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Majorana zero-energy modes are their own antiparticles, which are potential building blocks of topological quantum computing. Recently, there has been growing the interest in searching for Majorana zero modes in condensed matter physics. Semiconductor-superconductor hybrid systems have received particular attention because of easy realization and high-degree experimental control. The Majorana zero-energy modes are predicted to appear at two ends of a semiconductor nanowire, in the proximity of an s-wave superconductor and under a proper external magnetic field. Experimental signatures of Majorana zero modes in semiconductor-superconductor systems typically consist of zero-bias conductance peaks in tunneling spectra. So far it is universally received that an ideal semiconductor-superconductor hybrid structure should possess Majorana zero-energy modes. However, an unambiguous verification remains elusive because zero-bias conductance peaks can also have non-topological origins, such as Kondo effect, Andreev bound states or disorder effect. Therefore, it is important to investigate additional evidences to conclusively confirm the presence of Majorana zero modes in the hybrid solid state devices. It has been suggested that the Majorana-quantum dot hybrid system might be one of the solutions to the problem. Up to now, various Majorana-dot hybrid devices have been proposed to detect the existence of Majorana zero modes. Most of these studies mainly focused on the limits of transport at zero temperature, large bias voltage or zero frequency shot noise. Then a natural question is how the current correlations between the electrons transport through the topological nanowire, especially still in the zero-bias regime. In this paper, a specific spinless model consisting of a quantum dot tunnel-coupled to topological nanowire is considered. We present a systematic investigation of the electron transport by using a particle-number resolved master equation. We pay particular attention to the effects of Majorana's dynamics on the current fluctuations (shot noise) at nonzero temperature and finite bias voltage as well as at finite frequencies, especially in the low-bias regime. It is shown that the difference between the electrode currents combined with the low-bias oscillations of finite-frequency shot noise can identify Majorana zero modes from the usual resonant-tunneling levels. When there exist Majorana zero modes, on the one hand, the current difference depends on the asymmetry of electron tunneling rate. The asymmetric behaviors can expose the essential features of the Majorana zero modes since the symmetric current difference is zero. And the zero-bias conductance peak appears for the asymmetric coupling. Moreover, as the Majorana splitting energy increases, the current difference is suppressed while it is increased with the dot-wire coupling increasing. On the other hand, the dynamics of Majorana coherent oscillations between the dot and the wire is revealed in the finite-frequency shot noise. Due to the existence of Majorana zero modes the finite-frequency shot noise shows oscillations with a pronounced zero-frequency noise enhancement. Especially in the low-bias regime, the noise spectrum still exhibits an oscillation behavior which is absent from the large-bias voltage limit. Furthermore, with the Majorana splitting energy increasing, the oscillations of shot noise become more obvious, but the zero-frequency peak is lowered. When the dot is asymmetrically coupled to the electrode, the shot noise gradually changes into the super-Poissonian statistics from the sub-Poissonian statistics. This indicates the crossover from antibunched to bunched electron transport. As a result, the combination of the current difference and the low-bias oscillations of finite-frequency shot noise allows one to probe the presence of Majorana zero modes. It is therefore expected that the findings of this work can offer additional guides for experiments to identify signatures of Majorana zero modes in solid state sy
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Keywords:
- Majorana fermion /
- quantum dot /
- shot noise
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[1] Wilczek F 2009 Nat. Phys. 5 614
[2] Elliott S R, Franz M 2015 Rev. Mod. Phys. 87 137
[3] Moore G, Read N 1991 Nucl. Phys. B 360 362
[4] Nayak C, Wilczek F 1996 Nucl. Phys. B 479 529
[5] Nayak C, Simon S H, Stern A, Freedman M, DasSarma S 2008 Rev. Mod. Phys. 80 1083
[6] Alicea J 2012 Rep. Prog. Phys. 75 076501
[7] Sau J D, Lutchyn R M, Tewari S, DasSarma S 2010 Phys. Rev. Lett. 104 040502
[8] Lutchyn R M, Sau J D, DasSarma S 2010 Phys. Rev. Lett. 105 077001
[9] Oreg Y, Refael G, Oppen F V 2010 Phys. Rev. Lett. 105 177002
[10] Mourik V, Zuo K, Frolov S M, Plissard S R, Bakkers E P A M, Kouwenhoven L P 2012 Science 336 1003
[11] Das A, Ronen Y, Most Y, Oreg Y, Heiblum M, Shtrikman H 2012 Nat. Phys. 8 887
[12] Deng M T, Yu C L, Huang G Y, Larsson M, Caroff P, Xu H Q 2012 Nano Lett. 12 6414
[13] Nadj-Perge S, Drozdov I K, Li J, Chen H, Jeon S, Seo J, MacDonald A H, Bernevig B A, Yazdani A 2014 Science 346 602
[14] Albrecht S M, Higginbotham A P, Madsen M, Kuemmeth F, Jespersen T S, Nygard J, Krogstrup P, Marcus C M 2016 Nature 531 206
[15] Deng M T, Vaitiekenas S, Hansen E B, Danon J, Leijnse M, Flensberg K, Nygard J, Krogstrup P, Marcus C M 2016 Science 354 1557
[16] Nichele F, Drachmann A C C, Whiticar A M, O'Farrell E C T, Suominen H J, Fornieri A, Wang T, Gardner G C, Thomas C, Hatke A T, Krogstrup P, Manfra M J, Flensberg K, Marcus C M 2017 Phys. Rev. Lett. 119 136803
[17] Zhang H, Gl , Conesa-Boj S, Nowak M P, Wimmer M, Zuo K, Mourik V, de Vries F K, van Veen J, de Moor M W A, Bommer J D S, van Woerkom D J, Car D, Plissard S R, Bakkers E P A M, Quintero-Prez M, Cassidy M C, Koelling S, Goswami S, Watanabe K, Taniguchi T, Kouwenhoven L P 2017 Nat. Commun. 8 16025
[18] Alicea J, Oreg Y, Refael G, von Oppen F, Fisher M P A 2011 Nat. Phys. 7 412
[19] Haim A, Berg E, von Oppen F, Oreg Y 2015 Phys. Rev. Lett. 114 166406
[20] Bolech C J, Demler E 2007 Phys. Rev. Lett. 98 237002
[21] Bagrets D, Altland A 2012 Phys. Rev. Lett. 109 227005
[22] Goldhaber-Gordon D, Shtrikman H, Mahalu D, Abusch-Magder D, Meirav U, Kastner M 1998 Nature 391 156
[23] Kells G, Meidan D, Brouwer P W 2012 Phys. Rev. B 86 100503
[24] Liu D E, Baranger H U 2011 Phys. Rev. B 84 201308
[25] Cao Y, Wang P, Xiong G, Gong M, Li X Q 2012 Phys. Rev. B 86 115311
[26] Chen Q, Chen K Q, Zhao H K 2014 J. Phys.: Condens. Matter 26 315011
[27] Li Z Z, Lam C H, You J Q 2015 Sci. Rep. 5 11416
[28] Shang E M, Pan Y M, Shao L B, Wang B G 2014 Chin. Phys. B 23 057201
[29] Gong W J, Zhang S F, Li Z C, Yi G, Zheng Y S 2014 Phys. Rev. B 89 245413
[30] Jiang C, Lu G, Gong W J 2014 J. Appl. Phys. 116 103704
[31] Gong W J, Zhao Y, Gao Z, Zhang S F 2015 Curr. Appl. Phys. 15 520
[32] Wang S K, Jiao H J, Li F, Li X Q 2007 Phys. Rev. B 76 125416
[33] Li X Q, Cui P, Yan Y J 2005 Phys. Rev. Lett. 94 066803
[34] Luo J Y, Li X Q, Yan Y J 2007 Phys. Rev. B 76 085325
[35] DasSarma S, Sau J D, Stanescu T D 2012 Phys. Rev. B 86 220506
[36] Thielmann A, Hettler M H, Knig J, Schn G 2003 Phys. Rev. B 68 115105
[37] Aghassi J, Thielmann A, Hettler M H, Schn G 2006 Phys. Rev. B 73 195323
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