Conductance of a proximitized nanowire in the Coulomb blockade regime

Heck, Bernard van; Lutchyn, Roman M.; Glazman, L. I.

doi:10.1103/physrevb.93.235431

Cited by 110 publications

(187 citation statements)

References 86 publications

(172 reference statements)

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“…Of particular relevance to schemes for Majorana fusion-rule testing, braiding, and Majorana-based quantum computation [9][10][11][12] is the Majorana island geometry, in which the topological hybrid nanowire acquires a charging energy that lifts the degeneracy between occupied and empty Majorana states [6,[13][14][15][16], allowing for charge readout of the state parity.…”

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confidence: 99%

Transport Signatures of Quasiparticle Poisoning in a Majorana Island

et al. 2017

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We investigate effects of quasiparticle poisoning in a Majorana island with strong tunnel coupling to normal-metal leads. In addition to the main Coulomb blockade diamonds, "shadow" diamonds appear, shifted by 1e in gate voltage, consistent with transport through an excited (poisoned) state of the island. Comparison to a simple model yields an estimate of parity lifetime for the strongly coupled island (∼ 1 µs) and sets a bound for a weakly coupled island (> 10 µs). Fluctuations in the gate-voltage spacing of Coulomb peaks at high field, reflecting Majorana hybridization, are enhanced by the reduced lever arm at strong coupling. In energy units, fluctuations are consistent with previous measurements.Hybrid semiconductor-superconductor nanowire devices have been the focus of intense research in recent years [1-6] primarily because they are expected to support Majorana zero modes [7,8]. Of particular relevance to schemes for Majorana fusion-rule testing, braiding, and Majorana-based quantum computation [9][10][11][12] is the Majorana island geometry, in which the topological hybrid nanowire acquires a charging energy that lifts the degeneracy between occupied and empty Majorana states [6,[13][14][15][16], allowing for charge readout of the state parity.A fundamental bound to the coherence of Majorana based qubits is the parity lifetime of the Majorana state, limited by quasiparticle poisoning [9,17,18]. Studies on metallic superconductors have explored the associated poisoning rates in great detail [19][20][21][22][23][24][25][26][27][28], while experiments on semiconductor-superconductor hybrids have only established bounds on the relaxation rate of quasiparticles into the subgap state [29], with quantitative estimates for poisoning from external sources still pending.In this Letter, we use Coulomb blockade spectroscopy to quantify the quasiparticle poisoning time of a Majorana island. We find the poisoning time to a state with one extra quasiparticle in the BCS continuum to be ∼ 1 µs in the regime of relatively strong coupling between the island and the leads, and bounded from below by 10 µs in the less strongly coupled regime investigated in Ref. [29]. Our results demonstrate transport signatures of quasiparticle poisoning in Majorana islands up to the topological phase transition and place constraints on a relevant timescale for topological quantum computation and Majorana braiding.The device we investigate consisted of an MBE-grown [0001] wurtzite InAs nanowire with epitaxial Al on two of six facets [ Fig. 1(a)], which induces a hard superconducing gap in the nanowire [30,31]. The Al shell was removed on both ends using a chemical etch, leaving an Al island of length L ∼ 400 nm. Uncovered InAs segments at the wire ends are electrically contacted using normal-metal (Ti/Au) ohmic contacts. Lithographically patterned electrostatic gates near the ∼ 50 nm exposed segments next to the ohmic contacts were used to deplete carriers, bringing the device into the Coulomb blockade regime. Magnetic fields were applied per...

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Transport Signatures of Quasiparticle Poisoning in a Majorana Island

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“…While the full Hamiltonian (describing the 1D system, the superconductor, and the tunnel coupling) possesses only particle-hole symmetry and is thus in symmetry class D, it is possible to place the system in symmetry class DIII after integrating out the superconductor [47,[51][52][53][54][55][56][57] and projecting to an effective 1D model. (This is completely analogous to the case of a single Rashba nanowire coupled to an s-wave superconductor and subjected to an external magnetic field [6,7].…”

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“…We now project our system to an effective 1D model by integrating out the superconductor [47,[51][52][53][54][55][56][57]. The superconductor induces a self-energy on the 1D system given by…”

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DIII topological superconductivity with emergent time-reversal symmetry

et al. 2017

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We find a class of topological superconductors which possess an emergent time-reversal symmetry that is present only after projecting to an effective low-dimensional model. We show that a topological phase in symmetry class DIII can be realized in a noninteracting system coupled to an s-wave superconductor only if the physical time-reversal symmetry of the system is broken, and we provide three general criteria that must be satisfied in order to have such a phase. We also provide an explicit model which realizes the class DIII topological superconductor in 1D. We show that, just as in time-reversal invariant topological superconductors, the topological phase is characterized by a Kramers pair of Majorana fermions that are protected by the emergent time-reversal symmetry. DOI: 10.1103/PhysRevB.96.161407 Introduction. Topological superconductors have been intensively pursued in recent years [1][2][3] because the Majorana fermions which are localized to their boundaries have potential applications in the development of a topological quantum computer [4,5]. The most promising proposals to date for engineering topological superconductivity involve coupling a conventional superconductor either to a nanowire with Rashba spin-orbit interaction that is subjected to an external magnetic field or to a ferromagnetic atomic chain [27][28][29][30][31][32][33][34].Additionally, there have been several proposals to engineer topological superconductors in symmetry class DIII. Such systems possess both particle-hole symmetry and time-reversal symmetry [35], with the presence of time-reversal symmetry ensuring that the Majorana fermions existing at the boundaries of class DIII topological superconductors come in Kramers pairs. In one dimension (1D), where superconductivity is required to be induced by the proximity effect, it has been shown that a nontrivial topological phase in class DIII can be realized by proximity coupling a noninteracting multichannel Rashba nanowire to an unconventional superconductor [36][37][38][39] or to two conventional superconductors forming a Josephson junction with a phase difference of π [40]. Alternatively, an effective π -phase difference can be induced in a multichannel Rashba nanowire with repulsive electron-electron interactions [41] or in a system of two topological insulators coupled to a conventional superconductor via a magnetic insulator [42]. It has also been proposed to realize class DIII topological superconductivity in a system of two Rashba nanowires [43][44][45] or two topological insulators [46] coupled to a single conventional superconductor, but repulsive interactions are also necessary to reach the topological phase in these setups, which require a strength of induced crossed Andreev (interwire) pairing exceeding that of the direct (intrawire) pairing [47][48][49]. While it would be beneficial to engineer a DIII topological superconductor in a noninteracting 1D system coupled to a single conventional superconductor, as such a setup could avoid relying on unconventional superc...

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“…So far, analyses of the zero-bias conductance in these setups have mainly focused on the oscillations and intensity of individual peaks as a function of system parameters [11,17,18].…”

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Probing electron-hole components of subgap states in Coulomb blockaded Majorana islands

2018

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Recent tunneling spectroscopy experiments in semiconducting nanowires with proximity-induced superconductivity have reported robust zero-bias conductance peaks. Such a feature can be compatible with the existence of topological Majorana bound states (MBSs) and with a trivial Andreev bound state (ABS) near zero energy. Here, we argue that additional information, that can distinguish between the two cases, can be extracted from Coulomb-blockade experiments of Majorana islands. The key is the ratio of peak heights of consecutive conductance peaks give information about the electron and hole components of the lowest-energy subgap state. In the MBS case, this ratio goes to one half for long wires, while for short wires with finite MBS overlap it oscillates a function of Zeeman energy with the same period as the MBS energy splitting. We explain how the additional information might help to distinguish a trivial ABS at zero energy from a true MBS and show case examples.A semiconductor-superconductor hybrid nanowire system can exhibit a topological p-wave superconducting phase due to the interplay between Rashba spin-orbit coupling, induced s-wave superconductivity, and an appropriately applied Zeeman field [1,2]. The p-wave superconductor is of great interest because it can host Majorana bound states (MBS) [3], that may serve as elementary building blocks of a topologically protected quantum computer [4].In the last decade, the hunt for MBSs has led to an extensive study of these so-called Majorana nanowires, along with a growing list of theoretical predicted features of MBSs in these systems. The list includes an exponential suppression of MBS energy with the length of the wire [3], a 4π-periodic Josephson effect [3], a 2e 2 /hquantized zero-bias conductance peak [5][6][7], and nonabelian braiding statistics [8]. Since the first observations of a zero-bias peak on the background of a soft superconducting gap [9], advancements in material growth have enhanced the quality and resolution of experiments to a point where the more detailed features of the possible MBSs can be subjected to further experimental tests. The clean interface between Al and InAs in epitaxial nanowires has been shown to induce a hard superconducting gap in the nanowire, close to the gap of Al [10], which in turn enabled the observation of an exponential suppression of the oscillations of the lowest bound-state energy with increasing wire length in Coulomb-blockaded Majorana islands (CBMI) [11], as well as, more recently, a quantized zero-bias conductance of 2e 2 /h [12, 13].However, persistent zero-bias peaks in conductance measurements are not conclusive evidence for the existence of MBSs since other (topologically trivial) phenomena might give rise to zero-bias peaks as well. Trivial Andreev bound states (ABSs) with conductance features resembling MBSs might arise due to disorder [14], smooth confinement [15], and/or strongly coupled non-superconducting quantum dots at the ends of the nanowire [16]. Braiding experiments would give a conclusive ans...

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Conductance of a proximitized nanowire in the Coulomb blockade regime

Cited by 110 publications

References 86 publications

Transport Signatures of Quasiparticle Poisoning in a Majorana Island

Transport Signatures of Quasiparticle Poisoning in a Majorana Island

DIII topological superconductivity with emergent time-reversal symmetry

Probing electron-hole components of subgap states in Coulomb blockaded Majorana islands

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