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Chin. Phys. B, 2022, Vol. 31(2): 027101    DOI: 10.1088/1674-1056/ac140e

Invariable mobility edge in a quasiperiodic lattice

Tong Liu(刘通)1,†, Shujie Cheng(成书杰)2, Rui Zhang(张锐)1, Rongrong Ruan(阮榕榕)1, and Houxun Jiang(姜厚勋)1
1 School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;
2 Department of Physics, Zhejiang Normal University, Jinhua 321004, China
Abstract  We analytically and numerically study a 1D tight-binding model with tunable incommensurate potentials. We utilize the self-dual relation to obtain the critical energy, namely, the mobility edge. Interestingly, we analytically demonstrate that this critical energy is a constant independent of strength of potentials. Then we numerically verify the analytical results by analyzing the spatial distributions of wave functions, the inverse participation rate and the multifractal theory. All numerical results are in excellent agreement with the analytical results. Finally, we give a brief discussion on the possible experimental observation of the invariable mobility edge in the system of ultracold atoms in optical lattices.
Keywords:  Anderson localization      quasiperiodic      mobility edge      multifractal  
Received:  22 May 2021      Revised:  23 June 2021      Accepted manuscript online:  14 July 2021
PACS:  61.44.Fw (Incommensurate crystals)  
  71.10.Fd (Lattice fermion models (Hubbard model, etc.))  
  71.23.An (Theories and models; localized states)  
Fund: T. Liu acknowledges X.-J. Liu for fruitful discussion. This work was supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20200737), NUPTSF (Grants Nos. NY220090 and NY220208), and the National Natural Science Foundation of China (Grant No. 12074064), and the Innovation Research Project of Jiangsu Province, China (Grant No. JSSCBS20210521), and NJUPT-STITP (Grant No. XYB2021294).
Corresponding Authors:  Tong Liu     E-mail:

Cite this article: 

Tong Liu(刘通), Shujie Cheng(成书杰), Rui Zhang(张锐), Rongrong Ruan(阮榕榕), and Houxun Jiang(姜厚勋) Invariable mobility edge in a quasiperiodic lattice 2022 Chin. Phys. B 31 027101

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