Thermodynamics for Hofstadter butterflies

Charlista:  Natalia Cortés - UTFSM

Resumen: The movement of electrons in a pristine crystal is dictated by the tunneling probability between lattice sites. However, when subjected to a homogeneous magnetic field perpendicular to the lattice, the electron exhibits circular orbits. The resolution of these two combined scenarios became possible when D. Hofstadter solved the problem for electrons in a square lattice, revealing the Hofstadter butterfly. The butterfly is a fractal pattern that depicts the electron-allowed energies as a function of a dimensionless parameter α at zero temperature. In this work, we extend this analysis to a honeycomb lattice incorporating temperature effects. Connecting a tight-binding model and Fermi-Dirac statistics, we determine the electronic entropy and electronic specific heat for low and high temperatures. Our results unveil fractal patterns influenced by α, where temperature governs the overall structure. These theoretical insights into electronic processes with fractal-like patterns at different temperatures offer valuable perspectives that may contribute to understanding potential quantum mechanisms of tubular-like structures in biological systems, shedding light on quantum biology phenomena.