| 摘要: | 在這次計畫裡，我們想藉由曲面上的物理來研究: (1) 量子力學形式的力; (2) 在凝態物理中一些新穎或是經改變後的物理性質。在尚未透過實驗驗證之前，得益於現在各式各樣的物理系統出現，我們可以先利用這些平台來測試我們的理論。這些平台包括: 拓樸絕緣體 (以及其他拓樸材料，例如: Weyl 和 Dirac), 石墨烯 (以及其他有相對論特性相關的二維材料，例如: silicene 和 MoS2), 自旋電子學(包括其他磁性系統), 激發態系統 (plasmon, magnon 和 BEC 凝聚)。我們之前已經有利用規範理論來進行研究並且發現在平坦空間上新的物理現象, 例如:在2007年時我們發現自旋軌道自旋力矩, 發展出自旋力的概念以及預測出自旋霍爾導率中的必要修正。之後我們將會把這些理論拓展到自旋電子學、磁性以及拓樸材料或元件中的曲面系統。另一方面, 我們先前也利用過規範理論和一些普遍的量子力學方法來研究二維系統, 像是石墨烯。從先前的研究顯示, Berry 曲率會造成平坦空間上一些物理性質改變, 所以我們合理猜測相應產生的曲率 (能帶結構包含奈米尺度下的曲率) 會造成曲面系統上出現新穎的物理現象或是物理性質上的改變。我們認為奈米尺度下的曲面空間的效應可以等效於有一個很大的力作用在微小的物體上，這意味著這樣大的力是可以在奈米尺度間的物體互相轉換的。當有許多微小粒子, 例如說電子, 可以輕易地被傳輸時, 有可能這樣大的作用力或者壓力在微小空間中可以被傳遞。我們認為奈米尺度下彎曲面中的物理是和研究重力中的彎曲空間是相當的。這樣額外的力出現並不只影響到系統的力學性質, 其中意味的某些系統上物理性質也會隨之改變, 而這些物理性質可為: 電導率、介電性質、霍爾效應。事實上, 除了以上的改變之外, 這樣奈米尺度的曲率也會產生出新的物理量, 例如: 拓樸有序參數。對於未來的科技而言, 能發現出新的參數又或者是得出某些經改變後的參數是非常重要的事情。舉凡來說, 因為曲率而修正過的自旋力矩, 磁性異向性和自旋霍爾效應都會進一步的改良 MRAM 或者是使其有更多的功能。經修正後的介電性質會產生出新的表面 plasmon 或者 BEC 凝聚的行為。
In this project, we want to harness the physics of curved-space to study the physics of (1) Quantum mechanical forces, and (2) New or modified physical properties, in quantum condensed matter systems. We have the benefit of a variety of modern platforms on which this theory can be tested, on the theoretical level, which means at practically no experimental cost. The platforms encompass topological insulator (and other forms of topological materials like Weyl & Dirac), graphene (and other related relativistic 2D systems like silicene, MoS2), spintronics (and other magnetic systems), excited systems (plasmon, magnon, and their BEC condensates). We have used the gauge theoretical approach to study and discover new physical phenomena in flat space systems, e.g. we discovered spin orbit spin torque in 2007, developed the concept of spin forces, and predicted a necessary modification to the spin Hall conductivity. We would extend these theories to curved systems in the spintronic, magnetic and topological materials or devices. On the other hand, we had also studied 2D systems like graphene, using both gauge theoretic and ordinary quantum mechanics approaches. As previous efforts have shown that Berry curvature could lead to modifications of physical properties in flat space systems, we set vision on the possibility that a concomitant (hybrid) curvature (band-structure and nanoscale curve) could lead to the discovery or new or modified physical quantities in curved systems. We conceive that curved space on the nanoscale translates to large forces on small objects, and in small settings. This means that large forces can be transmitted on the scale of nanometer distances between objects. As small particles like electrons exist in abundance, and can be transported easily, potentially very large forces or pressures can be transmitted within very small spaces. We consider nanoscale curved structures and the physics therein equivalent to the curved space in the study of gravity. As the surface or line curvature depends in strength on the "degree" of curve on the surface - no theoretical constrain is placed on the strength of the forces that can be produced. This implies that potentially large mechanical impacts arising from electronic physics can be realized. We foresee future commercial applications of this research in vehicles, engines, or robotic systems that require precise and strong mechanical forces to operate. The generation of such precise forces will be energy-efficient, and produces low (no) heat. The effect of new forces are not necessarily restricted to mechanical deployment downright. The emergence of new forces also means many physical properties of readily understood systems will be modified. e.g. conductivity, dielectric properties, Hall effects. In fact, beyond just modifications, nanoscale curve might lead to new physical quantities like a topological order parameter. Discovery of new or modified quantities are important for future technologies. For example, curved-modified spin torque, magnetic anisotropy, spin Hall could lead to MRAM with improved or new functionalities. Modified dielectric properties could lead to new surface plasmon or BEC condensate behavior. |
