Towards a microscopic understanding of phonon heat conduction

Heat conduction by phonons is a ubiquitous process that incorporates a wide range of physics and plays an essential role in applications ranging from space power generation to LED lighting. Heat conduction has been studied for over two hundred years, yet many microscopic aspects of heat conduction have remained unclear in most crystalline solids, including which phonons carry heat and how natural and artificial structures scatter specific phonons. Fortunately, recent advances in both computation and experiment are enabling an unprecedented microscopic view of thermal transport by phonons. In this topical review, we provide an overview of these methods, the insights they are providing, and their impact on the science and engineering of heat conduction.