Quantitative characterization of flat band states in a molecular orbital model via hyperuniformity

The localization of electron states due to disorder, known as Anderson localization, has been actively studied. In recent years, there has been an interest on studying single-particle states with unique characteristics. Flat band systems are one of such examples, and indeed, there have been several reports of their distinctive behaviors to disorder [1, 2]. In our previous study [3], it also was suggested that flat band states in a model called molecular-orbital (MO) model [4] exhibit some distinct features. However, we find that the characterization methods used for single-particle wave functions, such as multifractal analysis, are ineffective for the flat band state due to the macroscopic degeneracy of the flat band.

In this work, to characterize the flat band state of the MO model, we employ a concept of hyperuniformity [5]. Hyperuniformity is a concept that quantifies the spatial fluctuation of distributions, and has recently been used for condensed matter systems, such as quasiperiodic systems [6]. In this presentation, we will show the results for quantitatively characterizing the features of the flat band states in a MO model with randomness using hyperuniformity [7].



[1] M. Goda, et al., PRL 96, 126401 (2006).

[2] J. T. Chalker, et al., PRB 82, 104209 (2010).

[3] T. Kuroda, et al., JPSJ 91, 044703 (2022).

[4] Y. Hatsugai, Annals of Physics 168453 (2021).

[5] S. Torquato, et al., PRE 68, 041113 (2003).

[6] S. Sakai, et al. PRB 105, 054202 (2022).

[7] T. Kuroda, T. Mizoguchi, Y. Hatsugai, in preparation.