Valley-polarized Josephson junctions as gate-tunable 0-π qubit platforms

Abstract Recently, gate-defined Josephson junctions based on magic-angle twisted bilayer graphene (MATBG) have been fabricated. In such a junction, local electrostatic gating can create two superconducting regions connected by an interaction-driven valley-polarized state as the weak link. Due to the spontaneous time-reversal and inversion symmetry breaking, novel phenomena such as the Josephson diode effect have been observed with zero external magnetic fields. Importantly, when the so-called nonreciprocity efficiency (which measures the sign and strength of the Josephson diode effect) changes sign, the energy-phase relation of the junction is approximately $F(\phi ) \propto \cos (2\phi )$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>F</mml:mi> <mml:mo>(</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo>)</mml:mo> <mml:mo>∝</mml:mo> <mml:mo>cos</mml:mo> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mi>ϕ</mml:mi> <mml:mo>)</mml:mo> </mml:math> where F is the free energy and ϕ is the phase difference of the two superconductors. In this work, we show that such a MATBG-based Josephson junction, when shunted by a capacitor, can be used to realize the long-sought-after 0- π qubits which are protected from local perturbation-induced decoherence. Interestingly, by changing the junction parameters to the regime where a large nonreciprocity efficiency is obtainable, transmon-like qubits with large anharmonicity can also be realized. The gate-defined Josephson junctions can be employed as platforms for realizing qubits that are protected from local perturbations.