Transport through a quantum dot coupled to two Majorana bound states

Abstract

We investigate electron transport inside a ring system composed of a quantum dot (QD) coupled to two Majorana bound states confined at the ends of a one-dimensional topological superconductor nanowire. By tuning the magnetic flux threading through the ring, the model system we consider can be switched into states with or without zero-energy modes when the nanowire is in its topological phase. We find that the Fano profile in the conductance spectrum due to the interference between bound and continuum states exhibits markedly different features for these two different situations, which consequently can be used to detect the Majorana zero-energy mode. Most interestingly, as a periodic function of magnetic flux, the conductance shows 2π periodicity when the two Majorana bound states are nonoverlapping (as in an infinitely long nanowire) but displays 4π periodicity when the overlapping becomes nonzero (as in a finite length nanowire). We map the model system into a QD–Kitaev ring in the Majorana fermion representation and affirm these different characteristics by checking the energy spectrum.

Keywords

quantum dot / Majorana bound states / Fano profile / QD–Kitaev ring / topologically trivial and nontrivial

References

[1] S. R. Elliott and M. Franz, Majorana fermions in nuclear, particle, and solid-state physics, Rev. Mod. Phys. 87(1), 137 (2015)

[2] T. D. Stanescu and S. Tewari, Majorana fermions in semiconductor nanowires: fundamentals, modeling, and experiment., J. Phys.: Condens. Matter 25(23), 233201 (2013)

[3] J. Alicea, New directions in the pursuit of Majorana fermions in solid state systems, Rep. Prog. Phys. 75(7), 076501 (2012)

[4] M. Stone and R. Roy, Edge modes, edge currents, and gauge invariance in p_x+ ip_ysuperfluids and superconductors, Phys. Rev. B 69(18), 184511 (2004)

[5] P. Fendley, M. P. A. Fisher, and C. Nayak, Edge states and tunneling of non-Abelian quasiparticles in the n= 5/2 quantum Hall state and p+ ipsuperconductors, Phys. Rev. B 75(4), 045317 (2007)

[6] S. Raghu, A. Kapitulnik, and S. A. Kivelson, Hidden quasi-one-dimensional superconductivity in Sr₂RuO₄, Phys. Rev. Lett. 105(13), 136401 (2010)

[7] S. B. Chung, H. J. Zhang, X. L. Qi, and S. C. Zhang, Topological superconducting phase and Majorana fermions in half-metal/superconductor heterostructures, Phys. Rev. B 84, 060510(R) (2011)

[8] R. M. Lutchyn, J. D. Sau, and S. Das Sarma, Majorana fermions and a topological phase transition in semiconductor–superconductor heterostructures, Phys. Rev. Lett. 105(7), 077001 (2010)

[9] Y. Oreg, G. Refael, and F. von Oppen, Helical liquids and Majorana bound states in quantum wires, Phys. Rev. Lett. 105(17), 177002 (2010)

[10] X. J. Liu, L. Jiang, H. Pu, and H. Hu, Probing Majorana fermions in spin–orbit-coupled atomic Fermi gases, Phys. Rev. A 85, 021603(R) (2012)

[11] C. Qu, Z. Zheng, M. Gong, Y. Xu, L. Mao, X. Zou, G. Guo, and C. Zhang, Topological superfluids with finitemomentum pairing and Majorana fermions, Nat. Commun. 4, 2710 (2013)

[12] C. Chen, Inhomogeneous topological superfluidity in one-dimensional spin–orbit-coupled Fermi gases, Phys. Rev. Lett. 111(23), 235302 (2013)

[13] J. Ruhman, E. Berg, and E. Altman, Topological states in a one-dimensional Fermi gas with attractive interaction, Phys. Rev. Lett. 114(10), 100401 (2015)

[14] N. B. Kopnin and M. M. Salomaa, Mutual friction in superfluid He3: Effects of bound states in the vortex core, Phys. Rev. B 44(17), 9667 (1991)

[15] X. L. Qi, T. L. Hughes, S. Raghu, and S. C. Zhang, Time-reversal-invariant topological superconductors and superfluids in two and three dimensions, Phys. Rev. Lett. 102(18), 187001 (2009)

[16] S. B. Chung and S. C. Zhang, Detecting the Majorana fermion surface state of He₃tB through spin relaxation, Phys. Rev. Lett. 103(23), 235301 (2009)

[17] S. Nadj-Perge, I. K. Drozdov, B. A. Bernevig, and A. Yazdani, Proposal for realizing Majorana fermions in chains of magnetic atoms on a superconductor, Phys. Rev. B 88, 020407(R) (2013)

[18] S. Nadj-Perge, I. K. Drozdov, J. Li, H. Chen, S. Jeon, J. Seo, A. H. MacDonald, B. A. Bernevig, and A. Yazdani, Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor, Science 346(6209), 602 (2014)

[19] H. Y. Hui, P. M. R. Brydon, J. D. Sau, S. Tewari, and S. Das Sarma, Majorana fermions in ferromagnetic chains on the surface of bulk spin–orbit coupled s-wave superconductors, Sci. Rep. 5, 8880 (2015)

[20] E. Dumitrescu, B. Roberts, S. Tewari, J. D. Sau, and S. Das Sarma, Majorana fermions in chiral topological ferromagnetic nanowires, Phys. Rev. B 91(9), 094505 (2015)

[21] T. D. Stanescu, R. M. Lutchyn, and S. Das Sarma, Majorana fermions in semiconductor nanowires, Phys. Rev. B 84(14), 144522 (2011)

[22] V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, and L. P. Kouwenhoven, Signatures of Majorana fermions in hybrid superconductorsemiconductor nanowire devices, Science 336(6084), 1003 (2012)

[23] M. T. Deng, C. L. Yu, G. Y. Huang, M. Larsson, P. Caroff, and H. Q. Xu, Anomalous zero-bias conductance peak in a Nb–InSb nanowire–Nb hybrid device, Nano Lett. 12(12), 6414 (2012)

[24] A. Das, Y. Ronen, Y. Most, Y. Oreg, M. Heiblum, and H. Shtrikman, Zero-bias peaks and splitting in an Al– InAs nanowire topological superconductor as a signature of Majorana fermions, Nat. Phys. 8(12), 887 (2012)

[25] A. D. K. Finck, D. J. Van Harlingen, P. K. Mohseni, K. Jung, and X. Li, Anomalous modulation of a zero-bias peak in a hybrid nanowire-superconductor device, Phys. Rev. Lett. 110(12), 126406 (2013)

[26] D. M. Badiane, M. Houzet, and J. S. Meyer, Nonequilibrium Josephson Effect through Helical Edge States, Phys. Rev. Lett. 107(17), 177002 (2011)

[27] P. A. Ioselevich and M. V. Feigel’man, Anomalous Josephson current via Majorana bound states in topological insulators, Phys. Rev. Lett. 106(7), 077003 (2011)

[28] A. M. Black-Schaffer and J. Linder, Majorana fermions in spin–orbit-coupled ferromagnetic Josephson junctions, Phys. Rev. B 84, 180509 (2011)

[29] B. H. Wu and J. C. Cao, Tunneling transport through superconducting wires with Majorana bound states, Phys. Rev. B 85(8), 085415 (2012)

[30] A. Zazunov, A. L. Yeyati, and R. Egger, Coulomb blockade of Majorana-fermion-induced transport, Phys. Rev. B 84(16), 165440 (2011)

[31] A. Ueda and T. Yokoyama, Anomalous interference in Aharonov–Bohm rings with two Majorana bound states, Phys. Rev. B 90, 081405(R) (2014)

[32] Y. Cao, P. Wang, G. Xiong, M. Gong, and X. Q. Li, Probing the existence and dynamics of Majorana fermion via transport through a quantum dot, Phys. Rev. B 86(11), 115311 (2012)

[33] W. J. Gong, Sh. F. Zhang, Zh. Ch. Li, G. Yi, and Y. S. Zheng, Detection of a Majorana fermion zero mode by a T-shaped quantum-dot structure, Phys. Rev. B 89(24), 245413 (2014)

[34] H. F. Lü, H. Z. Lu, and S. Q. Shen, Nonlocal noise cross correlation mediated by entangled Majorana fermions, Phys. Rev. B 86(7), 075318 (2012)

[35] H. F. Lü, H. Z. Lu, and S. Q. Shen, Current noise cross correlation mediated by Majorana bound states, Phys. Rev. B 90(19), 195404 (2014)

[36] H. F. Lü, H. Z. Lu, and S. Q. Shen, Enhanced current noise correlations in a Coulomb–Majorana device, Phys. Rev. B 93, 245418 (2016)

[37] K. Flensberg, Non-Abelian operations on Majorana fermions via single-charge control, Phys. Rev. Lett. 106(9), 090503 (2011)

[38] J. D. Sau, B. Swingle, and S. Tewari, Proposal to probe quantum nonlocality of Majorana fermions in tunneling experiments, Phys. Rev. B 92, 020511(R) (2015)

[39] D. E. Liu and H. U. Baranger, Detecting a Majoranafermion zero mode using a quantum dot, Phys. Rev. B 84, 201308(R) (2011)

[40] A. Y. Kitaev, Unpaired Majorana fermions in quantum wires, Physics-Uspekhi 44(10S), 131 (2001)

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Higher Education Press and Springer-Verlag Berlin Heidelberg