Effect of electron-hole inhomogeneity on specular Andreev reflection and Andreev retroreflection in a graphene-superconductor hybrid system

The electron-hole inhomogeneity in graphene has been confirmed to be a new type of charge disorder by recent experiments, and the largest energy displacement of electron and hole puddles with respect to the Dirac point can reach nearly 30 meV. Here we focus on how the electron-hole inhomogeneity affects the specular Andreev reflection as well as the Andreev retroreflection. In a four-terminal graphene-superconductor hybrid system, we find that the Andreev coefficients can hardly be affected even under a rather large electron-hole inhomogeneity (typically 30 meV), and the boundary distinguishing two Andreev reflections can well hold, although the strength of the charge puddles, W = 30 meV, is much larger than the superconductor gap, Delta = 1 meV. Furthermore, when charge puddles are two orders of magnitude larger than the superconductor gap, a specific kind of Andreev reflection can still be obviously detected. To quantitatively describe what degree of the boundary is blurred, a quantity D is introduced which measures the width of a crossover region between specular Andreev reflection and retroreflection in energy space. We confirm that the boundary blurring is much smaller than the charge puddle strength W. In addition, we study the effect of Anderson disorder for comparison, and we find that the boundary is held much more obviously in this case. Finally, the fluctuations of the Andreev reflection coefficient are studied. Under a typical experimental charge puddle, the fluctuations are very small when the energy of the particles is away from the boundary, again confirming that the retroreflection and specular reflection can be clearly distinguished and detected in the presence of the electron-hole inhomogeneity.