Analogies for Dirac fermions physics in graphene

Graphene monolayer was the first solid-state material to show a linear dispersion relation around the corners of the first Brillouin zone. This unusual dispersion relation led to specific physical phenomena, as well as to the possibility of testing ultra-relativistic particle theories. Since graphene discovery, many attempts have been made to mimic its properties in other solid-state structures as well as in specially designed photonic, phononic or elastic systems, with the aim of extending the study of graphene-inspired physics to situations that do not occur, or are difficult to control in natural graphene. At the same time, graphene, in the ballistic, collisionless transport regime, can implement systems and even devices in which charge carriers propagate in a similar way as classical optical fields in the respective systems or devices. The implementation of structures with analog characteristics to Dirac graphene fermions has proven fruitful to observe novel and/or unconventional phenomena in quantum or classical physical systems, revealing also the differences in behavior between these systems. The aim of the present review is to emphasize the value of using analogies for graphene fermions in order to develop new devices, and to further our knowledge and understanding of physics. Although the range of graphene physicsbased analogies is large, including those based only on similarities between theoretical formalisms, we have focused in this review on analogous structures or phenomena to those in graphene that can be or have been experimentally proven.