Density Functional Theory of Composite Fermions
ZHANG Yin-Han1 , SHI Jun-Ren2,3**
1 Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190
2 International Center for Quantum Materials, Peking University, Beijing 100871
3 Collaborative Innovation Center of Quantum Matter, Beijing 100871
Abstract :We construct a density functional theory for two-dimensional electron (hole) gases subjected to both strong magnetic fields and external potentials. In particular, we are focused on regimes near even-denominator filling factors, in which the systems form composite fermion liquids. Our theory provides a systematic and rigorous approach to determine the properties of ground states in a fractional quantum Hall regime that is modified by artificial structures. We also propose a practical way to construct an approximated functional.
出版日期: 2015-02-26
:
71.10.Pm
(Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.))
73.43.-f
(Quantum Hall effects)
75.75.Cd
(Fabrication of magnetic nanostructures)
71.15.Mb
(Density functional theory, local density approximation, gradient and other corrections)
[1] Klitzing K V, Dorda G and Pepper M 1980 Phys. Rev. Lett. 45 494
[2] Tsui D C, Stormer H L and Gossard A C 1982 Phys. Rev. Lett. 48 1559
[3] Polini M, Guinea F, Lewenstein M, Manoharan H C and Pellegrini V 2009 Nat. Nanotechnol. 4 625
[4] Evers W H, Goris B, Bals S, Casavola M, Graaf J D, Roij R V, Dijkstra M and Vanmaekelbergh D 2013 Nano Lett. 13 2317
[5] Zhang Y and Shi J 2014 Phys. Rev. Lett. 113 016801
[6] Vignale G and Rasolt M 1987 Phys. Rev. Lett. 59 2360
Vignale G and Rasolt M 1988 Phys. Rev. B 37 10685
[7] Giuliani G F and Vignale G 2005 Quantum Theory of the Electron Liquid (Cambridge: Cambridge University Press) chap 7 p 390
[8] Heinonen O, Lubin M I and Johnson M J 1995 Phys. Rev. Lett. 75 4110
[9] Jain J K 2007 Composite Fermions (Cambridge: Cambridge University Press) chap 5 p 105
[10] Heinonen O 1998 Composite Fermions (Singapore: World Scientific)
[11] Kalmeyer V and Zhang S C 1992 Phys. Rev. B 46 9889
[12] Willett R L, Ruel R R, West K W and Pfeiffer L N 1993 Phys. Rev. Lett. 71 3846
[13] Halperin B I, Lee P A and Read N 1993 Phys. Rev. B 47 7312
[14] Shi J, Vignale G, Xiao D and Niu Q 2007 Phys. Rev. Lett. 99 197202
[1]
. [J]. 中国物理快报, 2021, 38(8): 80202-.
[2]
. [J]. 中国物理快报, 2019, 36(10): 107102-.
[3]
. [J]. 中国物理快报, 2018, 35(7): 77101-.
[4]
. [J]. 中国物理快报, 2018, 35(4): 47101-.
[5]
. [J]. 中国物理快报, 2017, 34(6): 67401-.
[6]
. [J]. 中国物理快报, 2016, 33(05): 57402-057402.
[7]
HUANG Wei;WANG Zhao-Long;YAN Mu-Lin. Noncommutative Chern-Simons Description of the Fractional Quantum Hall Edge [J]. 中国物理快报, 2010, 27(6): 67304-067304.
[8]
PENG De-Jun;CHENG Fang;ZHOU Guang-Hui;. Alternating-Current Conductivity for a Two-Channel Interacting Quantum Wire [J]. 中国物理快报, 2007, 24(2): 520-523.
[9]
CHENG Kuan;LIU Yu-Liang. Numerical Study of Luttinger Liquid Regime of Two-Leg Hubbard Ladders [J]. 中国物理快报, 2005, 22(9): 2349-2352.
[10]
Z. Bentalha;M. Tahiri;B. Liani. One-Dimensional Anyon Lattice and slq (2) Algebra Realization [J]. 中国物理快报, 2005, 22(5): 1207-1209.
[11]
GU Bo;LOU Ji-Zhong;QIN Shao-Jing;XIANG Tao;. Exciton Excitations in a One-Dimensional Band Insulator with Hubbard Interactions [J]. 中国物理快报, 2004, 21(3): 530-533.