<p>Hybrid superconductor-semiconductor Josephson field-effect transistors (JoFETs) function as Josephson junctions with gate-tunable critical current. Additionally, they can feature a non-sinusoidal current-phase relation (CPR) containing multiple harmonics of the superconducting phase difference, a so-far underutilized property. Here we exploit this multi-harmonicity to create a Josephson circuit element with an almost perfectly <i>π</i>-periodic CPR, indicative of a largely dominant charge-4e supercurrent transport. We realize such a Josephson element, recently proposed as building block of a protected superconducting qubit, using a superconducting quantum interference device (SQUID) with low-inductance aluminum arms and two nominally identical JoFETs. The latter are fabricated from a SiGe/Ge/SiGe quantum-well heterostructure embedding a high-mobility two-dimensional hole gas. By carefully adjusting the JoFET gate voltages and finely tuning the magnetic flux through the SQUID close to half a flux quantum, we achieve a regime where the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41467_2025_56245_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sin (2\varphi )\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>sin</mi> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>φ</mi> </mrow> <mo>)</mo> </mrow> </math></EquationSource> </InlineEquation> component accounts for more than 95% of the total supercurrent. This result demonstrates a new promising route towards parity-protected superconducting qubits.</p>

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Gate- and flux-tunable sin(2φ) Josephson element with planar-Ge junctions

  • Axel Leblanc,
  • Chotivut Tangchingchai,
  • Zahra Sadre Momtaz,
  • Elyjah Kiyooka,
  • Jean-Michel Hartmann,
  • Frédéric Gustavo,
  • Jean-Luc Thomassin,
  • Boris Brun,
  • Vivien Schmitt,
  • Simon Zihlmann,
  • Romain Maurand,
  • Étienne Dumur,
  • Silvano De Franceschi,
  • François Lefloch

摘要

Hybrid superconductor-semiconductor Josephson field-effect transistors (JoFETs) function as Josephson junctions with gate-tunable critical current. Additionally, they can feature a non-sinusoidal current-phase relation (CPR) containing multiple harmonics of the superconducting phase difference, a so-far underutilized property. Here we exploit this multi-harmonicity to create a Josephson circuit element with an almost perfectly π-periodic CPR, indicative of a largely dominant charge-4e supercurrent transport. We realize such a Josephson element, recently proposed as building block of a protected superconducting qubit, using a superconducting quantum interference device (SQUID) with low-inductance aluminum arms and two nominally identical JoFETs. The latter are fabricated from a SiGe/Ge/SiGe quantum-well heterostructure embedding a high-mobility two-dimensional hole gas. By carefully adjusting the JoFET gate voltages and finely tuning the magnetic flux through the SQUID close to half a flux quantum, we achieve a regime where the \(\sin (2\varphi )\) sin ( 2 φ ) component accounts for more than 95% of the total supercurrent. This result demonstrates a new promising route towards parity-protected superconducting qubits.