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The Realization of Hofstadter Butterfly Spectrum in the Microwave

	International Journal of Scientific Research and Engineering Development (IJSRED)	Full Text:
	Published Issue : Volume-4 Issue-2
	Year of Publication : 2021
	Unique Identification Number : IJSRED-V4I2P117
	Authors : Tadele Tekeba Ergogo, JunYan Luo
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Abstract :

The Hofstadter butterfly is the emblem of a long-standing problem concerning the single-electron states in a periodic electric potential and a transverse, constant magnetic field. The experimental electromagnetic realization of the Hofstadter butterfly was done by studying the transmission of microwaves through an array of 100 scatterers inserted into a waveguide when the modulation length of this unidimensional periodic lattice changed. We demonstrate the method of calculating similar spectra for finite lattices in a magnetic field, by using the methods of transmission microwaves through an array of scatterers interpolate into a waveguide. For periodic sequences with varying period length the transmission bands reproduced the Hofstadter butterfly, originally predicted for the spectra of conduction electrons in strong magnetic fields. In the experiment it was used that the same transfer matrix formalism is applicable to both the microwave and the electronic systems.