Curvature-Induced Electrical Properties of Two-Dimensional Electrons on Carbon Nanotube Springs

This study investigates the mechanisms driving current flow in carbon nanotube (CNT) springs under mechanical strain, addressing the critical gap between experimental observations and theoretical modeling, particularly in asymmetric electrical responses. Leveraging the Dirac equation in curved spacetime, we analyze how curvature-induced scalar and pseudo-gauge potentials shape the behavior of two-dimensional electron gases confined to the curved surfaces of CNT springs. By incorporating time-dependent variations in the Lamé coefficient and curvature parameter, we propose an adiabatic evolution model to characterize strain-induced electronic behavior and develop an equivalent circuit model linking mechanical deformation to electronic dynamics. The analysis reveals asymmetric electrical responses, including time-dependent currents during stretching and compression cycles, driven by curvature-induced vector potential variations. Fourier analysis uncovers frequency components and phase relationships that explain these asymmetries. Theoretical predictions are validated against experimental data, highlighting curvature-driven energy band shifts, enhanced power output during stretching phases (peaking near 100 Hz), and a proportional relationship between strain and charge storage. These results not only provide a comprehensive theoretical framework for understanding strain-modulated electronic behavior but also underscore the potential of CNT springs in energy harvesting, wearable electronics, and advanced sensing applications. By bridging experimental observations and modeling, this study establishes a foundation for optimizing CNT springs in next-generation electromechanical systems.