Anomalous interference in Aharonov-Bohm rings with two Majorana bound states

Abstract

We investigate the conductance of an Aharonov-Bohm (AB) interferometer coupled to a quantum dot and two Majorana bound states on the edge of the topological superconductor with finite length. When the tunnel couplings between the Majorana bound states and the Aharonov-Bohm interferometer are fixed to the specific phase, the differential conductance becomes zero irrespective of all the parameters as long as the hoppings to the two Majorana fermions on the opposite side are equal. The conductance at the zero bias voltage does not change with the magnetic flux penetrating the ring for all cases. When the energy level of the quantum dot is equal to the energy of the Majorana bound states, the AB oscillation shows π periodicity due to the particle-hole symmetry. The breaking of the time-reversal symmetry of the topological superconductor results in 2π periodicity of the AB oscillation for the specific phase of the tunnel coupling while the time-reversal symmetry breaking leads to the mixing of the triplet and singlet states in the quantum dot in another specific phase. PACS numbers: 74.45.+c, 73.63.Kv, Exotic features of Majorana fermions [1] have been studied not only from the interest of the fundamental physics, but also from the application for quantum computing [2][3][4][5][6]. In recent years, Majorana fermions have been predicted in several setups with s-wave or d-wave superconductors [7-10]. It has been shown that Majorana fermions are manifested as a zero bias conductance peak in the normal metal/topological superconductor (TS) junctions [11][12][13]. Recently, the zero bias conductance peak due to Majorana bound states (MBSs) has been observed in these systems [14][15][16][17][18]. However, the signature is not enough to prove the existence of MBSs. The observed zero bias conductance peak is not quantized and it could occur even without MBSs in the presence of disorders [19][20][21][22][23]. Thus, alternative setups are necessary. Other setups are proposed to detect the phase information of transport electrons due to existence of the MBSs using interferometry of electron waves [24,25].These studies mentioned above have examined the class D TSs, in which one Majorana fermion emerges at the edge. When the time-reversal symmetry is preserved, the TS is classified into the class BDI. Then, two Majorana fermions can exist on the edge of the TS which has the integer topological number of 2 [26][27][28][29][30]. The BDI topological superconductors can be realized with superconductors coupled to the AIII topological insulators which show the quantum anomalous Hall effect [27,29,30]. Yamakage and Sato have reported that the zero bias conductance of the normal metal(N)-TS junction shows zero or 4e 2 /h value depending on the phase of the tunnel coupling between the normal metal and the TS [30].The Aharonov-Bohm (AB) ring with an embedded quantum dot attached to the normal lead has been studied in 2DEG in GaAs/AlGaAs heterostructures [31]. The high-order interference called the Fano resonance appears in the conductance ...

Multiscale entanglement renormalization ansatz for spin chains with continuously varying criticality

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Thermoelectric Effect in a Correlated Quantum Dot Side-Coupled to Majorana Bound States

“…Recently, optical schemes based on QD structure were also theoretically proposed to detect the MBSs with the help of optical pump-probe technique. [21,22] In ring-or T-shaped QDbased systems, the quantum interference phenomena are drastically affected by the MBSs [23][24][25] and then can be used for the detection scheme with the help of, for example, the Fano effect [26][27][28].…”

Probing the antisymmetric Fano interference assisted by a Majorana fermion

“…In such conditions, p-wave superconductivity is induced on the nanowire due to the so-called proximity effect. [5][6][7] In the context of quantum transport, [8][9][10][11][12][13][14][15][16][17][18][19] in particular for a single quantum dot (QD) hybridized with a Majorana bound state (MBS), a zero-bias anomaly (ZBA) 11,12 in the conductance is predicted to appear, given by G ¼ 0:5G 0 , where G 0 ¼ e 2 =h is the quantum of conductance. The ZBA has been observed experimentally in conductance measurements through a nanowire of indium antimonide merged to gold and niobium titanium nitride.…”