Goos-H\"anchen Shifts in Graphene-Based Linear Barrier

Using the energy spectrum of a system made of graphene subjected to a linear barrier potential, we study the Goos-H\"anshen shifts. The calculation is done by first determining the corresponding phase shifts via the transmission and reflection probabilities. Numerical analysis shows that the Goos-H\"anshen shifts depend strongly on the incident energy, barrier height and width, and vary positively or negatively under suitable conditions.