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Electrons moving in a periodic electric potential form Bloch energy
bands where the mass of electrons are effectively changed. In a strong
magnetic field, the cyclotron orbits of free electrons are quantized
and Landau levels forms with a massive degeneracy within. In 1976,
Hofstadter showed that for 2-dimensional electronic system, the
intriguing interplay between these two quantization effects can lead
into a self-similar fractal set of energy spectrum known as
"Hofstadter's Butterfly." Fascinating electron energy spectrum have
continued ever since. Recent
advent of graphene, where its Bloch electrons can be described by
Dirac fermions, provides a new opportunity to investigate this half
century old problem experimentally. In this presentation, I will
discuss the experimental realization Hofstadter's Butterfly via
substrate engineered graphene under extremely high magnetic fields
controlling two competing length scales governing Dirac-Bloch states
and Landau orbits, respectively.
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