Interplay between Majorana fermion and impurity in thermal-driven transport model

Niu Peng-Bin; Luo Hong-Gang

doi:10.7498/aps.70.20202241

Abstract

In quantum transport, especially in spintronics, its central theme is to manipulate spin degrees of freedom in solid-state systems, to understand the interaction between the particle spin and its solid-state environments and to make useful devices. Recently, Majorana fermion has been introduced into quantum transport and received much attention. In this paper, we study a thermal-driven transport model which consists of a quantum dot coupled with two normal metal leads, a impurity spin (whose angular quantum number is more than or equal to one-half) and a Majorana fermion. We focus on the interplay between Majorana fermion and the impurity in this exactly solvable model. It is found that the system can generate thermal-induced spin current, and the currents are affected by Majorana fermion and impurity. With large temperature difference, the currents are sensitive to gate voltage, and the quantitative relation between spin-up current and gate voltage tends to be linear when the coupling between Majorana and quantum dot is strong, showing Majorana fermion's robustness. In addition, the spin current induced by Majorana fermion exhibits an oscillating antisymmetric structure around zero-bias point. This spin current’s zero point is related to the angular quantum number of impurity spin. These results are expected to be useful in thermal-electric conversion devices, and may be observed in future experiments.

Keywords:

Authors and contacts

Niu Peng-Bin¹,
Luo Hong-Gang²

1.
Department of Physics, Shanxi Datong University, Datong 037009, China
2.
School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China

Corresponding author: Niu Peng-Bin, niupengbin@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11834005, 11674139)

FullText HTML

References

[1]	Majorana E 1937 Nuovo Cimento 14 171 Google Scholar
[2]	Nayak C, Simon S H, Stern A, Freedman M, Das Sarma S 2008 Rev. Mod. Phys. 80 1083 Google Scholar
[3]	Stern A 2010 Nature 464 187 Google Scholar
[4]	Chang C Z, Zhang J S, Feng X, et al. 2013 Science 340 167 Google Scholar
[5]	He K, Wang Y, Xue Q K 2014 Nat. Sci. Rev. 1 38 Google Scholar
[6]	王力, 刘静思, 李吉, 周晓林, 陈向荣, 刘超飞, 刘伍明 2020 69 010303 Google Scholar Wang L, Liu J S, Li J, Zhou X L, Chen X R, Liu C F, Liu W M 2020 Acta Phys. Sin. 69 010303 Google Scholar
[7]	李吉, 刘伍明 2018 67 110302 Google Scholar Li J, Liu W M 2018 Acta Phys. Sin. 67 110302 Google Scholar
[8]	刘静思, 李吉, 刘伍明 2017 66 130305 Google Scholar Liu J S, Li J, Liu W M 2017 Acta Phys. Sin. 66 130305 Google Scholar
[9]	Chen Y H, Tao H S, Yao D X, Liu W M 2012 Phys. Rev. Lett. 108 246402 Google Scholar
[10]	Jiang Z F, Li R D, Zhang S C, Liu W M 2005 Phys. Rev. B 72 045201
[11]	Zhang X L, Liu L F, Liu W M 2005 Sci. Rep. 3 2908
[12]	Reich E S 2012 Nature 483 132 Google Scholar
[13]	Brouwer P W 2012 Science 336 989 Google Scholar
[14]	Wilczek F 2012 Nature 486 195 Google Scholar
[15]	Read N, Green D 2000 Phys. Rev. B 61 10267 Google Scholar
[16]	Ivanov D A 2001 Phys. Rev. Lett. 86 268 Google Scholar
[17]	Lutchyn R M, Sau J D, Das Sarma S 2010 Phys. Rev. Lett. 105 077001 Google Scholar
[18]	Oreg Y, Refael G, von Oppen F 2010 Phys. Rev. Lett. 105 177002 Google Scholar
[19]	Liu D E, Baranger H U 2011 Phys. Rev. B 84 201308(R Google Scholar
[20]	Napitu B D 2015 Eur. Phys. J. B 88 290 Google Scholar
[21]	Lü H F, Lu H Z, Shen S Q 2014 Phys. Rev. B 90 195404 Google Scholar
[22]	Liu D E, Cheng M, Lutchyn R M 2015 Phys. Rev. B 91 081405(R Google Scholar
[23]	Huo D M 2016 Eur. Phys. J. B 89 174 Google Scholar
[24]	Niu P B, Liu L X, Su X Q, Dong L J, Shi Y L, Luo H G 2020 J. Magn. Magn. Mater. 506 166795 Google Scholar
[25]	Bauer G E, MacDonald A H, Maekawa S 2010 Solid State Commun. 150 459 Google Scholar
[26]	Bauer G E, Saitoh E, van Wees B J 2012 Nat. Mater. 11 391 Google Scholar
[27]	Staring A A M, Molenkamp L W, Alphenaar B W, et al. 1993 Europhys. Lett. 22 57 Google Scholar
[28]	Svensson S F, Hoffmann E A, Nakpathomkun N, et al. 2013 New J. Phys. 15 105011 Google Scholar
[29]	Sanchez D, Lopez R 2013 Phys. Rev. Lett. 110 026804 Google Scholar
[30]	Alidoust M, Halterman K, Valls O T 2015 Phys. Rev. B 92 014508 Google Scholar
[31]	Niu P B, Liu L X, Su X Q, Dong L J, Shi Y L, Luo H G 2020 Physica E 124 114313 Google Scholar
[32]	Niu P B, Wang Q, Nie Y H 2013 Chin. Phys. B 22 027307 Google Scholar
[33]	Flensberg K 2010 Phys. Rev. B 82 180516(R Google Scholar
[34]	Kostyrko T, Bulka B R 2005 Phys. Rev. B 71 235306 Google Scholar
[35]	Niu P B, Zhang Y Y, Wang Q, et al. 2012 Phys. Lett. A 376 1481 Google Scholar
[36]	Meir Y, Wingreen N S 1992 Phys. Rev. Lett. 68 2512 Google Scholar
[37]	Wang R Q, Sheng L, Shen R, Wang B, Xing D Y 2010 Phys. Rev. Lett. 105 057202 Google Scholar
[38]	Luo H G, Ying Z J, Wang S J 1999 Phys. Rev. B 59 9710 Google Scholar
[39]	Sun Q F, Guo H 2002 Phys. Rev. B 66 155308 Google Scholar

Cited By

图 1 模型示意图. 系统由量子点(QD)、杂质大自旋(S)和拓扑超导线组成, 拓扑超导线的两端有两个马约拉纳费米子. 系统两端连接两个金属电极, 电极两端施加温度差

Figure 1. Model Diagram. The system consists of a quantum dot, a local large spin and a topological superconductor which supports Majorana fermions. There is a temperature gradient applied to the system.

DownLoad: Full-Size Img PowerPoint

图 2 S = 1/2时自旋向上电流(a)、自旋向下电流(b)、自旋流(c)和电荷流(d)随温差的变化图

Figure 2. Spin-resolved currents (a), (b), spin current (c) and charge current (d) as a function of temperature difference for S = 1/2.

DownLoad: Full-Size Img PowerPoint

图 3 S = 1/2时自旋向上电流　(a)、自旋向下电流(b)、自旋流(c)和电荷流(d)随门电压的变化图

Figure 3. Spin-resolved currents (a), (b), spin current (c) and charge current (d) as a function of gate voltage for S = 1/2.

DownLoad: Full-Size Img PowerPoint

图 4 S = 1时自旋向上电流(a)、自旋向下电流(b)、自旋流(c)和电荷流(d)随门电压的变化图

Figure 4. Spin-resolved currents (a), (b), spin current (c) and charge current (d) as a function of gate voltage for S = 1.

DownLoad: Full-Size Img PowerPoint

map

[1]	Majorana E 1937 Nuovo Cimento 14 171 Google Scholar
[2]	Nayak C, Simon S H, Stern A, Freedman M, Das Sarma S 2008 Rev. Mod. Phys. 80 1083 Google Scholar
[3]	Stern A 2010 Nature 464 187 Google Scholar
[4]	Chang C Z, Zhang J S, Feng X, et al. 2013 Science 340 167 Google Scholar
[5]	He K, Wang Y, Xue Q K 2014 Nat. Sci. Rev. 1 38 Google Scholar
[6]	王力, 刘静思, 李吉, 周晓林, 陈向荣, 刘超飞, 刘伍明 2020 69 010303 Google Scholar Wang L, Liu J S, Li J, Zhou X L, Chen X R, Liu C F, Liu W M 2020 Acta Phys. Sin. 69 010303 Google Scholar
[7]	李吉, 刘伍明 2018 67 110302 Google Scholar Li J, Liu W M 2018 Acta Phys. Sin. 67 110302 Google Scholar
[8]	刘静思, 李吉, 刘伍明 2017 66 130305 Google Scholar Liu J S, Li J, Liu W M 2017 Acta Phys. Sin. 66 130305 Google Scholar
[9]	Chen Y H, Tao H S, Yao D X, Liu W M 2012 Phys. Rev. Lett. 108 246402 Google Scholar
[10]	Jiang Z F, Li R D, Zhang S C, Liu W M 2005 Phys. Rev. B 72 045201
[11]	Zhang X L, Liu L F, Liu W M 2005 Sci. Rep. 3 2908
[12]	Reich E S 2012 Nature 483 132 Google Scholar
[13]	Brouwer P W 2012 Science 336 989 Google Scholar
[14]	Wilczek F 2012 Nature 486 195 Google Scholar
[15]	Read N, Green D 2000 Phys. Rev. B 61 10267 Google Scholar
[16]	Ivanov D A 2001 Phys. Rev. Lett. 86 268 Google Scholar
[17]	Lutchyn R M, Sau J D, Das Sarma S 2010 Phys. Rev. Lett. 105 077001 Google Scholar
[18]	Oreg Y, Refael G, von Oppen F 2010 Phys. Rev. Lett. 105 177002 Google Scholar
[19]	Liu D E, Baranger H U 2011 Phys. Rev. B 84 201308(R Google Scholar
[20]	Napitu B D 2015 Eur. Phys. J. B 88 290 Google Scholar
[21]	Lü H F, Lu H Z, Shen S Q 2014 Phys. Rev. B 90 195404 Google Scholar
[22]	Liu D E, Cheng M, Lutchyn R M 2015 Phys. Rev. B 91 081405(R Google Scholar
[23]	Huo D M 2016 Eur. Phys. J. B 89 174 Google Scholar
[24]	Niu P B, Liu L X, Su X Q, Dong L J, Shi Y L, Luo H G 2020 J. Magn. Magn. Mater. 506 166795 Google Scholar
[25]	Bauer G E, MacDonald A H, Maekawa S 2010 Solid State Commun. 150 459 Google Scholar
[26]	Bauer G E, Saitoh E, van Wees B J 2012 Nat. Mater. 11 391 Google Scholar
[27]	Staring A A M, Molenkamp L W, Alphenaar B W, et al. 1993 Europhys. Lett. 22 57 Google Scholar
[28]	Svensson S F, Hoffmann E A, Nakpathomkun N, et al. 2013 New J. Phys. 15 105011 Google Scholar
[29]	Sanchez D, Lopez R 2013 Phys. Rev. Lett. 110 026804 Google Scholar
[30]	Alidoust M, Halterman K, Valls O T 2015 Phys. Rev. B 92 014508 Google Scholar
[31]	Niu P B, Liu L X, Su X Q, Dong L J, Shi Y L, Luo H G 2020 Physica E 124 114313 Google Scholar
[32]	Niu P B, Wang Q, Nie Y H 2013 Chin. Phys. B 22 027307 Google Scholar
[33]	Flensberg K 2010 Phys. Rev. B 82 180516(R Google Scholar
[34]	Kostyrko T, Bulka B R 2005 Phys. Rev. B 71 235306 Google Scholar
[35]	Niu P B, Zhang Y Y, Wang Q, et al. 2012 Phys. Lett. A 376 1481 Google Scholar
[36]	Meir Y, Wingreen N S 1992 Phys. Rev. Lett. 68 2512 Google Scholar
[37]	Wang R Q, Sheng L, Shen R, Wang B, Xing D Y 2010 Phys. Rev. Lett. 105 057202 Google Scholar
[38]	Luo H G, Ying Z J, Wang S J 1999 Phys. Rev. B 59 9710 Google Scholar
[39]	Sun Q F, Guo H 2002 Phys. Rev. B 66 155308 Google Scholar

Catalog

Vol. 70, Issue 11 - 2021-06-05

Metrics

Abstract views: 6065
PDF Downloads: 136
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板