Competição entre supercondutividade e ondas de densidade de carga em um sistema unidimensional

Abstract

The competition between superconductivity (SC) and charge density waves (CDW) has been widely studied in condensed matter physics due to its impact on strongly correlated electronic systems. While superconductivity arises from the formation of Cooper pairs, allowing for electrical conduction without resistance, charge density waves result from the periodic modulation of electronic density and can compete with SC, leading to complex electronic states. Understan ding this interaction is essential for the development of new quantum materials and potential applications in electronic devices. In this work, we investigate this competition using a theoretical model based on Ginzburg Landau theory to describe superconductivity and McMillan’s theory to model charge density wave formation. The adopted methodological approach involves formulating coupled differential equations for the superconducting and CDW order parameters, enabling the analysis of how these phases interact spatially throughout the material. To numerically solve these equations, we employ the split-operator technique, an efficient method for solving Schrödinger-type equations. The theoretical and computational analysis presented in this study contributes to understanding the fundamental mechanisms governing the coexistence and competition between SC and CDW, providing a foundation for future investigations in one-dimensional materials. Additionally, the numerical methods implemented can be extended to other contexts in condensed matter physics, allowing for broader simulations in correlated quantum systems.