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Non-classical state effect on the persistent current in one-dimensional mesoscopic ring with electron-phonon interaction

Liang Guo-Dong Luo Zhi-Hua

Non-classical state effect on the persistent current in one-dimensional mesoscopic ring with electron-phonon interaction

Liang Guo-Dong, Luo Zhi-Hua
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  • Based on the efficacy of the phonon coherent state and with consideration of the non-classical effect of the squeezed state of phonon, the influence of the electron-magnon interaction and the electron-phonon interaction on the persistent current in one-dimensional mesoscopic ring is studied. Compared with the free ring, our study shows that in one-dimensional mesoscopic ring, the amplitude of the persistent current exponentially diminishes due to the electron-magnon interaction. For the normal state electron, the interaction of the electron-phonon causes the persistent current to weakendce to the Debye-Waller effect. However, taking the correlation between the hopping electron states and the one-phonon coherent states into the equation, the ground energy of the mesoscopic system is declined in a large scale. In result, the persistent current In is increased substantially. On the other hand, taking the behavior of the two-phonon coherent state into account, as the effect of the squeezed states of phonons maintains the phase coherence of electrons, so the Debye-Waller attenuation is weakened effectively. Especially, when the squeezed angle is larger, because of the non-adiabatic correlation between the squeezed-phonon states and the coherent states of phonon, it causes a significant decline in the ground state energy and a significant increase in the squeezed angle, thus persistent current has a even more significant increase. It should be pointed out, that the persistent current shows period oscillation as the external magnetic flux changes. Even the external magnetic flux Φem=0, still the persistent current of the intrinsic has I ~ n≠0. The system continuoues to support the equilibrium spin and charge flow, the external magnetic flux only plays the role of an adiabatic parameter.
    • Funds:
    [1]

    Buttiker M, Imry Y, Landauer R 1983 Phys. Lett. A 96 365

    [2]
    [3]

    Chandrasekhar V, Webb R A, Brady M J, Ketchen M B, Gailagher W J, Kleinsasser A 1991 Phys. Rev. Lett. 67 3578

    [4]

    55 4287 (in Chinese) [谌雄文、 贺达江、吴绍全、宋克慧 2006物理学报 55 4287] [21] Dajkal J,Szopal M, Voardas, Zipperl 2004 Phys. Rev. B 69 45305

    [5]

    Cheung H F, Gefen Y, Riedel E K, Shih W H 1988 Phys. Rev. B 37 6050

    [6]

    Ambegaoker V, Eckern U 1990 Phys. Lett. 65 381

    [7]

    Altshuler B L, Gelfan Y, Imry Y 1991 Phys. Rev. Lett. 66 88

    [8]

    Bouzerar G, Poilblanc D, Monlambaux G 1994 Phys. Rev. B 49 8258

    [9]

    Lévy L P, Dolan G, Dansmuir J, Bouchait H 1990 Phys. Rev. Lett. 64 2074

    [10]

    Mailly D, Chapelier C, Benoid A 1993 Phys. Rev. Lett. 70 2120

    [11]

    Grüner G 1994 Rev. Mod. Phys. 66 1

    [12]

    Ye J F, Ye H, Ding G H 2003 Acta Phys. Sin. 52 468 (in Chinese) [叶剑斐、 叶 辉、 丁国辉 2003年物理学报 52 468]

    [13]

    Giamarchi T, Shastry B S 1995 Phys. Rev. B51 10915

    [14]

    Wang J, Ma Z S 1995 Phys. Rev. B52 14892

    [15]

    Liang S D,Bai Y H, Beng B 2006 Phys. Rev. B 74 113304

    [16]

    Citro R,Romeo F 2007 Phys. Rev. B 75 73306

    [17]

    Sun Q F, Xie X C, Wang J 2007 Phys. Rev. Lett. 98 196801

    [18]

    Niliionl J, Hans-Peter Eckler, Johanness-onr 2007 Phys. Rev. B 76 73408

    [19]

    Zhao H K 2005 Phys. Lett. A 342 468

    [20]

    Liang F Y, Li H M, Li Y J 2006 Acta Phys. Sin. 55 830 (in Chinese) [梁芳营、 李汉明、 李英骏 2006 年物理学报 55 830]

    [21]

    Wu S Q, He Z, Yan, C H, Chen X W, Sun W L 2006 Acta Phys. Sin. 55 1413 (in Chinese) [吴绍全、 何 忠、 阎从华、 谌雄文、 孙威立 2006 年物理学报 55 1413]

    [22]

    Chen X W, He D J, Wu S Q, Song K H 2006 Acta Phys. Sin.

    [23]

    Sheng J S, Kai Chang 2006 Phys. Rev. B 74 235315

    [24]

    Wu J N, Chang M C 2005 Phys. Rev. B 72 172405

    [25]

    Ji Y H, liu Y M, Xin J Z, Xie F S, Lei M S 2004 Acta Phys. Sin. 53 1207 (in Chinese) [嵇英华、 刘咏梅、 辛建之、 谢芳森、 雷敏生 2004 物理学报 53 1027]

    [26]

    Wu S Q, Sun W L, Yu W L, Wang S J 2005 Acta Phys. Sin. 54 2910 (in Chinese) [吴绍全、 孙威立、 余万伦、 王顺金 2005 物理学报 54 2910]

    [27]

    Wu Hong 2008 Chin. Phys. B 17 3026

    [28]

    Liu P, Xiong S J 2009 Chin. Phys. B 18 5414

    [29]

    Xu N, Ding J W, Ma M M, Tang X 2010 Chin. Phys. B 19 016101

    [30]

    Ma M M, Ding J W, Chen H B, Xu N 2009 Acta Phys. Sin. 58 2726 (in Chinese)[马明明、 丁建文、陈宏波、徐 宁2009物理学报 58 2726]

    [31]

    Xu N, Ding J W, Chen H B, Ma M M 2009 Chine. Phys. B 18 2030

    [32]

    Hamutal B S, Ora Entin-Wohlman, Imryl Y 2009 Phys. Rev. B 80 02459

    [33]

    Bouchiat H 2008 Mesoscopics Phys. 1 7

    [34]

    Zelgak O, Murthy 2008 Phys. Rev. B 78 125305

    [35]

    Feilhauer J, Mo ko M 2008 Physica E 40 1582

    [36]

    Loss D, Goldbart P 1991 Phys. Rev. B 43 13762 Loss D, Goldbart P 1992 Phys. Rev. B 45 13544

    [37]

    Kusakabe K, Aoki H 1994 Phys. Rev. Lett. 72 144

    [38]

    Majernikava E, Koval J 1998 Physica 37 23

    [39]

    Ivanov V A, Zhuravlev M Ye, Murayama Y, Nakajima S 1996 JETP Lett. 64 148

    [40]

    Wu S S, Ma Z S 1996 Phys. Rev. B 53 16372

  • [1]

    Buttiker M, Imry Y, Landauer R 1983 Phys. Lett. A 96 365

    [2]
    [3]

    Chandrasekhar V, Webb R A, Brady M J, Ketchen M B, Gailagher W J, Kleinsasser A 1991 Phys. Rev. Lett. 67 3578

    [4]

    55 4287 (in Chinese) [谌雄文、 贺达江、吴绍全、宋克慧 2006物理学报 55 4287] [21] Dajkal J,Szopal M, Voardas, Zipperl 2004 Phys. Rev. B 69 45305

    [5]

    Cheung H F, Gefen Y, Riedel E K, Shih W H 1988 Phys. Rev. B 37 6050

    [6]

    Ambegaoker V, Eckern U 1990 Phys. Lett. 65 381

    [7]

    Altshuler B L, Gelfan Y, Imry Y 1991 Phys. Rev. Lett. 66 88

    [8]

    Bouzerar G, Poilblanc D, Monlambaux G 1994 Phys. Rev. B 49 8258

    [9]

    Lévy L P, Dolan G, Dansmuir J, Bouchait H 1990 Phys. Rev. Lett. 64 2074

    [10]

    Mailly D, Chapelier C, Benoid A 1993 Phys. Rev. Lett. 70 2120

    [11]

    Grüner G 1994 Rev. Mod. Phys. 66 1

    [12]

    Ye J F, Ye H, Ding G H 2003 Acta Phys. Sin. 52 468 (in Chinese) [叶剑斐、 叶 辉、 丁国辉 2003年物理学报 52 468]

    [13]

    Giamarchi T, Shastry B S 1995 Phys. Rev. B51 10915

    [14]

    Wang J, Ma Z S 1995 Phys. Rev. B52 14892

    [15]

    Liang S D,Bai Y H, Beng B 2006 Phys. Rev. B 74 113304

    [16]

    Citro R,Romeo F 2007 Phys. Rev. B 75 73306

    [17]

    Sun Q F, Xie X C, Wang J 2007 Phys. Rev. Lett. 98 196801

    [18]

    Niliionl J, Hans-Peter Eckler, Johanness-onr 2007 Phys. Rev. B 76 73408

    [19]

    Zhao H K 2005 Phys. Lett. A 342 468

    [20]

    Liang F Y, Li H M, Li Y J 2006 Acta Phys. Sin. 55 830 (in Chinese) [梁芳营、 李汉明、 李英骏 2006 年物理学报 55 830]

    [21]

    Wu S Q, He Z, Yan, C H, Chen X W, Sun W L 2006 Acta Phys. Sin. 55 1413 (in Chinese) [吴绍全、 何 忠、 阎从华、 谌雄文、 孙威立 2006 年物理学报 55 1413]

    [22]

    Chen X W, He D J, Wu S Q, Song K H 2006 Acta Phys. Sin.

    [23]

    Sheng J S, Kai Chang 2006 Phys. Rev. B 74 235315

    [24]

    Wu J N, Chang M C 2005 Phys. Rev. B 72 172405

    [25]

    Ji Y H, liu Y M, Xin J Z, Xie F S, Lei M S 2004 Acta Phys. Sin. 53 1207 (in Chinese) [嵇英华、 刘咏梅、 辛建之、 谢芳森、 雷敏生 2004 物理学报 53 1027]

    [26]

    Wu S Q, Sun W L, Yu W L, Wang S J 2005 Acta Phys. Sin. 54 2910 (in Chinese) [吴绍全、 孙威立、 余万伦、 王顺金 2005 物理学报 54 2910]

    [27]

    Wu Hong 2008 Chin. Phys. B 17 3026

    [28]

    Liu P, Xiong S J 2009 Chin. Phys. B 18 5414

    [29]

    Xu N, Ding J W, Ma M M, Tang X 2010 Chin. Phys. B 19 016101

    [30]

    Ma M M, Ding J W, Chen H B, Xu N 2009 Acta Phys. Sin. 58 2726 (in Chinese)[马明明、 丁建文、陈宏波、徐 宁2009物理学报 58 2726]

    [31]

    Xu N, Ding J W, Chen H B, Ma M M 2009 Chine. Phys. B 18 2030

    [32]

    Hamutal B S, Ora Entin-Wohlman, Imryl Y 2009 Phys. Rev. B 80 02459

    [33]

    Bouchiat H 2008 Mesoscopics Phys. 1 7

    [34]

    Zelgak O, Murthy 2008 Phys. Rev. B 78 125305

    [35]

    Feilhauer J, Mo ko M 2008 Physica E 40 1582

    [36]

    Loss D, Goldbart P 1991 Phys. Rev. B 43 13762 Loss D, Goldbart P 1992 Phys. Rev. B 45 13544

    [37]

    Kusakabe K, Aoki H 1994 Phys. Rev. Lett. 72 144

    [38]

    Majernikava E, Koval J 1998 Physica 37 23

    [39]

    Ivanov V A, Zhuravlev M Ye, Murayama Y, Nakajima S 1996 JETP Lett. 64 148

    [40]

    Wu S S, Ma Z S 1996 Phys. Rev. B 53 16372

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Publishing process
  • Received Date:  31 May 2010
  • Accepted Date:  28 June 2010
  • Published Online:  15 March 2011

Non-classical state effect on the persistent current in one-dimensional mesoscopic ring with electron-phonon interaction

  • 1. (1)Department of Optoelectronic Engineering, Jinan University, Guangzhou 510632, China; (2)Department of Physics, Guangdong University of Education, Guangzhou 510303, China

Abstract: Based on the efficacy of the phonon coherent state and with consideration of the non-classical effect of the squeezed state of phonon, the influence of the electron-magnon interaction and the electron-phonon interaction on the persistent current in one-dimensional mesoscopic ring is studied. Compared with the free ring, our study shows that in one-dimensional mesoscopic ring, the amplitude of the persistent current exponentially diminishes due to the electron-magnon interaction. For the normal state electron, the interaction of the electron-phonon causes the persistent current to weakendce to the Debye-Waller effect. However, taking the correlation between the hopping electron states and the one-phonon coherent states into the equation, the ground energy of the mesoscopic system is declined in a large scale. In result, the persistent current In is increased substantially. On the other hand, taking the behavior of the two-phonon coherent state into account, as the effect of the squeezed states of phonons maintains the phase coherence of electrons, so the Debye-Waller attenuation is weakened effectively. Especially, when the squeezed angle is larger, because of the non-adiabatic correlation between the squeezed-phonon states and the coherent states of phonon, it causes a significant decline in the ground state energy and a significant increase in the squeezed angle, thus persistent current has a even more significant increase. It should be pointed out, that the persistent current shows period oscillation as the external magnetic flux changes. Even the external magnetic flux Φem=0, still the persistent current of the intrinsic has I ~ n≠0. The system continuoues to support the equilibrium spin and charge flow, the external magnetic flux only plays the role of an adiabatic parameter.

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