Phonons, pseudo-magnetic fields, and their effects on quantum transport in graphene

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This proposal aims at a deeper theoretical understanding of quantum transport in strain-engineered graphene monolayer devices. Within an effective low-energy theory, the strain-induced elastic deformation of the sample results in a pseudo-magnetic field, coupled to the Dirac fermions in a graphene. When an electric current flows, current-induced forces will build up and affect the mechanical motion. We have the following three goals: First, we wish to understand the current-induced forces acting on a suspended graphene layer, taking into account both the minimal coupling to the pseudo-magnetic field and a capacitive coupling to a backgate. The resulting Langevin equation for the maximum deflection of the layer involves various current-induced forces, for which our previous work provides general scattering matrix expressions. We will then numerically solve the resulting Langevin equation and thereby determine the frequency shift and the quality factor as a function of the applied bias voltage. In addition, backaction effects will be considered for the electrical conductance and for shot noise. Since new effects occur when at least two modes are involved, as a second goal, we will study the current-induced motion of various strain-induced configurations in graphene. Concrete examples include a Gaussian bump and the one-dimensional mechanical step or barrier. Using the general scattering matrix expressions, we will compute all current-induced forces for these setups. The resulting Langevin dynamics will be studied numerically. We will search for parameter regimes where the center-of-mass variable moves when an electronic current flows. The third goal of this project is to analyze the zero-energy modes in a strained graphene waveguide when electron-electron interactions are included. We will assume that the pseudo-magnetic field is engineered such that there are two parallel zero field lines which guide counter-propagating chiral snake states. These are the energetically closest modes to the zero-energy flat band, which does not carry any current. For a system close to the Dirac point, one expects insulating behavior. However, interactions mix the zero modes with the snake states, and one may engineer an exotic conducting Luttinger liquid.