Theory of Composite Fermions

本基金支持量子霍尔效应的研究。大约十年前，这位PI提出了复合费米子的概念，它是由一个电子和偶数个通量量子组成的复合物，当一层中的电子受到强磁场作用时形成。独立的复合费米子气体是对分数量子霍尔效应和半填充朗道能级附近费米海的物理理解的概念基础。为了结合复合费米子之间相互作用的影响，该PI开发了一种基于波函数的方法，该方法已经成功地为几个实验提供了见解。在目前的资助期内，他计划进一步建设。特别是，他计划探索独立的复合费米子图像分解和不稳定性产生的条件。他想研究低密度电子（没有任何磁场）的复合费米子不稳定性对铁磁性的对应，这是70年前由布洛赫首次讨论的。当一层电子受到高磁场时，它们的运动变得强相关，并导致整数和分数量子霍尔效应。大约十年前，这个PI提出了一个简单而深刻的框架，称为复合费米子，来描述与分数量子霍尔效应相关的特性。在过去的十年里，这个概念装置在理解实验结果方面取得了巨大的成功，并帮助发展了洞察力和直觉。目前的拨款以一种新的方式进行：虽然过去的研究仅限于自由复合费米子，但这种观点何时会失效，当失效时发生了什么，之后又会发生什么？＊＊＊

This grant supports work on quantum Hall effect. Nearly a decade ago, this PI proposed the notion of composite fermions, objects which are complexes consisting of an electron and an even number of flux quanta, formed when electrons in a layer are subjected to intense magnetic fields. A gas of independent composite fermions is the conceptual foundation underneath a physical understanding of fractional quantum Hall effect as well as the Fermi sea in the vicinity of a half-filled landau level. To incorporate effects of interaction between the composite fermions this PI has developed a wavefunction based approach, which has been successful in providing insight into several experiments. In the current grant period, he plans to build further. In particular, he plans to explore the conditions where the independent composite fermion picture breaks down and instabilities set in. He wants to study the composite fermion counterpart of instability towards ferromagnetism in low-density electrons (without any magnetic field), which was first discussed by Bloch seventy years ago.%%%When a layer of electrons is subjected to high magnetic fields, their motion becomes strongly correlated and leads to integer and fractional quantum Hall effects. Some ten years ago, this PI proposed a simple, insightful framework, called composite fermions, to describe the properties associated with fractional quantum Hall effect. Over the past ten years, this conceptual device has been immensely successful in understanding experimental results and has helped develop insight and intuition. The current grant proceeds with a new twist: while the past studies have been limited to free composite fermions, when does this view break down, what happens when the breakdown occurs and what happens afterwards?***