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In this paper, the quantum coherence effect in spin-orbit coupled quantum dots system is studied. The average current, shot noise and skewness of the system are calculated by using the full counting statistics approach of the transport system. It is found that the shot noise decreases with the spin-orbit coupling increasing. More importantly, the current, noise and skewness fluctuate periodically with the magnetic flux. And the oscillation period is not affected by the strength of spin-orbit coupling, spin polarization and dynamic coupling asymmetry.
[1] Lucignano P, Jouault B, Tagliacozzo A 2004 Phys. Rev. B 69 4Google Scholar
[2] Kouwenhoven L P, Austing D G, Tarucha S 2001 Rep. Prog. Phys. 64 6Google Scholar
[3] Souza F M, Egues J C, Jauho A P 2007 Phys. Rev. B 75 165303Google Scholar
[4] Świrkowicz R, Wilczyński M, Wawrzyniak M, Barnaś J 2006 Phys. Rev. B 73 193312Google Scholar
[5] Martinek J, Sindel M, Borda L, Barnaś J, Bulla R, König J, Schön G, Maekawa S, von Delft J 2005 Phys. Rev. B 72 121302(R)
[6] Elste F, Timm C 2006 Phys. Rev. B 73 235305Google Scholar
[7] Weymann I, Barnaś J, König J, Martinek J, Schön G 2005 Phys. Rev. B 72 113301Google Scholar
[8] Cottet A, Belzig W, Bruder C 2004 Phys. Rev. Lett. 92 206801Google Scholar
[9] Datta S, Houten H V 1996 Phys. Today 49 5Google Scholar
[10] Nazarov Y V 1993 Physica B 189 57Google Scholar
[11] Gurvitz S A, Lipkin H J, Prager Y S 1996 Phys. Lett. A 212 91Google Scholar
[12] Gurvitz S A, Prager Y S 1996 Phys. Rev. B 53 15932Google Scholar
[13] Li X Q, Luo J Y, Yang Y G 2005 Phys. Rev. B 71 205304Google Scholar
[14] Kampen N G V 1983 Phys. Today 36 278Google Scholar
[15] Fu B, Zhang L, Wei Y D, Wang J 2017 Phys. Rev. B 96 115410Google Scholar
[16] Kilgour M, Agarwalla B K, Segal D 2019 J. Chem. Phys. 150 8Google Scholar
[17] Bagrets D A, Nazarov Y V 2003 Phys. Rev. B 67 085316Google Scholar
[18] Luo J Y, Shen Y, He X L, Li X Q, Yan Y J 2011 Phys. Lett. A 376 59Google Scholar
[19] Levitov L S, Lesovik G B 1993 JETP Lett. 58 230Google Scholar
[20] Blanter Y M, Büttiker M 2000 Phys. Rep. 336 1Google Scholar
[21] Timofeev A V, Meschke M, Peltonen J T, Heikkila T T, Pekola J P 2007 Phys. Rev. Lett. 98 207001Google Scholar
[22] Sukhorukov E V, Jordan A N, Gustavsson S, Leturcq R, Ihn T, Ensslin K 2007 Nat. Phys. 3 243Google Scholar
[23] Gershon G, Bomze Y, Sukhorukov E V, Reznikov M 2008 Phys. Rev. Lett. 101 016803Google Scholar
[24] Flindt C, Fricke C, Hohls F, Novotný T, Netočný K, Brandes T, Haug R J 2009 Proc. Natl. Acad. Sci. U. S. A. 106 10116Google Scholar
[25] Gabelli J, Reulet B 2009 Phys. Rev. B 80 161203(R)
[26] GustavssonS, Leturcq R, Studer M, Shorubalko I, Ihn T, Ensslin K, Driscoll D C, Gossard A C 2009 Surf. Sci. Rep. 64 191Google Scholar
[27] Masne Q L, Pothier H, Birge N O, Urbina C, Esteve D 2009 Phys. Rev. Lett. 102 067002Google Scholar
[28] Ubbelohde N, Fricke C, Flindt C, Hohls F, Haug R J 2012 Nat. Commun. 3 612Google Scholar
[29] Reulet B, Senzier J, Prober D E 2003 Phys. Rev. Lett. 91 196601Google Scholar
[30] Bomze Y, Gershon G, Shovkun D, Levitov L S, Reznikov M 2005 Phys. Rev. Lett. 95 176601Google Scholar
[31] Gustavsson S, Leturcq R, Simovic B, Schleser R, Ihn T, Studerus P, Ensslin K, Driscoll D C, Gossard A C 2006 Phys. Rev. Lett. 96 076605Google Scholar
[32] Fujisawa T, Hayashi T, Tomita R, Hirayama Y 2006 Science 312 1634Google Scholar
[33] Maisi V F, Kambly D, Flindt C, Pekola J P 2014 Phys. Rev. Lett. 112 036801Google Scholar
[34] Braggio A, Köenig J, Fazio R 2006 Phys. Rev. Lett. 96 026805Google Scholar
[35] Muzykantskii B A, Khmelnitskii D E 1994 Phys. Rev. B 50 3982Google Scholar
[36] Belzig W, Nazarov Y V 2001 Phys. Rev. Lett. 87 067006Google Scholar
[37] Belzig W, Nazarov Y V 2001 Phys. Rev. Lett. 87 197006Google Scholar
[38] Shelankov A, Rammer J 2003 Europhys. Lett. 63 485Google Scholar
[39] Bulashenko O M 2005 J. Stat. Mech. 15 8Google Scholar
[40] Taddei F, Fazio R 2002 Phys. Rev. B 65 075317Google Scholar
[41] Kindermann M 2005 Phys. Rev. B 71 165332Google Scholar
[42] Ankerhold J, Grabert H 2005 Phys. Rev. Lett. 95 186601Google Scholar
[43] Tobiska J, Nazarov Y V 2004 Phys. Rev. Lett. 93 106801Google Scholar
[44] Stegmann P, König J, Weiss S 2018 Phys. Rev. B 98 035409Google Scholar
[45] Aharonov Y, Bohm D 1959 Phys. Rev. 115 485Google Scholar
[46] Aikawa H, Kobayashi K, Sano A, Katsumoto S, Iye Y 2004 Phys. Rev. Lett. 92 176802Google Scholar
[47] Xu G, Broholm C, Soh Y A, Aeppli G, Ditusa J F, Chen Y, Kenzelmann M, Frost C D, Ito T, Oka K 2007 Science 317 5841Google Scholar
[48] Xu W, Guo Y 2005 Phys. Lett. A 340 281Google Scholar
[49] Wolf S A, Awschalom D D, Buhrman R A, Daughton J M, Molnar S V, Roukes M L, Chtchelkanova A Y, Treger D M 2001 Science 294 1488Google Scholar
[50] Zutic I, Fabian J, Sarma S D 2004 Rev. Mod. Phys. 76 323Google Scholar
[51] Datta S, Das S 1990 Appl. Phys. Lett. 56 665Google Scholar
[52] Miller J B, Zumbühl D M, Marcus C M, Lyanda-Geller Y B, Gossard A C 2003 Phys. Rev. Lett. 90 076807Google Scholar
[53] Manchon A, Koo H C, Nitta J, Frolov S M, Duine R A 2015 Nat. Mater. 14 9Google Scholar
[54] Sheng L, Sheng D N, Ting C S 2005 Phys. Rev. Lett. 94 016602Google Scholar
[55] Ogloblya O V, Kuznetsova G M 2013 Physica B 424 47Google Scholar
[56] Chi F, Li S S 2006 J. Appl. Phys. 100 11Google Scholar
[57] Žutić I, Fabian J, Sarma S D 2001 Appl. Phys. Lett. 79 1558Google Scholar
[58] Schmidt G, Ferrand D, Molenkamp L W, Filip A T, Wees B J V 2000 Phys. Rev. B 62 8Google Scholar
[59] Wu M W, Zhou J, Shi Q W 2004 Appl. Phys. Lett. 85 1012Google Scholar
[60] Ohe J I, Yamamoto M, Ohtsuki T, Nitta J 2004 Phys. Rev. B 72 041308Google Scholar
[61] Souma S, Nikolić B K 2004 Phys. Rev. B 70 195346Google Scholar
[62] Sun Q F, Wang J, Guo H 2005 Phys. Rev. B 71 165310Google Scholar
[63] Sun Q F, Xie X C 2005 Phys. Rev. B 71 155321Google Scholar
[64] Belzig W 2005 Phys. Rev. B 71 161301Google Scholar
[65] Streltsov A, Adesso G, Plenio M B 2017 Rev. Mod. Phys. 89 041003Google Scholar
[66] Hu M L, Hu X, Wang J, Yi P, Zhang Y R, Fan H 2018 Phys. Rep. 1 762Google Scholar
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图 1 自旋轨道耦合常数
${\alpha _{{\text{SO}}}}$ 不同时, (a)平均电流$\left\langle I \right\rangle $ , (b)散粒噪声${F_{\text{a}}}$ 和(c)偏斜${S_{\text{k}}}$ 随磁通$\zeta $ 振荡图.${\varepsilon }_{1}=1, $ $ {\varepsilon }_{2}=3, {\varGamma }_{\text{L}}={\varGamma }_{\text{R}}=0.01, p=0.1$ Fig. 1. (a) Average current
$\left\langle I \right\rangle $ , (b) shot noise${F_{\text{a}}}$ and (c) skewness${S_{\text{k}}}$ fluctuation diagram in different spin-orbit coupling strength${\alpha _{{\text{SO}}}}$ .${\varepsilon }_{1}=1, {\varepsilon }_{2}=3, {\varGamma }_{\text{L}}={\varGamma }_{\text{R}}=0.01, $ $ p=\mathrm{0.1}$ 图 2 非对称动力耦合下, (a)平均电流
$\left\langle I \right\rangle $ , (b)散粒噪声${F_{\text{a}}}$ 和(c)偏斜${S_{\text{k}}}$ 随磁通$\zeta $ 振荡图.${\varepsilon }_{1}=1,\; {\varepsilon }_{2}=3, $ $ \; {\alpha }_{\text{SO}}=0.3,\; p=0.1$ Fig. 2. (a) Average current
$\left\langle I \right\rangle $ , (b) shot noise${F_{\text{a}}}$ and (c) skewness${S_{\text{k}}}$ fluctuation diagram for asymmetric dot-electrode coupling.${\varepsilon }_{1}=1,\; {\varepsilon }_{2}=3,\; {\alpha }_{\text{SO}}=0.3,\; p=\mathrm{0.1}$ 图 3 自旋极化率
$p$ 不同时, (a)平均电流$\left\langle I \right\rangle $ , (b)散粒噪声${F_{\text{a}}}$ 和(c)偏斜${S_{\text{k}}}$ 随磁通$\zeta $ 振荡图.${\varepsilon }_{1}=1, \;{\varepsilon }_{2}=3, $ $ \;{\alpha }_{\text{SO}}=0.3,\; {\varGamma }_{\text{L}}={\varGamma }_{\text{R}}=0.01$ Fig. 3. (a) Average current
$\left\langle I \right\rangle $ , (b) shot noise${F_{\text{a}}}$ and (c) skewness${S_{\text{k}}}$ with magnetic flux oscillation with different spin polarization$p$ .${\varepsilon }_{1}=1,\; {\varepsilon }_{2}=3,\; {\alpha }_{\text{SO}}=0.3,\; {\varGamma }_{\text{L}}={\varGamma }_{\text{R}}= $ $ \mathrm{0.01}$ -
[1] Lucignano P, Jouault B, Tagliacozzo A 2004 Phys. Rev. B 69 4Google Scholar
[2] Kouwenhoven L P, Austing D G, Tarucha S 2001 Rep. Prog. Phys. 64 6Google Scholar
[3] Souza F M, Egues J C, Jauho A P 2007 Phys. Rev. B 75 165303Google Scholar
[4] Świrkowicz R, Wilczyński M, Wawrzyniak M, Barnaś J 2006 Phys. Rev. B 73 193312Google Scholar
[5] Martinek J, Sindel M, Borda L, Barnaś J, Bulla R, König J, Schön G, Maekawa S, von Delft J 2005 Phys. Rev. B 72 121302(R)
[6] Elste F, Timm C 2006 Phys. Rev. B 73 235305Google Scholar
[7] Weymann I, Barnaś J, König J, Martinek J, Schön G 2005 Phys. Rev. B 72 113301Google Scholar
[8] Cottet A, Belzig W, Bruder C 2004 Phys. Rev. Lett. 92 206801Google Scholar
[9] Datta S, Houten H V 1996 Phys. Today 49 5Google Scholar
[10] Nazarov Y V 1993 Physica B 189 57Google Scholar
[11] Gurvitz S A, Lipkin H J, Prager Y S 1996 Phys. Lett. A 212 91Google Scholar
[12] Gurvitz S A, Prager Y S 1996 Phys. Rev. B 53 15932Google Scholar
[13] Li X Q, Luo J Y, Yang Y G 2005 Phys. Rev. B 71 205304Google Scholar
[14] Kampen N G V 1983 Phys. Today 36 278Google Scholar
[15] Fu B, Zhang L, Wei Y D, Wang J 2017 Phys. Rev. B 96 115410Google Scholar
[16] Kilgour M, Agarwalla B K, Segal D 2019 J. Chem. Phys. 150 8Google Scholar
[17] Bagrets D A, Nazarov Y V 2003 Phys. Rev. B 67 085316Google Scholar
[18] Luo J Y, Shen Y, He X L, Li X Q, Yan Y J 2011 Phys. Lett. A 376 59Google Scholar
[19] Levitov L S, Lesovik G B 1993 JETP Lett. 58 230Google Scholar
[20] Blanter Y M, Büttiker M 2000 Phys. Rep. 336 1Google Scholar
[21] Timofeev A V, Meschke M, Peltonen J T, Heikkila T T, Pekola J P 2007 Phys. Rev. Lett. 98 207001Google Scholar
[22] Sukhorukov E V, Jordan A N, Gustavsson S, Leturcq R, Ihn T, Ensslin K 2007 Nat. Phys. 3 243Google Scholar
[23] Gershon G, Bomze Y, Sukhorukov E V, Reznikov M 2008 Phys. Rev. Lett. 101 016803Google Scholar
[24] Flindt C, Fricke C, Hohls F, Novotný T, Netočný K, Brandes T, Haug R J 2009 Proc. Natl. Acad. Sci. U. S. A. 106 10116Google Scholar
[25] Gabelli J, Reulet B 2009 Phys. Rev. B 80 161203(R)
[26] GustavssonS, Leturcq R, Studer M, Shorubalko I, Ihn T, Ensslin K, Driscoll D C, Gossard A C 2009 Surf. Sci. Rep. 64 191Google Scholar
[27] Masne Q L, Pothier H, Birge N O, Urbina C, Esteve D 2009 Phys. Rev. Lett. 102 067002Google Scholar
[28] Ubbelohde N, Fricke C, Flindt C, Hohls F, Haug R J 2012 Nat. Commun. 3 612Google Scholar
[29] Reulet B, Senzier J, Prober D E 2003 Phys. Rev. Lett. 91 196601Google Scholar
[30] Bomze Y, Gershon G, Shovkun D, Levitov L S, Reznikov M 2005 Phys. Rev. Lett. 95 176601Google Scholar
[31] Gustavsson S, Leturcq R, Simovic B, Schleser R, Ihn T, Studerus P, Ensslin K, Driscoll D C, Gossard A C 2006 Phys. Rev. Lett. 96 076605Google Scholar
[32] Fujisawa T, Hayashi T, Tomita R, Hirayama Y 2006 Science 312 1634Google Scholar
[33] Maisi V F, Kambly D, Flindt C, Pekola J P 2014 Phys. Rev. Lett. 112 036801Google Scholar
[34] Braggio A, Köenig J, Fazio R 2006 Phys. Rev. Lett. 96 026805Google Scholar
[35] Muzykantskii B A, Khmelnitskii D E 1994 Phys. Rev. B 50 3982Google Scholar
[36] Belzig W, Nazarov Y V 2001 Phys. Rev. Lett. 87 067006Google Scholar
[37] Belzig W, Nazarov Y V 2001 Phys. Rev. Lett. 87 197006Google Scholar
[38] Shelankov A, Rammer J 2003 Europhys. Lett. 63 485Google Scholar
[39] Bulashenko O M 2005 J. Stat. Mech. 15 8Google Scholar
[40] Taddei F, Fazio R 2002 Phys. Rev. B 65 075317Google Scholar
[41] Kindermann M 2005 Phys. Rev. B 71 165332Google Scholar
[42] Ankerhold J, Grabert H 2005 Phys. Rev. Lett. 95 186601Google Scholar
[43] Tobiska J, Nazarov Y V 2004 Phys. Rev. Lett. 93 106801Google Scholar
[44] Stegmann P, König J, Weiss S 2018 Phys. Rev. B 98 035409Google Scholar
[45] Aharonov Y, Bohm D 1959 Phys. Rev. 115 485Google Scholar
[46] Aikawa H, Kobayashi K, Sano A, Katsumoto S, Iye Y 2004 Phys. Rev. Lett. 92 176802Google Scholar
[47] Xu G, Broholm C, Soh Y A, Aeppli G, Ditusa J F, Chen Y, Kenzelmann M, Frost C D, Ito T, Oka K 2007 Science 317 5841Google Scholar
[48] Xu W, Guo Y 2005 Phys. Lett. A 340 281Google Scholar
[49] Wolf S A, Awschalom D D, Buhrman R A, Daughton J M, Molnar S V, Roukes M L, Chtchelkanova A Y, Treger D M 2001 Science 294 1488Google Scholar
[50] Zutic I, Fabian J, Sarma S D 2004 Rev. Mod. Phys. 76 323Google Scholar
[51] Datta S, Das S 1990 Appl. Phys. Lett. 56 665Google Scholar
[52] Miller J B, Zumbühl D M, Marcus C M, Lyanda-Geller Y B, Gossard A C 2003 Phys. Rev. Lett. 90 076807Google Scholar
[53] Manchon A, Koo H C, Nitta J, Frolov S M, Duine R A 2015 Nat. Mater. 14 9Google Scholar
[54] Sheng L, Sheng D N, Ting C S 2005 Phys. Rev. Lett. 94 016602Google Scholar
[55] Ogloblya O V, Kuznetsova G M 2013 Physica B 424 47Google Scholar
[56] Chi F, Li S S 2006 J. Appl. Phys. 100 11Google Scholar
[57] Žutić I, Fabian J, Sarma S D 2001 Appl. Phys. Lett. 79 1558Google Scholar
[58] Schmidt G, Ferrand D, Molenkamp L W, Filip A T, Wees B J V 2000 Phys. Rev. B 62 8Google Scholar
[59] Wu M W, Zhou J, Shi Q W 2004 Appl. Phys. Lett. 85 1012Google Scholar
[60] Ohe J I, Yamamoto M, Ohtsuki T, Nitta J 2004 Phys. Rev. B 72 041308Google Scholar
[61] Souma S, Nikolić B K 2004 Phys. Rev. B 70 195346Google Scholar
[62] Sun Q F, Wang J, Guo H 2005 Phys. Rev. B 71 165310Google Scholar
[63] Sun Q F, Xie X C 2005 Phys. Rev. B 71 155321Google Scholar
[64] Belzig W 2005 Phys. Rev. B 71 161301Google Scholar
[65] Streltsov A, Adesso G, Plenio M B 2017 Rev. Mod. Phys. 89 041003Google Scholar
[66] Hu M L, Hu X, Wang J, Yi P, Zhang Y R, Fan H 2018 Phys. Rep. 1 762Google Scholar
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