Josephson energy of superconducting junctions: amorphous versus crystalline tunnel barriers
Abstract
The Josephson energy EJ is a key parameter governing the properties of transmon superconducting qubits. In Al/AlOx/Al junctions, EJ is set by electron tunneling through an ultrathin oxide barrier and therefore depends exponentially on the atomic structure of the barrier. We compute EJ by first-principles device modeling based on the NEGF-DFT quantum-transport method, comparing a junction with a crystalline Al2O3 barrier against ten junctions with melt--quenched amorphous Al2O3 barriers of the same thickness. From the Fermi-level transmission and the Ambegaokar--Baratoff relation, we obtain a mean EJ/h of $2.78$ GHz for the amorphous ensemble, with a standard deviation of $4.67$ GHz, compared with $0.73$ GHz for the crystalline reference; individual amorphous values span nearly two orders of magnitude. Scattering-state analysis shows that transport is quantum tunneling and that the variability originates from stoichiometric inhomogeneity of the amorphous oxide: Al-rich, low-barrier regions can connect into percolation-like tunneling pathways that strongly enhance the conductance. A realistic 200×200 nm2 junction self-averages over more than 2×104 such microscopic regions. These results establish a quantitative atomistic route from oxide microstructure to the superconducting-circuit energy scale EJ.
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BibTeX
@misc{zhang2026josephson,
title = {{Josephson energy of superconducting junctions: amorphous versus crystalline tunnel barriers}},
author = {Wanting Zhang and Aldilene Saraiva-Souza and Félix Beaudoin and Xianghua Kong and Hong Guo and Yu Zhu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09426},
eprint = {2609.09426},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09426},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Josephson energy of superconducting junctions: amorphous versus crystalline tunnel barriers
AU - Wanting Zhang
AU - Aldilene Saraiva-Souza
AU - Félix Beaudoin
AU - Xianghua Kong
AU - Hong Guo
AU - Yu Zhu
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09426
UR - https://arxiv.org/abs/2609.09426
AB - The Josephson energy E_J is a key parameter governing the properties of transmon superconducting qubits. In Al/AlO_x/Al junctions, E_J is set by electron tunneling through an ultrathin oxide barrier and therefore depends exponentially on the atomic structure of the barrier. We compute E_J by first-principles device modeling based on the NEGF-DFT quantum-transport method, comparing a junction with a crystalline Al_2O_3 barrier against ten junctions with melt--quenched amorphous Al_2O_3 barriers of the same thickness. From the Fermi-level transmission and the Ambegaokar--Baratoff relation, we obtain a mean E_J/h of $2.78$ GHz for the amorphous ensemble, with a standard deviation of $4.67$ GHz, compared with $0.73$ GHz for the crystalline reference; individual amorphous values span nearly two orders of magnitude. Scattering-state analysis shows that transport is quantum tunneling and that the variability originates from stoichiometric inhomogeneity of the amorphous oxide: Al-rich, low-barrier regions can connect into percolation-like tunneling pathways that strongly enhance the conductance. A realistic 200×200 nm^2 junction self-averages over more than 2×10^4 such microscopic regions. These results establish a quantitative atomistic route from oxide microstructure to the superconducting-circuit energy scale E_J.
ER -