Quantum phase transition in a double quantum dot Josephson junction driven by electron-electron interactions

Abstract

In this work, we employ a surrogate BCS model with discrete energy levels to investigate a hybrid system comprising two quantum dots (QD1 and QD2), where QD1 is tunnel coupled to two superconducting leads, and QD2 is only tunnel coupled to QD1. Through exact diagonalization of this system, we obtain numerically exact solutions that enable rigorous computation of key physical quantities. Our analysis reveals a rich phase diagram featuring multiple controllable phase transitions mediated by quantum dot electron-electron interaction strength. Specifically, the system first undergoes an initial phase transition when tuning QD2's electron-electron interaction strength while maintaining QD1 in the noninteracting regime. Subsequent adjustment of QD1's electron-electron interaction strength induces a secondary phase transition, followed by a third transition arising from interdot electron-electron interaction modulation. Furthermore, we demonstrate that parallel magnetic field application can drive reversible ferromagnetic-antiferromagnetic phase transitions under specific parameter conditions. Finally, we report the emergence of nonlocal magnetization phenomena when subjecting QD1 to weak magnetic fields. And our results demonstrate that the orientation of nonlocal magnetization can be precisely manipulated through adjustment of the onsite interaction strength U2 in QD2. Our research demonstrates significant control capabilities: we show Josephson current direction in double quantum dot Josephson junctions can be manipulated through electron-electron interaction strength modulation. Furthermore, nonlocal magnetization orientation can be switched by tuning onsite interactions within individual QD.

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