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Based on a tight-binding disordered model describing a single electron band, a model of quasi-one-dimensional disordered systems with several chainsis established, and the direct current (dc) and alternating current (ac) conductance formula are obtained. By calculation, the dependence of the dc and ac conductivity on the disorder mode, dimension, temperature, and electric field is studied. The results indicate that the dc and ac conductivity of the systems decreases with the increase of the degree of lattices energy disorder, while the off-diagonal disorder can enhance the electrical conductivity of the system. Meanwhile, the conductivity increases with the increase of the number of chains in the systems. The model also quantitatively explains the temperature and electric field dependence of the conductivity of the system, that is, in diagonal disordered systems, the ac conductivity of the systems increases with the increasing of temperature, in off-diagonal disordered systems, the ac conductivity of the systems decreases with the increasing of temperature, while the dc conductivity of the systems in all disordered modes increases with the increasing of temperature. In addition, the dc conductivity of the quasi-one-dimensional disordered systems increases with the increasing of the strength of dc electric field, showing the non-Ohm’s law conductivity characteristics, and the larger the number of chains in systemis, the more slowly the dc conductivity of systems increases with the increasing electric field. The ac conductivity quasi-one-dimensional disordered systems increases as the frequency of the external electric field rises, satisfying the relation σac(ω)∝ω2[In(1/ω)]2.
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Keywords:
- quasi-one-dimensional disordered systems /
- hopping conductivity /
- diagonal disorder /
- off-diagonal disorder
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[2] Rodin A S, Fogler M M 2009 Phys. Rev. B 80 155435
[3] Maul R, Wenzel W 2009 Phys. Rev. B 80 045424
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[6] Ben-Naim E, Krapivsky P L 2009 Phys. Rev. Lett. 102 190602
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[13] Ivanov D A, Ostrovsky P M, Skvortsov M A 2009 Phys. Rev. B 79 205108
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[15] Carpena P, Bemaola-Galvan P, Ivanov P C, Stanley H E 2002 Nature 418 955
[16] Dean P, Martin J L 1960 Proc. Roy. Soc. A 259 409
[17] Dean P 1960 Proc. Roy. Soc. 254 507
[18] Dean P 1972 Rev. Mod. Phys. 44 127
[19] Wu S Y, Tung C, Schwartz M 1974 J. Math. Phys.15 938
[20] Wu S Y, Zheng Z B 1981 Prog. Phys. 1 125 (in Chinese) [吴式玉、郑兆勃 1981 物理学进展 1 125]
[21] Wu S Y, Zheng Z B 1981 Phys. Rev. B 24 4787
[22] Miller A, Abraham E 1960 Phys. Rev. 120 745
[23] Ambegaokar V, Halperin B I, Langer J S 1971 Phys. Rev. B 4 2612
[24] Fogler M M, Kelley R S 2005 Phys. Rev. Lett. 95 166604
[25] Mcinnes J A, Butcher P N, Triberis G P 1990 J. Phys. Condens. Matter 2 7861
[26] Galperin Y M 1999 Doped Semiconductors:Role of Disorder (Lectures at Lund University)
[27] Xu H, Zeng H T 1992 Acta Phys. Sin. 41 1666(in Chinese) [徐 慧、曾红涛 1992 41 1666]
[28] Pasveer W F, Bobbert P A, Huinink H P, Michels M A J 2005 Phys. Rev. B 72 174204
[29] Lazaros K G, Bijan M, Laurens D A S 2003 Phys. Rev. B 67 165417
[30] Rosenow B, Nattermann T 2006 Phys. Rev. B 73 085103
[31] Ma S S, Xu H, Li Y F, Zhang P H 2007 Acta Phys. Sin. 56 5394(in Chinese) [马松山、徐 慧、李燕峰、张鹏华 2007 56 5394]
[32] Ma S S, Xu H, Wang H Y, Guo R 2009 Chin. Phys. B 18 3591
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[1] Anderson P W 1958 Phys. Rev. 109 1492
[2] Rodin A S, Fogler M M 2009 Phys. Rev. B 80 155435
[3] Maul R, Wenzel W 2009 Phys. Rev. B 80 045424
[4] Hu D S, Lu X J, Zhang Y M, Zhu C P 2009 Chin. Phys. B 18 2498
[5] Bascones E, Estévez V, Trinidad J A, MacDonald A H 2008 Phys. Rev. B 77 245422
[6] Ben-Naim E, Krapivsky P L 2009 Phys. Rev. Lett. 102 190602
[7] Brower P W, Mudry C, Simons B D, Altland A 1998 Phys. Rev. Lett. 81 862
[8] Sedrakyan T, Alexander O 2004 Phys. Rev. B 70 214206
[9] Hjort M, Stafstrom S 2000 Phys. Rev. B 62 5245
[10] Xu H 1997 Chin. J. Comp. Phys.14 574 (in Chinese) [徐 慧 1997 计算物理 14 574]
[11] Song Z Q, Xu H, Li Y F, Liu X L 2005 Acta Phys. Sin.54 2198 (in Chinese) [宋招权、徐 慧、李燕峰、刘小良 2005 物 理学报 54 2198] 〖12] Liu X L, Xu H, Ma S S, Song Z Q, Deng C S 2006 Acta Phys. Sin. 55 2492(in Chinese) [刘小良、徐 慧、马松山、宋招权、邓超生 2006 55 2492]
[12] Gallos L K, Movaghar B, Siebbeles L D A 2003 Phys. Rev. B 67 165417
[13] Ivanov D A, Ostrovsky P M, Skvortsov M A 2009 Phys. Rev. B 79 205108
[14] Kiwi M, Ramirez R, Trias A 1978 Phys. Rev. B 17 3063
[15] Carpena P, Bemaola-Galvan P, Ivanov P C, Stanley H E 2002 Nature 418 955
[16] Dean P, Martin J L 1960 Proc. Roy. Soc. A 259 409
[17] Dean P 1960 Proc. Roy. Soc. 254 507
[18] Dean P 1972 Rev. Mod. Phys. 44 127
[19] Wu S Y, Tung C, Schwartz M 1974 J. Math. Phys.15 938
[20] Wu S Y, Zheng Z B 1981 Prog. Phys. 1 125 (in Chinese) [吴式玉、郑兆勃 1981 物理学进展 1 125]
[21] Wu S Y, Zheng Z B 1981 Phys. Rev. B 24 4787
[22] Miller A, Abraham E 1960 Phys. Rev. 120 745
[23] Ambegaokar V, Halperin B I, Langer J S 1971 Phys. Rev. B 4 2612
[24] Fogler M M, Kelley R S 2005 Phys. Rev. Lett. 95 166604
[25] Mcinnes J A, Butcher P N, Triberis G P 1990 J. Phys. Condens. Matter 2 7861
[26] Galperin Y M 1999 Doped Semiconductors:Role of Disorder (Lectures at Lund University)
[27] Xu H, Zeng H T 1992 Acta Phys. Sin. 41 1666(in Chinese) [徐 慧、曾红涛 1992 41 1666]
[28] Pasveer W F, Bobbert P A, Huinink H P, Michels M A J 2005 Phys. Rev. B 72 174204
[29] Lazaros K G, Bijan M, Laurens D A S 2003 Phys. Rev. B 67 165417
[30] Rosenow B, Nattermann T 2006 Phys. Rev. B 73 085103
[31] Ma S S, Xu H, Li Y F, Zhang P H 2007 Acta Phys. Sin. 56 5394(in Chinese) [马松山、徐 慧、李燕峰、张鹏华 2007 56 5394]
[32] Ma S S, Xu H, Wang H Y, Guo R 2009 Chin. Phys. B 18 3591
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