Temperature Dependence of Friedel Oscillations in Dirac Hybrid Systems

Abstract

Friedel oscillations represent a fundamental quantum phenomenon in condensed matter physics, manifesting as spatial modulations in the charge density around impurities or defects in electronic systems. This theoretical study investigates the temperature dependence of Friedel oscillations in Dirac hybrid systems, which combine conventional electron gas regions with Dirac materials, such as graphene or topological insulators. We employed a finite-temperature Green's function formalism within the linear response theory framework to derive analytical expressions for the screened potential and charge density oscillations. Our analysis revealed that temperature effects introduce significant modifications to both the amplitude and decay characteristics of Friedel oscillations at the interface between the conventional and Dirac regions. We demonstrate that thermal broadening of the Fermi distribution leads to exponential suppression of the oscillation amplitudes at distances comparable to the thermal length scale. Furthermore, we identify a crossover temperature regime in which quantum oscillations transition from quantum-coherent to classical screening behavior. The results indicate that hybrid systems exhibit enhanced temperature sensitivity compared with purely Dirac or conventional systems, with implications for scanning tunneling microscopy measurements and quantum device applications. This work provides a comprehensive theoretical framework for understanding charge redistribution phenomena in next-generation electronic materials operating at finite temperatures.