耦合Majorana束缚态T形双量子点中的Andreev反射
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摘要
研究了连接在正常金属电极和超导电极之间的耦合Majorana束缚态(MBSs)T形双量子点结构中的Andreev反射.研究发现,对于T形双量子点结构,当入射能量等于边耦合量子点能级时Andreev反射电导出现Fano振荡,连接MBSs之后,零费米能附近出现一对新的Fano型振荡峰.如果忽略两个MBSs之间的相互作用,零费米能点的Andreev反射电导为定值1/2G_0(G_0=2e~2/h),不受量子点能级、双量子点之间耦合强度以及量子点与MBSs之间的耦合强度的影响.此外,在没有耦合MBSs的T形双量子点结构中,调节双量子点间的耦合强度可以使零费米能附近的Andreev反射电导出现由共振带向反共振带的转变,而耦合MBSs之后,又可以使反共振消失转而出现新的共振峰.
Owing to their potential applications in topological quantum computation and because of their fundamental interest,Majorana fermions are currently attracting increasing attention. Numerous theoretical and experimental studies exactly show that the quantum dot(QD) structure is a good candidate for the detection of Majorana bound state(MBSs). QD system has many unique transport properties and interesting quantum phenomena, such as quantum interference effect,Fano effect, etc. In addition, compared with a single QD, a coupled QD structure has many adjustable parameters,and thus has more important theoretical and practical value, which provides an excellent platform to detect MBSs. In addition, QD coupled with normal metallic conductor and with superconducting electrode structure exhibits interesting transport properties. One of these properties is the so-called Andreev reflection(AR). Especially, in the subgap regime,the current almost entirely originates from the anomalous Andreev channel; such spectroscopy can thus directly probe any in-gap state. In the present paper, we consider a T-shaped double QD structure with side-coupled to MBSs and investigate the transport properties through the system by adding a normal and a superconducting lead. We calculate the AR conductance through the system in the subgap transport. Here we focus on the effects of MBSs on AR through the system. We find that the AR conductance presents a resonant peak around zero Fermi energy when only one QD(QD_1) connects to metal and superconducting leads. As a consequence of quantum interference, when using another QD_2 side-attached to QD_1, a pair of new Fano-type resonant peaks appear and is distributed aside the zero point and the Fano antiresonant point is at the energy level of the QD_2. If an MBS is introduced to couple to QD_2, the AR conductance shows several new features. First, a pair of new Fano-type resonance curves appears and the original ones also persist except for the position shifting. In addition, the AR conductance value at the zero Fermi energy point is exactly equal to 1/2G_0(G_0 = 2e~2/h) in the presence of QD-MBS coupling and zero inter-MBS coupling, which is not dependent on the inert-dot coupling nor the energy levels of QD nor the strength of the QD-MBS coupling. This feature is different from which the T-shaped DQD structure side-coupled to a traditional fermions, showing the robust properties of the Majorana fermions. We also show that in the Andreev reflection conductance curves appear resonance zone changes into antiresonance near zero Fermi energy by adjusting the coupling strength between the double quantum dots in the system without MBSs, while the antiresonance disappears and new resonance peaks appear if an MBS is introduced to couple to QD_2. We hope that these results will be helpful for understanding the quantum interference in MBS-assisted AR and may find significant applications, especially in quantum computation.
Owing to their potential applications in topological quantum computation and because of their fundamental interest,Majorana fermions are currently attracting increasing attention. Numerous theoretical and experimental studies exactly show that the quantum dot(QD) structure is a good candidate for the detection of Majorana bound state(MBSs). QD system has many unique transport properties and interesting quantum phenomena, such as quantum interference effect,Fano effect, etc. In addition, compared with a single QD, a coupled QD structure has many adjustable parameters,and thus has more important theoretical and practical value, which provides an excellent platform to detect MBSs. In addition, QD coupled with normal metallic conductor and with superconducting electrode structure exhibits interesting transport properties. One of these properties is the so-called Andreev reflection(AR). Especially, in the subgap regime,the current almost entirely originates from the anomalous Andreev channel; such spectroscopy can thus directly probe any in-gap state. In the present paper, we consider a T-shaped double QD structure with side-coupled to MBSs and investigate the transport properties through the system by adding a normal and a superconducting lead. We calculate the AR conductance through the system in the subgap transport. Here we focus on the effects of MBSs on AR through the system. We find that the AR conductance presents a resonant peak around zero Fermi energy when only one QD(QD_1) connects to metal and superconducting leads. As a consequence of quantum interference, when using another QD_2 side-attached to QD_1, a pair of new Fano-type resonant peaks appear and is distributed aside the zero point and the Fano antiresonant point is at the energy level of the QD_2. If an MBS is introduced to couple to QD_2, the AR conductance shows several new features. First, a pair of new Fano-type resonance curves appears and the original ones also persist except for the position shifting. In addition, the AR conductance value at the zero Fermi energy point is exactly equal to 1/2G_0(G_0 = 2e~2/h) in the presence of QD-MBS coupling and zero inter-MBS coupling, which is not dependent on the inert-dot coupling nor the energy levels of QD nor the strength of the QD-MBS coupling. This feature is different from which the T-shaped DQD structure side-coupled to a traditional fermions, showing the robust properties of the Majorana fermions. We also show that in the Andreev reflection conductance curves appear resonance zone changes into antiresonance near zero Fermi energy by adjusting the coupling strength between the double quantum dots in the system without MBSs, while the antiresonance disappears and new resonance peaks appear if an MBS is introduced to couple to QD_2. We hope that these results will be helpful for understanding the quantum interference in MBS-assisted AR and may find significant applications, especially in quantum computation.
引文
[1]Majorana E 1937 Nuovo Cimento 14 171
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[3]Das A,Ronen Y,Most Y,Oreg Y,Heiblum M,Shtrikman H 2012 Nat.Phys.8 887
[4]Leijnse M,Flensberg K 2011 Phys.Rev.Lett.107210502
[5]Zhang D P,Tian G S 2015 Chin.Phys.B 24 080401
[6]Fu L,Kane C L 2008 Phys.Rev.Lett.100 096407
[7]Sau J D,Lutchyn R M,Tewari S,Das Sarma S 2010Phys.Rev.Lett.104 040502
[8]Mourik V,Zuo K,Frolov S M,Plissard S R,Bakkers E P A M,Kouwenhoven L P 2012 Science 336 1003
[9]Flensberg K 2011 Phys.Rev.Lett.106 090503
[10]Oreg Y,Refael G,von Oppen F 2010 Phys.Rev.Lett.105 177002
[11]Lutchyn R M,Sau J D,Das Sarma S 2010 Phys.Rev.Lett.105 077001
[12]Deng M T,Yu C L,Huang G Y,Larsson M,Caroff P,Xu H Q 2012 Nano Lett.12 6414
[13]Tang H Z,Zhang Y T,Liu J J 2015 AIP Adv.5 127129
[14]Liu D E,Baranger H U 2011 Phys.Rev.B 84 201308
[15]Liu J,Wang J,Zhang F C 2014 Phys.Rev.B 90 035307
[16]Wang N,LüS H,Li Y X 2014 J.Appl.Phys.115 083706
[17]Li Y X,Bai Z M 2013 J.Appl.Phys.114 033703
[18]Gong W J,Zhang S F,Li Z C,Yi G Y,Zheng Y S 2014Phys.Rev.B 89 245413
[19]Dessotti F A,de Souza R M,Souza F M,Seridonio A C2014 J.Appl.Phys.116 173701
[20]Zhou Y,Guo J H 2015 Acta Phys.Sin.64 167302(in Chinese)[周洋,郭健宏2015物理学报64 167302]
[21]Nilsson J,Akhmerov A R,Beenakker C W J 2008 Phys.Rev.Lett.101 120403
[22]LüH F,Lu H Z,Shen S Q 2014 Phys.Rev.B 90 195404
[23]Wang S X,Li Y X,Liu J J 2016 Chin.Phys.B 25 037304
[24]Zocher B,Rosenow B 2013 Phys.Rev.Lett.111 036802
[25]Leijinse M,Flensberg K 2011 Phys.Rev.B 84 140501
[26]Fano U 1961 Phys.Rev.124 1866
[27]Sun Q F,Wang J,Lin T H 1999 Phys.Rev.B 59 3831
[28]Sun Q F,Wang J,Lin T H 2001 Phys.Rev.Lett.87176601
[29]Barański J,Domański T 2015 Chin.Phys.B 24 017304
[30]Fazio R,Raimondi R 1998 Phys.Rev.Lett.80 2913
[31]Haug H,Jauho A P 1998 Quantum Kinetics in Transport and Optics of Semiconductors(Berlin:Springer-Verlag)p181
[32]Yeyati A L Cuevas J C,López-Dávalos A,MartínRodero A 1997 Phys.Rev.B 55 R6137
[33]Cuevas J C,Martín-Rodero A,Yeyati A L 1996 Phys.Rev.B 54 7366
[34]Barański J,Domański T 2015 Chin.Phys.B 24 017304
[2]Alicea J,Oreg Y,Refael G,von Oppen F,Fisher M P A 2011 Nat.Phys.7 412
[3]Das A,Ronen Y,Most Y,Oreg Y,Heiblum M,Shtrikman H 2012 Nat.Phys.8 887
[4]Leijnse M,Flensberg K 2011 Phys.Rev.Lett.107210502
[5]Zhang D P,Tian G S 2015 Chin.Phys.B 24 080401
[6]Fu L,Kane C L 2008 Phys.Rev.Lett.100 096407
[7]Sau J D,Lutchyn R M,Tewari S,Das Sarma S 2010Phys.Rev.Lett.104 040502
[8]Mourik V,Zuo K,Frolov S M,Plissard S R,Bakkers E P A M,Kouwenhoven L P 2012 Science 336 1003
[9]Flensberg K 2011 Phys.Rev.Lett.106 090503
[10]Oreg Y,Refael G,von Oppen F 2010 Phys.Rev.Lett.105 177002
[11]Lutchyn R M,Sau J D,Das Sarma S 2010 Phys.Rev.Lett.105 077001
[12]Deng M T,Yu C L,Huang G Y,Larsson M,Caroff P,Xu H Q 2012 Nano Lett.12 6414
[13]Tang H Z,Zhang Y T,Liu J J 2015 AIP Adv.5 127129
[14]Liu D E,Baranger H U 2011 Phys.Rev.B 84 201308
[15]Liu J,Wang J,Zhang F C 2014 Phys.Rev.B 90 035307
[16]Wang N,LüS H,Li Y X 2014 J.Appl.Phys.115 083706
[17]Li Y X,Bai Z M 2013 J.Appl.Phys.114 033703
[18]Gong W J,Zhang S F,Li Z C,Yi G Y,Zheng Y S 2014Phys.Rev.B 89 245413
[19]Dessotti F A,de Souza R M,Souza F M,Seridonio A C2014 J.Appl.Phys.116 173701
[20]Zhou Y,Guo J H 2015 Acta Phys.Sin.64 167302(in Chinese)[周洋,郭健宏2015物理学报64 167302]
[21]Nilsson J,Akhmerov A R,Beenakker C W J 2008 Phys.Rev.Lett.101 120403
[22]LüH F,Lu H Z,Shen S Q 2014 Phys.Rev.B 90 195404
[23]Wang S X,Li Y X,Liu J J 2016 Chin.Phys.B 25 037304
[24]Zocher B,Rosenow B 2013 Phys.Rev.Lett.111 036802
[25]Leijinse M,Flensberg K 2011 Phys.Rev.B 84 140501
[26]Fano U 1961 Phys.Rev.124 1866
[27]Sun Q F,Wang J,Lin T H 1999 Phys.Rev.B 59 3831
[28]Sun Q F,Wang J,Lin T H 2001 Phys.Rev.Lett.87176601
[29]Barański J,Domański T 2015 Chin.Phys.B 24 017304
[30]Fazio R,Raimondi R 1998 Phys.Rev.Lett.80 2913
[31]Haug H,Jauho A P 1998 Quantum Kinetics in Transport and Optics of Semiconductors(Berlin:Springer-Verlag)p181
[32]Yeyati A L Cuevas J C,López-Dávalos A,MartínRodero A 1997 Phys.Rev.B 55 R6137
[33]Cuevas J C,Martín-Rodero A,Yeyati A L 1996 Phys.Rev.B 54 7366
[34]Barański J,Domański T 2015 Chin.Phys.B 24 017304