Thermal Gradient Generates Entangled Electrons

Thermoelectric effects, which convert temperature differences into electricity, have broad applications in energy harvesting and quantum technologies. In hybrid normal metal-superconductor-normal metal structures, non-local thermoelectricity arising from Cooper pair splitting and elastic co-tunneling was theoretically predicted but not experimentally confirmed. This study demonstrates the existence of the Seebeck effect in a graphene-based Cooper pair splitter, providing a tool for generating entangled electrons.

The key finding is that a thermal gradient across a quantum dot-superconductor-quantum dot device induces non-local currents, with contributions from both Cooper pair splitting and elastic co-tunneling processes. These contributions can be tuned by adjusting the gate potentials, allowing control over the relative strengths of each process. This tunability enables testing of fundamental theoretical concepts related to entanglement transport in graphene systems.

The methodology involved fabricating a device with aluminum superconducting leads connected to two graphene quantum dots. Side gates independently tuned the resonance levels of the dots, while a resistive heater imposed a thermal gradient. Measurements of thermoelectric currents were conducted using lock-in techniques, with temperatures monitored via superconductor-graphene-superconductor Josephson junction thermometers. Theoretical modeling employed Landauer formalism for coherent transport and scattering matrix approaches for incoherent effects, comparing predictions with experimental data.

Results analysis revealed that non-local currents, though small (5–10% of total currents), change sign at conductance peak maxima and follow patterns predicted by theory. Figures 2 and 3 in the paper show maps of non-local currents and their symmetric and anti-symmetric combinations, aligning with theoretical models that incorporate Fano resonances and energy-dependent transmission probabilities. The Seebeck coefficient in the quantum dots reached values up to approximately 100 μV/K, consistent with prior graphene studies.

In context, the authors highlight that this work establishes thermal gradients as a primus motor for generating entangled electrons in Cooper pair splitters. The ability to tune between elastic co-tunneling and Cooper pair splitting regimes offers a platform for thermodynamic experiments and applications where electrical drives are impractical. The significance lies in directly validating theoretical predictions and providing a method to manipulate entangled electron pairs without external voltage biases.

Limitations include the small magnitude of non-local currents and challenges in accurately measuring superconductor temperatures. The study notes that incoherent effects may explain additional features in local thermoelectric currents at low heating voltages, not fully captured by coherent models. Unresolved issues involve the exact mechanisms behind Fano resonance splittings and the influence of inelastic relaxation processes.

References: [1] G. B. Lesovik et al., Eur. Phys. J. B 24, 287–290 (2001). [2] P. Recher et al., Phys. Rev. B 63, 165314 (2001). [3] R. Sánchez et al., Phys. Rev. B 98, 241414 (2018). [4] N. S. Kirsanov et al., Phys. Rev. B 99, 115127 (2019). [5] R. Hussein et al., Phys. Rev. B 99, 075429 (2019).