低维材料不断涌现的新奇性质吸引着科学研究者的目光. 除了电子的量子输运行为之外, 人们也陆续发现和确认了热输运中显著的量子行为,如热导低温量子化、声子子带、尺寸效应、瓶颈效应等. 这些小尺度体系的热输运性质可以很好地用非平衡格林函数来描述. 本文首先介绍了量子热输运的特性、声子非平衡格林函数方法及其在低维纳米材料中的研究进展; 其次回顾了近年来在一系列低维材料中发现的热-自旋输运现象.这些自旋热学现象展现了全新的热电转换机制, 有助于设计新型的热电转换器件, 同时也给出了用热产生自旋流的新途径; 最后介绍了线性响应理论以及在此理论框架下结合声子、电子非平衡格林函数方法进行的一些有益的探索. 量子热输运的研究对热效应基础研究以及声子学器件、能量转换器件的发展有着不可替代的重要作用.%Emerging novel properties of nanomaterials have been attracting attention. Besides quantum electronic transport properties, the breakdown of classical Fourier's law and other significant quantum thermal behaviors such as quantized thermal conductance, phonon subbands, size effects, the bottleneck effect, and even interaction between heat and spin degrees of freedom have also been revealed over the past two decades. These phenomena can be well captured by the nonequilibrium Green's function (NEGF) method, which is pretty simple under ballistic or quasi-ballistic regimes. In this review, we mainly focus on two aspects: quantum phonon transport and thermal-spin transport in low-dimensional nanostructures. First, we present a brief history of researches on thermal transport in nanostructures, summarize basic characteristics of quantum thermal transport, and then describe the basic algorithm and framework of the phonon NEGF method. Compared with other methods, the NEGF method facilitates numerical calculations and can systematically incorporate quantum many-body effects. We further demonstrate the power of phonon NEGF method by recent research progress: from the phonon NEGF method, distinct behaviors of phonon transport compared with those of electrons, intrinsic anisotropy of phonon transport, radial strain within elastic regime as quantum perturbation, two kinds of interfacial transport behaviors, defect-induced localization of local phonon density of states, unobservable phonon local-ization, etc, have been discovered in some particular low-dimensional nanomaterials or nanostructures. Second, the new concept of "spin caloritronics", which is devoted to the study of thermally induced spin-related transport in magnetic systems and offers a brand-new way to realize thermal-spin or thermoelectric energy conversion, is also introduced. After concisely discussing the spin Seebeck effect, spin-dependent Seebeck effect, and magneto-Seebeck effect, we present the linear response theory with spin degree of freedom and show that by combining with linear response theory, NEGF method is also applicable for studying spin caloritronics, especially spin thermoelectrics. Finally, recent research on quantum dot models or numerical calculation of real materials give hints to the searching for high-ZT materials. With the ever-increasing demand for energy and increasing power density in highly integrated circuits, quantum thermal trans-port properties are not only of fundamental interest, but also crucial for future developing electronic devices. Relevant researches also pave the way to spin thermoelectrics, which has vast potential in thermoelectric spintronic devices and energy harvesting.
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