Phonons as Quantum Transducer Utilizing the Phonon Drag Effect

The emergence of novel nanostructured materials in recent decades presents rich opportunities for the realization of phonon-based quantum computing. One of the challenges is the sensitive detection of a single phonon without destroying it. While how a densely populated phonon bath destroys quantum coherence has long been understood, only recently has it come to be appreciated that phonons may instead provide an effective means to transmit quantum information when excited in sufficiently small numbers coherently. The strong coupling of phonons to other quasiparticles (electrons, photons, or spins) makes them well suited for this task. Exploration of phonon detection requires suitable techniques to source and detect phonon fluxes.  Here, we demonstrate the idea of exploiting the electron-phonon coupling in a van der Waals heterostructure via the phonon drag effect as a sensitive phonon detector.   We consider a single layer or AB-stacked bilayer graphene on top of a multi-layer hexagonal boron nitride (hBN) in this heterostructure. We assume that a surface polar phonon (SPP) in the hBN layer is excited and propagates across the hBN layer, which plays the role of a phononic waveguide.  We calculate electron-phonon coupling for electrons in graphene with this non-equilibrium SPP in the hBN layer and determine phonon drag voltage by solving the Boltzmann transport equation.  Our numerical results demonstrate that the drag voltage is on the scale of a few microvolts, which is well above the detection limit in the typical experimental setups.