Spin current pumping in helical Luttinger liquids

Physical Review B - Condensed Matter and Materials Physics

Volumn 87, Issue 24, 2013, Pages

  Ferraro, D ^a,b,c,d   Dolcetto, G ^a,b,c   Citro, R ^e,f   Romeo, F ^e,f   Sassetti, M ^a,b  

^a UNIVERSITY OF GENOA   (Italy)

^b CNR SPIN   (Italy)

^c INFN SEZIONE DI GENOVA   (Italy)

^d UNIVERSITÉ DE LYON   (France)

^e UNIVERSITY OF SALERNO   (Italy)

^f CNR SPIN SALERNO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84879700439     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.87.245419     Document Type: Article

References (49)

1. M. Konig, H. Buhmann, L. W. Molenkamp, T. Hughes, C.-X. Liu, X.-L. Qi, and S.-C. Zhang, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.77.031007 77, 031007 (2008).
2. X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.83.1057 83, 1057 (2011).
3. C. L. Kane and E. J. Mele, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.146802 95, 146802 (2005). (Pubitemid 41777602)
4. C. L. Kane and E. J. Mele, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.226801 95, 226801 (2005). (Pubitemid 41776999)
5. B. A. Bernevig and S.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.106802 96, 106802 (2006).
6. B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Science SCIEAS 0036-8075 10.1126/science.1133734 314, 1757 (2006). (Pubitemid 44969083)
7. M. Konig, S. Weidmann, C. Brune, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, and S.-C. Zhang, Science SCIEAS 0036-8075 10.1126/science.1148047 318, 766 (2007). (Pubitemid 351411764)
8. A. Roth, C. Brne, H. Buhmann, L. W. Molenkamp, J. Maciejko, X.-L. Qi, and S.-C. Zhang, Science SCIEAS 0036-8075 10.1126/science.1174736 325, 294 (2009).
9. C. Wu, B. A. Bernevig, and S.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.106401 96, 106401 (2006);
10. G. Dolcetto, N. Traverso Ziani, M. Biggio, F. Cavaliere, and M. Sassetti, arXiv: 1306.1145.
11. M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.82.3045 82, 3045 (2010).
12. J. Maciejko, C. Liu, Y. Oreg, X.-L. Qi, C. Wu, and S.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.256803 102, 256803 (2009).
13. Y. Tanaka, A. Furusaki, and K. A. Matveev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.236402 106, 236402 (2011).
14. E. Eriksson, A. Strom, G. Sharma, and H. Johannesson, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.86.161103 86, 161103 (R) (2012).
15. C.-Y. Hou, E.-A. Kim, and C. Chamon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.076602 102, 076602 (2009).
16. J. C. Y. Teo and C. L. Kane, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.235321 79, 235321 (2009).
17. A. Strom and H. Johannesson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.096806 102, 096806 (2009).
18. G. Dolcetto, S. Barbarino, D. Ferraro, N. Magnoli, and M. Sassetti, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.85.195138 85, 195138 (2012);
19. G. Dolcetto, F. Cavaliere, D. Ferraro, and M. Sassetti, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.87.085425 87, 085425 (2013).
20. C. de C. Chamon, D. E. Freed, S. A. Kivelson, S. L. Sondhi, and X. G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.55.2331 55, 2331 (1997).
21. F. Dolcini, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.165304 83, 165304 (2011).
22. F. Romeo, R. Citro, D. Ferraro, and M. Sassetti, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.86.165418 86, 165418 (2012).
23. P. Virtanen and P. Recher, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.115332 83, 115332 (2011).
24. R. Citro, F. Romeo, and N. Andrei, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.84.161301 84, 161301 (R) (2011).
25. D. J. Thouless, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.27.6083 27, 6083 (1983).
26. V. Krueckl and K. Richter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.107.086803 107, 086803 (2011);
27. L. B. Zhang, F. Cheng, F. Zhai, and K. Chang, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.081402 83, 081402 (R) (2011).
28. C. Xu and J. E. Moore, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.73. 045322 73, 045322 (2006). (Pubitemid 43270648)
29. T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, Oxford, 2003).
30. M. Sassetti and B. Kramer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.1485 80, 1485 (1998);
31. E. Miranda, Braz. J. Phys. BJPHE6 0103-9733 10.1590/S0103- 97332003000100002 33, 3 (2003).
32. Note that this Hamiltonian is formally analogous to the one of a spinless Luttinger liquid. This is due to the fact that in this system the spin degree of freedom is redundant once identified the direction of propagation (right or left) along the edge.
33. T. L. Schmidt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.107. 096602 107, 096602 (2011).
34. As stated before, more complicated multiple electron tunneling processes, namely, tunneling of charged and spinful particle pairs (Refs. and), affect the transport properties of the system for strong enough (repulsive or attractive) interaction (K < 1 / √ 3 or K > √ 3). The range of K considered in this paper allows us to safely neglect these contributions.
35. J. I. Vayrynen and T. Ojanen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.076803 106, 076803 (2011).
36. R. Citro, N. Andrei, and Q. Niu, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.68.165312 68, 165312 (2003).
37. T. Martin, in Nanophysics: Coherence and Transport, Les Houches Session LXXXI, edited, H. Bouchiat, (Elsevier, Amsterdam, 2005).
38. A. Kamenev and A. Levchenko, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730902850504 58, 197 (2009).
39. D. Ferraro, A. Braggio, N. Magnoli, and M. Sassetti, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.085323 82, 085323 (2010).
40. M. Carrega, D. Ferraro, A. Braggio, N. Magnoli, and M. Sassetti, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.107.146404 107, 146404 (2011).
41. G. Cuniberti, M. Sassetti, and B. Kramer, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.57.1515 57, 1515 (1998);
42. M. Carrega, D. Ferraro, A. Braggio, N. Magnoli, and M. Sassetti, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/14/2/023017 14, 023017 (2012).
43. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integral, Series and Products (Academic, London, 1994).
44. P. Sharma and C. Chamon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.096401 87, 096401 (2001).
45. P. Sharma and C. Chamon, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.68.035321 68, 035321 (2003).
46. M. Konig, Phys. Rev. X 10.1103/PhysRevX.3.021003 3, 021003 (2003).
47. C.-X. Liu, J. C. Budich, P. Recher, and B. Trauzettel, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.035407 83, 035407 (2011).
48. N. Paradiso, S. Heun, S. Roddaro, D. Venturelli, F. Taddei, V. Giovannetti, R. Fazio, G. Biasiol, L. Sorba, and F. Beltram, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.155305 83, 155305 (2011).
49. D. Chevallier, J. Rech, T. Jonckheere, C. Wahl, and T. Martin, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.155318 82, 155318 (2010).