| Summary: | The AC conductivity response of disordered materials follows a universal power law of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>σ</mi><mo>′</mo></msup><mrow><mo>(</mo><mi>ω</mi><mo>)</mo></mrow><mo>∝</mo><msup><mi>ω</mi><mi>n</mi></msup></mrow></semantics></math></inline-formula> at the low frequency regime, with the power exponent values in the range 0 < <i>n</i> < 1. At the high frequency regime, in many experimental data of different disordered materials, superlinear values of the power exponent <i>n</i> were observed. The observed superlinear values of the power exponent are usually within <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>n</mi><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula>, but in some cases values <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>></mo><mn>2</mn></mrow></semantics></math></inline-formula> were detected. The present work is based on the definitions of electromagnetic theory as well as the Havriliak–Negami equation and the damped harmonic oscillator equation, which are widely used for the description of dielectric relaxation mechanisms and vibration modes in the THz frequency region, respectively. This work focuses mainly on investigating the parameters that affect the power exponent and the range of possible <i>n</i> values.
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