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

本提案旨在对应变工程石墨烯单层器件中的量子输运有更深入的理论理解。在一个有效的低能理论中，应变引起的样品弹性变形产生伪磁场，与石墨烯中的狄拉克费米子耦合。当有电流流过时，电流产生的力就会增加并影响机械运动。我们有以下三个目标：首先，我们希望了解作用在悬浮石墨烯层上的电流诱导力，同时考虑到与伪磁场的最小耦合和与后门的电容耦合。所得的层最大挠度朗之万方程涉及各种电流诱导力，我们之前的工作提供了一般的散射矩阵表达式。然后，我们将数值求解得到的朗之万方程，从而确定频移和质量因子作为施加偏置电压的函数。此外，还将考虑电导和散粒噪声的反作用。由于当至少涉及两种模式时，新的效应就会发生，作为第二个目标，我们将研究石墨烯中各种应变诱导构型的电流诱导运动。具体的例子包括高斯凹凸和一维机械台阶或障碍。使用一般的散射矩阵表达式，我们将计算这些装置的所有电流诱导力。所得的朗格万动力学将进行数值研究。我们将寻找当电子电流流动时质心变量移动的参数体系。该项目的第三个目标是分析应变石墨烯波导中包含电子-电子相互作用时的零能量模式。我们将假设伪磁场被设计成有两条平行的零场线来引导反向传播的手性蛇形态。这些是能量上最接近零能平带的模式，它不携带任何电流。对于接近狄拉克点的系统，我们期望它有绝缘行为。然而，相互作用将零模式与蛇态混合在一起，人们可以设计出一种奇异的导电卢廷格液体。

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.