Dirac cones are ubiquitous to non-trivial quantum matter and are
expected to boost and reshape the field of modern electronics.
Particularly relevant examples where these cones arise are
topological insulators and graphene. From a fundamental
perspective, this thesis proposes schemes towards modifying basic
properties of these cones in the aforementioned materials. The
thesis begins with a brief historical introduction which is
followed by an extensive chapter that endows the reader with the
basic tools of symmetry and topology needed to understand the
remaining text. The subsequent four chapters are devoted to the
reshaping of Dirac cones by external fields and delta doping. At
all times, the ideas discussed in the second chapter are always a
guiding principle to understand the phenomena discussed in those
four chapters. As a result, the thesis is cohesive and represents a
major advance in our understanding of the physics of Dirac
materials.
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