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Superconductor Science and Technology

Normal-state conductance used to probe superconducting tunnel junctions for quantum computing

Carlos Chaparro, Richard D. Bavier, Yong-Seung Kim, Eunyoung Kim, Jeffrey S. Kline, David P. Pappas, Seongshik Oh

Published Mar 3, 2010• 1 citation
Publisher

Abstract

Here we report normal-state conductance measurements of three different types of superconducting tunnel junctions that are being used or proposed for quantum computing applications: p-Al/a-AlO/p-Al, e-Re/e-AlO/p-Al, and e-V/e-MgO/p-V, where p stands for polycrystalline, e for epitaxial, and a for amorphous. All three junctions exhibited significant deviations from the parabolic behavior predicted by the WKB approximation models. In the p-Al/a-AlO/p-Al junction, we observed enhancement of tunneling conductances at voltages matching harmonics of Al–O stretching modes. On the other hand, such Al–O vibration modes were missing in the epitaxial e-Re/e-AlO/p-Al junction. This suggests that absence or existence of the Al–O stretching mode might be related to the crystallinity of the AlO tunnel barrier and the interface between the electrode and the barrier. In the e-V/e-MgO/p-V junction, which is one of the candidate systems for future superconducting qubits, we observed suppression of the density of states at zero bias. This implies that the interface is electronically disordered, presumably due to oxidation of the vanadium surface underneath the MgO barrier, even if the interface was structurally well ordered, suggesting that the e-V/e-MgO/p-V junction will not be suitable for qubit applications in its present form. This also demonstrates that the normal-state conductance measurement can be effectively used to screen out low quality samples in the search for better superconducting tunnel junctions.

DOI
10.1088/0953-2048/23/4/045002

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Here we report normal-state conductance measurements of three different types of superconducting tunnel junctions that are being used or proposed for quantum computing applications: p-Al/a-AlO/p-Al, e-Re/e-AlO/p-Al, and e-V/e-MgO/p-V, where p stands for polycrystalline, e for epitaxial, and a for amorphous. All three junctions exhibited significant deviations from the parabolic behavior predicted by the WKB approximation models. In the p-Al/a-AlO/p-Al junction, we observed enhancement of tunneling conductances at voltages matching harmonics of Al–O stretching modes. On the other hand, such Al–O vibration modes were missing in the epitaxial e-Re/e-AlO/p-Al junction. This suggests that absence or existence of the Al–O stretching mode might be related to the crystallinity of the AlO tunnel barrier and the interface between the electrode and the barrier. In the e-V/e-MgO/p-V junction, which is one of the candidate systems for future superconducting qubits, we observed suppression of the density of states at zero bias. This implies that the interface is electronically disordered, presumably due to oxidation of the vanadium surface underneath the MgO barrier, even if the interface was structurally well ordered, suggesting that the e-V/e-MgO/p-V junction will not be suitable for qubit applications in its present form. This also demonstrates that the normal-state conductance measurement can be effectively used to screen out low quality samples in the search for better superconducting tunnel junctions.
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Abstract Approaches to developing large-scale superconducting quantum processors must cope with the numerous microscopic degrees of freedom that are ubiquitous in solid-state devices. State-of-the-art superconducting qubits employ aluminium oxide (AlO x ) tunnel Josephson junctions as the sources of nonlinearity necessary to perform quantum operations. Analyses of these junctions typically assume an idealized, purely sinusoidal current–phase relation. However, this relation is expected to hold only in the limit of vanishingly low-transparency channels in the AlO x barrier. Here we show that the standard current–phase relation fails to accurately describe the energy spectra of transmon artificial atoms across various samples and laboratories. Instead, a mesoscopic model of tunnelling through an inhomogeneous AlO x barrier predicts percent-level contributions from higher Josephson harmonics. By including these in the transmon Hamiltonian, we obtain orders of magnitude better agreement between the computed and measured energy spectra. The presence and impact of Josephson harmonics has important implications for developing AlO x -based quantum technologies including quantum computers and parametric amplifiers. As an example, we show that engineered Josephson harmonics can reduce the charge dispersion and associated errors in transmon qubits by an order of magnitude while preserving their anharmonicity.
Josephson junctions are the key components used in superconducting qubits for quantum computing. The advancement of quantum computing is limited by a lack of stability and reproducibility of qubits, which ultimately originates in the amorphous tunnel barrier of the Josephson junctions and other material imperfections. Pinholes in the junction have been suggested as one of the possible contributors to these instabilities, but evidence of their existence and the effect they might have on transport is unclear. We use molecular dynamics to create three-dimensional atomistic models to describe $\mathrm{Al}\text{\ensuremath{-}}{\mathrm{AlO}}_{x}\text{\ensuremath{-}}\mathrm{Al}$ tunnel junctions, showing that pinholes form when oxidation of the barrier is incomplete. Following this, we use the atomistic model and simulate the electronic transport properties for tunnel junctions with different barrier thicknesses using the nonequilibrium Green's function formalism. We observe that pinholes may contribute to excess quasiparticle current flow in $\mathrm{Al}\text{\ensuremath{-}}{\mathrm{AlO}}_{x}\text{\ensuremath{-}}\mathrm{Al}$ tunnel junctions with thinner barriers, and in thicker barriers we observe weak-points that facilitate leakage currents even when the oxide is continuous. We find that the disordered nature of the amorphous barrier results in significant variations in the transport properties. Additionally, we determine the current-phase relationship for our atomistic structures, confirming that devices with pinholes and weak-points cause a deviation from the ideal sinusoidal Josephson relationship.
The aluminum oxide tunnel junction is a key component of the majority of superconducting quantum devices. For high-quality, reproducible, and scalably manufacturable qubits, the ability to fabricate Josephson junctions (JJs) with a targeted critical current and high uniformity is essential. We use first-principles modeling to assess fundamental aspects of the atomic structure of both amorphous and crystalline aluminum oxide tunnel junctions and relate the structure to predicted performance metrics. We use modified ab initio molecular dynamics to develop realistic models of the tunnel junction, from which interface roughness and local thickness fluctuations are analyzed in an unbiased manner by training a neural network to identify the boundary between metal and oxide. We show that the effective thickness of the insulating part of the junction can be different from the apparent physical thickness. We calculate the rate of Cooper pair tunneling for the atomically resolved electrostatic potential using direct numerical solution in 3D, which shows a channeling effect that impacts the junction critical current. The predicted critical current is a useful JJ design parameter that can be accessed from the ab initio calculations without fitting parameters. To assess the limits of uniformity and fabrication choices (e.g., oxidation vs epitaxy), we compare the amorphous junctions to crystalline models, which show order of magnitude more efficient tunneling compared to the amorphous case, underlining the connection between atomistic structure and Cooper pair tunneling efficiency. Further, this work provides a foundation for ab initio materials design and evaluation to help accelerate future development of improved tunnel junctions.
In view of future macroscopic quantum experiments, we have fabricated prototypes of charge qubits (with tunable Josephson coupling and capacitive gate) provided with capacitively coupled readout single-electron transistor electrometers. The devices are prepared by electron beam direct-writing in conjunction with material deposition by sputtering. All leads are made of Al, and the AlO/sub x/ tunnel barriers are generated by local thermal oxidizing of the surface of the base striplines. The island electrodes are made of Al or Nb in a subsequent deposition step. In the case of Nb it is suitable to protect the barriers by a thin sputtered Al film first. The small-area (100 nm/spl times/100 nm) tunnel junctions have capacitances in the order of a few 10/sup -16/ F; their resistances can be adjusted in a wide range from k/spl Omega/ to M/spl Omega/ with an on-chip spread of less than 10%. The (double) superconducting gap energy was determined to be about 0.4 meV for Al and 1.4 meV for Nb, respectively. Measuring the so-called Coulomb staircase, we have demonstrated the operation of both qubit boxes and sub-e electrometers.
Abstract Improving the coherence of superconducting qubits is a fundamental step towards the realization of fault-tolerant quantum computation. However, coherence times of quantum circuits made from conventional aluminum-based Josephson junctions are limited by the presence of microscopic two-level systems in the amorphous aluminum oxide tunnel barriers. Here, we have developed superconducting qubits based on NbN/AlN/NbN epitaxial Josephson junctions on silicon substrates which promise to overcome the drawbacks of qubits based on Al/AlOx/Al junctions. The all-nitride qubits have great advantages such as chemical stability against oxidation, resulting in fewer two-level fluctuators, feasibility for epitaxial tunnel barriers that reduce energy relaxation and dephasing, and a larger superconducting gap of ~5.2 meV for NbN, compared to ~0.3 meV for aluminum, which suppresses the excitation of quasiparticles. By replacing conventional MgO by a silicon substrate with a TiN buffer layer for epitaxial growth of nitride junctions, we demonstrate a qubit energy relaxation time $${T}_{1}=16.3\;{{\upmu }}{{{{{\rm{s}}}}}}$$ T 1 = 16.3 μ s and a spin-echo dephasing time $${T}_{2}=21.5\;{{\upmu }}{{{{{\rm{s}}}}}}$$ T 2 = 21.5 μ s . These significant improvements in quantum coherence are explained by the reduced dielectric loss compared to the previously reported $${T}_{1}\approx {T}_{2}\approx 0.5\;{{\upmu }}{{{{{\rm{s}}}}}}$$ T 1 ≈ T 2 ≈ 0.5 μ s of NbN-based qubits on MgO substrates. These results are an important step towards constructing a new platform for superconducting quantum hardware.