A transmon qubit realized by exploiting the superconductor-insulator transition

TL;DR

This paper introduces a monolithic, oxide-free NbN-based weak-link qubit (planaron) by exploiting a thickness-driven superconductor-insulator transition (SIT) in a single NbN film. Using atomic layer deposition and etching, the authors create planar weak links that realize a transmon-like qubit with a measured anharmonicity of about 235 MHz and a total linewidth near 15 MHz, while operating in a high-gap material that could enable higher-temperature operation. They provide extensive transport and microwave evidence suggesting the presence of highly transparent conduction channels near the SIT and discuss how these channels influence the current-phase relation and qubit properties. The work highlights a scalable fabrication route for high-gap superconducting qubits and prompts further SIT investigations in finite-size patches, with potential impact in higher-frequency and higher-temperature quantum devices.

Abstract

Superconducting qubits are among the most promising platforms for realizing practical quantum computers. One requirement to create a quantum processor is nonlinearity, which in superconducting circuits is typically achieved by sandwiching a layer of aluminum oxide between two aluminum electrodes to form a Josephson junction. These junctions, however, face several limitations that hinder their scalability: the small superconducting gap of aluminum necessitates millikelvin operating temperatures, the material interfaces lead to dissipation, and the sandwich geometry adds unwelcome capacitance for high-frequency applications. In this work, we address all three limitations using a novel superconducting weak link based on the superconductor-insulator transition. By locally thinning a single film of niobium nitride, we exploit its thickness-driven superconductor-insulator transition to form a weak link employing only atomic layer deposition and atomic layer etching. We utilize our weak links to produce a transmon qubit, '$planaron$', with a measured anharmonicity of $α/2π= 235$ MHz; at present, the linewidth is $κ/2π= 15 \mathrm{\: MHz}$. The high superconducting gap of niobium nitride can enable operation at elevated temperatures in future devices, and the fully planar geometry of the weak link eliminates superfluous material interfaces and capacitances. The investigation of small patches of material near the SIT can shed new light on the nature of the transition, including the role of dissipation and finite-size effects.

Figures (14)

• Figure 1: ALD- and ALE-driven SIT in NbN thin films DC transport experimental data on the thickness-driven SIT in NbN films obtained by a) atomic layer deposition (ALD) and b) atomic layer etching (ALE). The two panels show that film resistance per square, $R_s$, varies as a function of thickness, $d_{\mathrm{ALD}}$ and $d_{\mathrm{ALE}}$, and temperature. A separation between a superconducting ($dR_s(T)/dT > 0$) and an insulating ($dR_s(T)/dT < 0$) behavior is observed for an ALD-driven SIT around $d^{\mathrm{ALD}}_c\sim 3$ nm. Horizontal dashed lines in a,b) mark a sheet resistance per square of $R_Q=6.45\rm \:k\Omega$. Within experimental uncertainties, the ALE-driven transition occur at a similar thickness. c) Optical image of a representative CPW resonator chip with locally tuned thickness. The image shows two out of four resonators capacitively coupled to a transmission line (TL) with varying gaps between center conductor and ground plane ($\mathrm{gap = \{6,\:24,\:48,\:72\}~\mu m}$). Dark grey is the sapphire substrate, light grey is ALE-thinned NbN containing the CPW resonators, and white is the unetched film containing the transmission line. d) Left axis: Measured quality factors of NbN CPW resonators at single photon power. Quality factors of $\sim10^6$ are obtained for ALE etched films (pink, purple, orange circles), independent of both kinetic inductance and the gap between the center conductor and the ground plane. Unetched films (black circles) show a reduced quality factor which depends on the gap (see Supplemental Information for discussion). Right axis: The normal-state sheet resistance, $R_N$, for each film is obtained from DC Hall bar measurements on the same chip and plotted as a function of the kinetic inductance, $L_K$, extracted from CPW measurements (teal squares). The relation is in good agreement with Mattis-Bardeen (black solid line). Black square marks Mattis-Bardeen prediction when $R_N=R_Q$.
• Figure 2: Single-film planar weak links a) Schematic phase diagram of the superconductor-insulator transition (SIT) tuned by film thickness. The quantum critical point (QPC) is marked at the critical thickness, $d_c$, that separates superconducting, $S$, from insulating, $I$, behavior near zero temperature. b) Atomic force microscopy (AFM) of a single-film weak link fabricated from a thick ALD-NbN film with a starting thickness of $d_S$, corresponding to a point deep in the superconducting phase, see panel a). Next, a local ALE etch defines the weak link with a thickness, $d_I$ of $\sim 2.5\:\rm nm$ corresponding to a point deep in the insulating phase. c, d) The $I-V$characteristic of link with $l = 20 \mathrm{\: nm}$. For sufficiently short links, we observe a supercurrent branch. e, f) The $I-V$ characteristics of two longer weak links, both with $l = 50 \mathrm{\: nm}$. As the length is increased, the supercurrent branch disappears and no current flows until a critical voltage $V_c\gg2\Delta_{\rm NbN}/e$ is reached.
• Figure 3: Planaron qubit a) Top: Geometry of the superconducting junction type, represented with a butterfly symbol. Bottom: The weak link is shunted with a large capacitor and directly coupled to a transmission line in a hanger-style geometry. b) Measured change in complex transmission coefficient, $\delta S_{21}$, as a function of drive power on the planaron qubit. Note that we subtract the high-power response of the system (listed applied powers account for total attenuation of the setup, which is calibrated using data in Fig. \ref{['fig3']}d). We also scale the measurement by $\kappa_t/\kappa_c$, such that the radius of the circle is unity at low drive powers. c) We extract the Rabi frequency, $\Omega_R$, using Eq. (\ref{['squash']}) and plot it as a function of the drive amplitude. The Rabi rate is linear in drive amplitude as expected (black line). d) Two-tone spectroscopy of the planaron qubit. A drive is applied on resonance with the $|0\rangle \rightarrow|1\rangle$ transition. The frequency of a second probe tone is then swept to search for the $|1\rangle \rightarrow|2\rangle$ transition. The $S_{21}$ of the undriven planaron is subtracted from the results to make the resonance clearer. This subtraction results in a brightening of the $|0\rangle \rightarrow|1\rangle$ transition with drive power as the phase roll disappears [see main text]. At moderately high power, a second phase roll appears signifying the $|1\rangle \rightarrow|2\rangle$ transition. Sidebands are also observed at high drive powers due to the Aulter-Townes effect. They are fitted to the expected model (dashed pink lines) as described in main text. e) A line cut at $P_{RF}=-3 \:\mathrm{dBm}$ (-138 dBm at the device) displays two clear peaks $\sim 235$ MHz apart quantifying the anharmonicity, $\alpha/2\pi$, of the planaron qubit.
• Figure 4: Critical current evolution with temperature a, b) A monotonic decrease in critical current, $I_c$, is observed when the temperature is increased from 3 K to 10 K. We define $I_c$ as the boundary between a measured zero differential resistance, $dV/dI$, and the onset of measurable finite $dV/dI$. Both weak links inherit large-gap properties of NbN, resulting in a measured critical current that goes to zero near $\sim 7-8$ K. c, d) Line cuts of panels a, b) are taken along the directions indicated by orange and purple arrows; they illustrate how critical current at each temperature, $I_c(T)$, is extracted from differential resistance measurements. Vertical dashed lines in panels c, d) mark the threshold for $I_c$. We note the transition becomes progressively less sharp at elevated temperatures. In this regime, we define the threshold as approximately the onset of a change in differential resistance, i.e. when $d^2V/dI^2\neq 0$. e, f) Critical current evolution with temperature is modeled assuming we are in the diffusive limit using Eq. (\ref{['critical current']}) with the diffusion coefficient, $D$, as the only one free parameter (pink curve). The best fit to this data results in small values of e) $D$: $1.1 \:\mathrm{cm^2/s}$ and f) $0.2 \:\mathrm{cm^2/s}$, see main text for discussion on effects of localization. Close to zero temperature we plot the separately measured values of $I_c$ (black solid circles) alongside the predicted values (pink solid circles), assuming diffusive the limit.
• Figure 5: Integer and half Shapiro features a, b) DC response under the influence of RF radiation fixed at $6.8\: \mathrm{GHz}$. The irradiation leads to integer steps in the measured voltage in units of the microwave field, $2eV/hf_{RF}$, with corresponding lobes of zero differential resistance, $dV/dI$, between steps. c, d) Line cuts taken at two intermediate microwave powers show rounded integer Shapiro steps in $I-V$ and corresponding peaks in measured conductance, $dI/dV$. e, f) Maps of measured voltage in units of microwave field and measured differential resistance show rounded half Shapiro steps develop in a representative sample with a fixed frequency of $12.75 \:\mathrm{GHz}$. g, h) Line cuts at two intermediate microwave powers show both integer and half steps with corresponding conductance peaks.