, resulting in the emergence of a touching point, a quasi-flat band, and localized lattice site behavior in the local density of states. Additionally, we present theoretical results for a long-wavelength low-energy model that accounts for next-nearest-neighbor hopping terms. Furthermore, we theoretically examine the model's behavior under an external magnetic field by employing Peierl's substitution, a commonly used technique in theoretical physics to incorporate magnetic fields into lattice models. Our theoretical findings suggest that, owing to the exceptional electron mobility, the highly degenerate eigenenergy associated with the Aharonov-Bohm caging mechanism may not manifest in the proposed experiment.
- E. Y. Andrei and A. H. MacDonald, Graphene bilayers with a twist, Nat. Mater. 19, 1265 (2020).
- R. J. Baxter, Colorings of a hexagonal lattice, J. Math. Phys. 11, 784 (1070).
- B. Sutherland, Localization of electronic wave functions due to local topology, Phys. Rev. B 34, 5208 (1986).
- E. H. Lieb, Two theorems on the Hubbard model, Phys. Rev. Lett. 62, 1201 (1989).
- H. Aoki, M. Ando, and H. Matsumura, Hofstadter butterflies for flat bands, Phys. Rev. B 54, R17296 (1996).
- D. L. Bergman, C. Wu, and L. Balents, Band touching from real-space topology in frustrated hopping models, Phys. Rev. B 78, 125104 (2008).
- J.-W. Rhim and B.-J. Yang, Classification of flat bands according to the band-crossing singularity of Bloch wave functions, Phy. Rev. B 99, 045107 (2019).
- A. Graf and F. Piéchon, Berry curvature and quantum metric in n𝑛nitalic_n-band systems: An eigenprojector approach, Phys. Rev. B 104, 085114 (2021).
- A. Aspuru-Guzik and P. Walther, Photonic quantum simulators, Nat. Phys. 8, 285 (2012).
- R. P. Feynman, Simulating physics with computers, Int. J. Theor. Phys. 21, 467 (1982).
- E. Altman et al., Quantum simulators: Architectures and opportunities, PRX Quantum 2, 017003 (2021).
- D. Bercioux and S. Otte, Solid-state platforms, Nat. Phys. 13, 628 (2017).
- N. Goldman, D. F. Urban, and D. Bercioux, Topological phases for fermionic cold atoms on the lieb lattice, Phys. Rev. A 83, 063601 (2011).
- D. Bercioux, N. Goldman, and D. F. Urban, Topology-induced phase transitions in quantum spin Hall lattices, Phys. Rev. A 83, 023609 (2011).
- J. Vidal, R. Mosseri, and B. Douçot, Aharonov-Bohm cages in two-dimensional structures, Phys. Rev. Lett. 81, 5888 (1998).
- C. C. Naud, G. G. Faini, and D. D. Mailly, Aharonov-Bohm cages in 2D normal metal networks, Phys. Rev. Lett. 86, 5104 (2001).
- S. M. Zhang and L. Jin, Compact localized states and localization dynamics in the dice lattice, Phys. Rev. B 102, 054301 (2020).
- M. O. Goerbig, Electronic properties of graphene in a strong magnetic field, Rev. Mod. Phys. 83, 1193 (2011).
- H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13, 5188 (1976).
- A. Graf and F. Piéchon, Designing flat-band tight-binding models with tunable multifold band touching points, Phys. Rev. B 104, 195128 (2021).
- M. Gell-Mann, Symmetries of baryons and mesons, Phys. Rev. 125, 1067 (1962).
- D. Bercioux, O. Dutta, and E. Rico, Solitons in One-Dimensional Lattices with a Flat Band, Ann. Phys. (Berl.) 529, 1600262 (2017).
- R. Peierls, Zur Theorie des Diamagnetismus von Leitungselektronen, Z. Phys. 80, 763 (1933).
- D. R. Hofstadter, Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields, Phys. Rev. B 14, 2239 (1976).
- M. F. Barnsley, Fractal functions and interpolation, Constr. approx. 2, 303 (1986).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.