Understanding the fundamental link between structure and functionalization is
crucial for the design and optimization of functional materials, since
different structural configurations could trigger materials to demonstrate
diverse physical, chemical, and electronic properties. However, the correlation
between crystal structure and thermal conductivity (\k{appa}) remains
enigmatic. In this study, taking two-dimensional (2D) carbon allotropes as
study cases, we utilize phonon Boltzmann transport equation (BTE) along with
machine learning force constant potential to thoroughly explore the complex
folding structure of pure sp2 hybridized carbon materials from the perspective
of crystal structure, mode-level phonon resolved thermal transport, and atomic
interactions, with the goal of identifying the underlying relationship between
2D geometry and \k{appa}. We propose two potential structure evolution
mechanisms for targeted thermal transport properties: in-plane and out-of-plane
folding evolutions, which are generally applicable to 2D carbon allotropes. It
is revealed that the folded structure produces strong symmetry breaking, and
simultaneously produces exceptionally strongly suppressed phonon group
velocities, strong phonon-phonon scattering, and weak phonon hydrodynamics,
which ultimately lead to low \k{appa}. The insight into the folded effect of
atomic structures on thermal transport deepens our understanding of the
relationship between structure and functionalization, which offers
straightforward guidance for designing novel nanomaterials with targeted
\k{appa}, as well as propel developments in materials science and engineering