Detecting a Majorana-fermion zero mode using a quantum dot

Abstract

We propose an experimental setup for detecting a Majorana zero mode consisting of a spinless quantum dot coupled to the end of a p-wave superconducting nanowire. The Majorana bound state at the end of the wire strongly influences the conductance through the quantum dot: Driving the wire through the topological phase transition causes a sharp jump in the conductance by a factor of 1/2. In the topological phase, the zero-temperature peak value of the dot conductance (i.e., when the dot is on resonance and symmetrically coupled to the leads) is e 2 /2h. In contrast, if the wire is in its trivial phase, the conductance peak value is e 2 /h, or if a regular fermionic zero mode occurs on the end of the wire, the conductance is 0. The system can also be used to tune Flensberg's qubit system [Phys. Rev. Lett. 106, 090503 (2011)] to the required degeneracy point.Majorana fermions, an exotic type of quasiparticle with non-Abelian statistics, are attracting a great deal of attention due to both their fundamental interest and their potential application for decoherence-free quantum computation. Several ways to realize unpaired Majorana fermions in a vortex core in a p-wave superconductor 1-6 and superfluid 7,8 have been proposed. Majorana bound states (MBSs) may also be realized at the ends of a one-dimensional p-wave superconductor 9 for which the proposed system is a semiconductor nanowire with Rashba spin-orbit interaction to which both a magnetic field and proximity-induced s-wave pairing are added. 10,11 In view of these proposals, how to detect and verify the existence of MBSs becomes a key issue. Suggestions include noise measurements, 12,13 resonant Andreev reflection by a scanning tunneling miscroscope (STM), 14 and 4π periodic Majorana-Josephson currents. [9][10][11]15 With regard to quantum computation, the braiding of Majorana bound states in a network of wires by applying a "keyboard" of individually tunable gates 16 leads to nontrivial computation. Note that all the detecting methods proposed to date, 9-15 involving electron transfer into or out of MBSs, will destroy the qubit information. In addition, such braiding cannot result in universal quantum computation; it must be supplemented by a topologically unprotected π/8 phase gate. 17 Recently, Flensberg introduced a system consisting of a quantum dot coupled to two MBSs (MBS-dot-MBS) through which this π/8 phase gate can be achieved. 18 A key point is that the system must be fine tuned so that the ground state is degenerate. 18 In this Rapid Communication, we consider a spinless quantum dot coupled to a MBS at the end of a p-wave superconducting (SC) nanowire, and study the conductance G through the dot by adding two external leads (schematic in Fig. 1). We find that the conductance is independent of the properties of the MBS, the nanowire, or the superconductor. The dependence of G on the dot properties has the same functional form whether a MBS is present or not. Therefore, the conductance behavior can be conveniently summarized by its peak value, when the ...

Probing Fractional Josephson Junction with a Quantum Dot

“…It can be opposed to the process of electron tunneling from the dot into a single Majorana end state [16], in which this conversion does not take place. Taking into account Eqs.…”

Quantum transport through a quantum dot structure side coupled with many quantum-dot and Majorana-bound-state pairs

“…In 2011, Liu and Baranger propose a spinless QD coupled the end of a superconducting nanowire to detect the Majorana zero mode. 12 In 2012, Cao et al investigate the transport through a QD system coupled with MBSs and find that under the finite bias voltage a subtraction of the source and drain currents can expose the essential features of the Majorana fermion. 13 More recently, the studies on the quantum transport through the QDs coupled with the MBSs are further extended to the multi-QD systems.…”

Isolating Majorana fermions with finite Kitaev nanowires and temperature: the universality of the the zero-bias conductance

“…This demands manufacturing long KNWs to prevent the MBSs overlapping and the consequent ZBP quenching at very low temperatures, what is considered a hard experimental challenge [17][18][19][20][21][22][23][24][25][26] . In this work, we explore the quantum dot (QD)-Kitaev nanowire (KNW) hybrid setup [27][28][29][30][31][32][33][34][35] sketched in Fig. 1 based on the recent experimental advances achieved by Deng et al 26 in verifying the leakage of the MBS zeromode into the QD, which was first predicted theoretically in Ref.…”

“…[27], here expressed differently for convenience once we target to show the system universality. (13) and (17) with crossover temperatures T1 (Eq.…”