Planar Josephson Junction Topological Qubit

The planar Josephson junction (pJJ) topological qubit hosts Majorana zero modes at the ends of a topological superconducting channel formed in a two-dimensional electron gas (2DEG) sandwiched between two superconducting leads. Unlike nanowire-based approaches, the pJJ geometry uses a lithographically defined junction in a planar 2DEG — offering better scalability, easier fabrication, and less stringent magnetic field alignment requirements.

Figure

Description

Physical mechanism

A 2DEG with strong Rashba spin-orbit coupling (typically InAs or InAs/Al heterostructures) is contacted by two superconducting leads separated by a narrow gap. When an in-plane Zeeman field is applied and the superconducting phase difference $\phi$ across the junction is tuned near $\pi$, the 1D channel between the leads enters a topological superconducting phase. Majorana zero modes appear at the channel endpoints.

Key advantages over nanowires

• Planar geometry: Compatible with standard lithographic fabrication and scalable architectures
• Relaxed field alignment: Does not require precise magnetic field alignment along a 1D wire axis
• Phase control: The superconducting phase difference $\phi$ provides an additional tuning knob — at $\phi =\pi$, topological protection is maximized across a wide parameter range
• Diagnostic tools: The critical current shows a sharp minimum at the topological phase transition, providing an in-situ probe

Experimental progress

Fornieri et al. (2019, Nature) observed signatures of topological superconductivity in InAs 2DEG-Al planar Josephson junctions, including closing and reopening of the superconducting gap as a function of in-plane field. Ren et al. (2019) independently demonstrated similar signatures in epitaxial Al-InAs devices.

Hamiltonian

The Bogoliubov-de Gennes Hamiltonian for the junction region:

$H=\left(\frac{p^2}{2m^{\ast }}-\mu \right){\tau }_z+\alpha (p_x{\sigma }_y-p_y{\sigma }_x){\tau }_z+V_Z{\sigma }_x+\Delta (y){\tau }_x$

where $\alpha$ is the Rashba coefficient, $V_Z$ is the Zeeman energy, $\Delta (y)$ is the proximity-induced pairing (nonzero under the leads, zero in the junction), and $\tau$, $\sigma$ are Nambu and spin Pauli matrices. The topological phase transition occurs when:

$V_Z>\sqrt{{\mu }^2+{\Delta }_{\text{ind}}^2}$

at phase difference $\phi =\pi$, with the topological gap $\propto \alpha$.

Performance Metrics

Metric	Value	Notes	Fidelity reference
Topological gap	~20–50 μeV	At optimal field/phase	pientka-2017-planar-jj
Operating temperature	<100 mK	Dilution refrigerator	fornieri-2019-planar-jj
Junction width	50–150 nm	Lithographically defined	fornieri-2019-planar-jj
Phase tunability	Full 0–2π	Via flux through SQUID loop	pientka-2017-planar-jj

Scaling Considerations

• Fabrication: Fully planar, compatible with semiconductor foundry processes
• Networks: Multiple junctions can be patterned on a single 2DEG chip for braiding operations
• Tetron geometry: Microsoft’s Majorana 1 processor uses related InAs/Al heterostructure physics in an H-shaped tetron layout
• Phase control: SQUID-loop geometries allow electrical tuning of $\phi$ without external flux

Linked Papers

• pientka-2017-planar-jj
• fornieri-2019-planar-jj

Related Entries

• majorana-topological-qubit
• andreev-spin-qubit
• gatemon