Please wait a minute...
Chin. Phys. B, 2013, Vol. 22(11): 117501    DOI: 10.1088/1674-1056/22/11/117501
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES Prev   Next  

Analytical thermodynamical properties of a two-dimensional electron gas in a magnetic field

Chen Jin-Wang (陈金望), Pan Xiao-Yin (潘孝胤)
Department of Physics, Ningbo University, Ningbo 315211, China
Abstract  Analytical expressions for the thermodynamical properties of a two-dimensional electron gas in a perpendicular magnetic field are derived. This is accomplished by first deriving the general expression for the thermodynamical potential, and then employing this result to obtain the corresponding expression for the two-dimensional gas. The chemical potential and magnetization are studied as a function of temperature and magnetic field, and shown to be in agreement with prior work. It is also shown that the results are close to those obtained by assuming a Gaussian density of states for the Landau levels.
Keywords:  thermodynamical potential      magnetization      de Hass–van Alphen effect      density of states  
Received:  12 April 2013      Revised:  06 May 2013      Accepted manuscript online: 
PACS:  75.20.-g (Diamagnetism, paramagnetism, and superparamagnetism)  
  71.70.Di (Landau levels)  
  71.18.+y (Fermi surface: calculations and measurements; effective mass, g factor)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11275100) and the K. C. Wong Magna Foundation of Ningbo University, China.
Corresponding Authors:  Pan Xiao-Yin     E-mail:  panxiaoyin@nbu.edu.cn

Cite this article: 

Chen Jin-Wang (陈金望), Pan Xiao-Yin (潘孝胤) Analytical thermodynamical properties of a two-dimensional electron gas in a magnetic field 2013 Chin. Phys. B 22 117501

[1] Shoenberg D 1984 Magnetic Oscillations in Metals (Cambridge: Cambridge University Press)
[2] de Haas W J and van Alphen P M 1930 Proc. Neth. R. Acad. Sci. 33 1106
[3] de Haas W J and van Alphen P M 1930 Commun. Phys. Lab. Leiden 208d 212a
[4] Lifshitz I M and Kosevich A M 1955 Zh. Eksp. Teor. Fiz. 29 730
[5] Peierls R 1933 Z. Phys. 81 186
[6] Stormer H L, Haavasoja T, Narayanamurti V, Gossard A C and Wiegmann W 1983 J. Vac. Sci. Technol. B 2 423
[7] Gornik E, Lassnig R and Strasser G 1985 Phys. Rev. Lett. 54 1820
[8] Wang J K, Campbell J H, Tsui D C and Cho A Y 1988 Phys. Rev. B 38 6174
[9] Eisenstein J P, Stormer H L, Narayanamurti V, Cho A Y, Gossard A C and Tu C W 1985 Phys. Rev. Lett. 55 875
[10] Templeton I M 1988 J. Appl. Phys. 64 3570
[11] Potts A, Shepherd R, Herrenden-Harker W G, Elliott M, Jones C L, Usher A, Jones G A, Ritchie D A, Linfield E H and Grimshaw M 1996 J. Phys.: Condens. Matter 8 5189
[12] Wiegers S A J, Specht M, Lévy L P, Simmons M Y, Ritchie D A, Cavanna A, Etienne B, Martinez G and Wyder P 1997 Phys. Rev. Lett. 79 3238
[13] Meinel I, Hengstmann T, Grundler D and Heitmann D 1999 Phys. Rev. Lett. 82 819
[14] Harris J G E, Knobel R, Maranowski K D, Gossard A C, Samarth N and Awschalom D D 2001 Phys. Rev. Lett. 86 4644
[15] Usher A and Elliott M 2009 J. Phys.: Condens. Matter 21 103202
[16] Vagner I D, Maniv T and Ehrenfreund E 1983 Phys. Rev. Lett. 51 1700
[17] Vagner I D and Maniv T 1985 Phys. Rev. B 32 8398
[18] Landau L D 1930 Z. Phys. 64 629
[19] Zawadzki W 1983 Solid State Commun. 47 317
[20] Zawadzki W and Lassnig R 1984 Surf. Sci. 142 225
[21] Zawadzki W 1984 J. Phys. C 17 L145
[22] Shoenberg D 1984 J. Low Tem. Phys. 56 417
[23] Wang L and O’Connell R F 1987 Phys. Stat. Sol. (b) 144 781
[24] Wang L and O’Connell R F 1989 Phys. Stat. Sol. (b) 153 343
[25] Champel T and Mineev V P 2001 Philos. Mag. B 81 55
[26] Champel T 2001 Phys. Rev. B 64 054407
[27] Ishihara A and Kojima D Y 1979 Phys. Rev. B 19 846
[28] Shiwa Y and Ishihara A 1983 Phys. Rev. B 27 4743
[29] Sondheimer D and Wilson A H 1951 Proc. Roy. Soc. A 210 173
[30] Ando T, Flower A B and Stern F 1982 Rev. Mod. Phys. 54 437
[31] Luttinger J M 1961 Phys. Rev. 121 1251
[32] Engelsberg S and Simpson G 1970 Phys. Rev. B 2 1657
[33] Bauer S H 1939 J. Chem. Phys. 7 1097
[34] Yang W 1988 Phys. Rev. A 38 5504
[35] Yu B R 1948 J. Exp. Theor. Phys. 18 1081
[36] van Zyl B P and Hutchinson D A W 2004 Phys. Rev. B 69 024520
[37] Alexandrov A S and Bratkovsky A M 1996 Phys. Rev. Lett. 76 1308
[38] SchwarzMP,WildeMA, Groth S, Grundler D, Heyn Ch and Heitmann D 2002 Phys. Rev. B 65 245315
[39] Fang C, Wang Z G, Li S S and Zhang P 2009 Chin. Phys. B 18 4430
[40] Fu Z G, Wang Z G, Li S S and Zhang P 2011 Chin. Phys. B 20 058103
[1] Vortex bound states influenced by the Fermi surface anisotropy
Delong Fang(方德龙). Chin. Phys. B, 2023, 32(3): 037403.
[2] Orbital torque of Cr-induced magnetization switching in perpendicularly magnetized Pt/Co/Pt/Cr heterostructures
Hongfei Xie(谢宏斐), Yuhan Chang(常宇晗), Xi Guo(郭玺), Jianrong Zhang(张健荣), Baoshan Cui(崔宝山), Yalu Zuo(左亚路), and Li Xi(席力). Chin. Phys. B, 2023, 32(3): 037502.
[3] Anisotropic superconducting properties of FeSe0.5Te0.5 single crystals
Jia-Ming Zhao(赵佳铭) and Zhi-He Wang(王智河). Chin. Phys. B, 2022, 31(9): 097402.
[4] Magnetic properties of a mixed spin-3/2 and spin-2 Ising octahedral chain
Xiao-Chen Na(那小晨), Nan Si(司楠), Feng-Ge Zhang(张凤阁), and Wei Jiang(姜伟). Chin. Phys. B, 2022, 31(8): 087502.
[5] Effect of the magnetization parameter on electron acceleration during relativistic magnetic reconnection in ultra-intense laser-produced plasma
Qian Zhang(张茜), Yongli Ping(平永利), Weiming An(安维明), Wei Sun(孙伟), and Jiayong Zhong(仲佳勇). Chin. Phys. B, 2022, 31(6): 065203.
[6] Magnetic and magnetocaloric effect in a stuffed honeycomb polycrystalline antiferromagnet GdInO3
Yao-Dong Wu(吴耀东), Wei-Wei Duan(段薇薇), Qiu-Yue Li(李秋月), Yong-Liang Qin(秦永亮),Zhen-Fa Zi(訾振发), and Jin Tang(汤进). Chin. Phys. B, 2022, 31(6): 067501.
[7] Temperature-dependent structure and magnetization of YCrO3 compound
Qian Zhao(赵前), Ying-Hao Zhu(朱英浩), Si Wu(吴思), Jun-Chao Xia(夏俊超), Peng-Fei Zhou(周鹏飞), Kai-Tong Sun(孙楷橦), and Hai-Feng Li(李海峰). Chin. Phys. B, 2022, 31(4): 046101.
[8] In-plane current-induced magnetization reversal of Pd/CoZr/MgO magnetic multilayers
Jing Liu(刘婧), Caiyin You(游才印), Li Ma(马丽), Yun Li(李云), Ling Ma(马凌), and Na Tian(田娜). Chin. Phys. B, 2022, 31(12): 127502.
[9] Experimental observation of interlayer perpendicular standing spin wave mode with low damping in skyrmion-hosting [Pt/Co/Ta]10 multilayer
Zhen-Dong Chen(陈振东), Mei-Yang Ma(马眉扬), Sen-Fu Zhang(张森富), Mang-Yuan Ma(马莽原), Zi-Zhao Pan(潘咨兆), Xi-Xiang Zhang(张西祥), Xue-Zhong Ruan(阮学忠), Yong-Bing Xu(徐永兵), and Fu-Sheng Ma(马付胜). Chin. Phys. B, 2022, 31(11): 117501.
[10] Photoreflectance system based on vacuum ultraviolet laser at 177.3 nm
Wei-Xia Luo(罗伟霞), Xue-Lu Liu(刘雪璐), Xiang-Dong Luo(罗向东), Feng Yang(杨峰), Shen-Jin Zhang(张申金), Qin-Jun Peng(彭钦军), Zu-Yan Xu(许祖彦), and Ping-Heng Tan(谭平恒). Chin. Phys. B, 2022, 31(11): 110701.
[11] Multiple modes of perpendicular magnetization switching scheme in single spin—orbit torque device
Tong-Xi Liu(刘桐汐), Zhao-Hao Wang(王昭昊), Min Wang(王旻), Chao Wang(王朝), Bi Wu(吴比), Wei-Qiang Liu(刘伟强), and Wei-Sheng Zhao(赵巍胜). Chin. Phys. B, 2022, 31(10): 107501.
[12] Role of compositional changes on thermal, magnetic, and mechanical properties of Fe-P-C-based amorphous alloys
Indah Raya, Supat Chupradit, Mustafa M Kadhim, Mustafa Z Mahmoud, Abduladheem Turki Jalil, Aravindhan Surendar, Sukaina Tuama Ghafel, Yasser Fakri Mustafa, and Alexander N Bochvar. Chin. Phys. B, 2022, 31(1): 016401.
[13] Probing the magnetization switching with in-plane magnetic anisotropy through field-modified magnetoresistance measurement
Runrun Hao(郝润润), Kun Zhang(张昆), Yinggang Li(李迎港), Qiang Cao(曹强), Xueying Zhang(张学莹), Dapeng Zhu(朱大鹏), and Weisheng Zhao(赵巍胜). Chin. Phys. B, 2022, 31(1): 017502.
[14] Strain-dependent resistance and giant gauge factor in monolayer WSe2
Mao-Sen Qin(秦茂森), Xing-Guo Ye(叶兴国), Peng-Fei Zhu(朱鹏飞), Wen-Zheng Xu(徐文正), Jing Liang(梁晶), Kaihui Liu(刘开辉), and Zhi-Min Liao(廖志敏). Chin. Phys. B, 2021, 30(9): 097203.
[15] Magnetization relaxation of uniaxial anisotropic ferromagnetic particles with linear reaction dynamics driven by DC/AC magnetic field
Yu-Song Hu(胡玉松), Min Jiang(江敏), Tao Hong(洪涛), Zheng-Ming Tang(唐正明), and Ka-Ma Huang(黄卡玛). Chin. Phys. B, 2021, 30(9): 090202.
No Suggested Reading articles found!