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Spectral function analysis on the Holstein polaron problem : extraction of the self-energy and coupling strength, and their implications for angle resolved photoemission spectroscopy Veenstra, Christian Neil


This thesis first reviews and examines the Angle Resolved Photoemission Spectroscopy (ARPES) experiment. It is shown that the spectral density function, familiar from the Green's function method of studying correlated systems, can be directly measured. A model spectral function with a nontrivial self-energy is then used to test an improvement to a recently arrived method[15,17] to analyze ARPES data. This new method relies on self-consistency between the real and imaginary parts of the self-energy (as measured through the Kramers-Kronig transform) to overcome the requirement of knowing the bare electronic structure. Through this, the method extracts both the complex self-energy and the bare electronic structure from the spectral function. The method described here is an improvement on this idea as previously implemented in that a strict form for the bare band dispersion (previously considered linear or quadratic) is never assumed. Although the method here utilized a polynomial of arbitrary degree, it could be trivially expanded to use any other functional form so long as both the value and first derivative are known analytically as a function of the fitting parameters. Using Mona Berciu's first order momentum average (MA) approximation[2] as implemented by Glen Goodvin[8] the spectral function as well as momentum independent self-energy were calculated for the Holstein polaron for a wide range of parameters. It was found that self-consistent spectral function analysis was highly successful at extracting the self energy and bare electronic dispersion from the spectral function over a consistent subset of these parameters. For studies outside this range of parameters the more traditional ARPES analysis method of measuring renormalization is also examined.

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