Edge and impurity in condensed matter land

黃文敏(Wen-Min Huang)

指導教授 ： 林秀豪

國立清華大學/理學院/物理學系/博士(2009年)

摘要

In this thesis, we study the response function or electronic properties in condensed matter system with impurities or an edge. It is well-know that the magnetic impurities will induce the Ruderman-Kittel-Kasuya-Yosida exchange coupling, mediated by free itinerant carries. However, it is less study what electronic properties of the itinerant carries will reshape the famous RKKY interaction. Here, we show that the exchange coupling induced by a magnetic impurity depends on the Fermi surface topology of the itinerant carrier in the two-dimensional free electron gases with the Rashba type spin-orbital interaction. By both numeric and analytic methods, we clearly demonstrate that the Fermi surface topology greatly alters the property of mediated exchange coupling in two-dimensional Rashba gas system. In addition, inclusion of finite spin relaxation always makes the non-collinear spiral exchange interaction dominant. Meanwhile, this exploration encourages us to build up a trilayer magnetic junction for application.

Next, switching attention to edge physics. In condensed matter systems, the physical properties at the edge are often tied up with related bulk properties.
Andreev edge state in a superconductor, for instance, is tied up with the pairing symmetry in the bulk. Inspire of that, we study the Andreev edge states with different pairing symmetries and boundary topologies on semi-infinite triangular lattice, and hope to shad light on determining the pairing symmetry of Na$_x$CoO$_2$$cdot y$H$_2$O. By developing a general mapping from the two dimensional lattice to the one dimensional tight-binding model, we show that the phase diagram of the Andreev edge states depends on the pairing symmetry and also the boundary topology. We also compute the momentum-resolved local density of states near the edge which is helpful to predict the hot spots which are measurable in Fourier transformed scanning tunneling spectroscopy.

The general methods also help us to calculate the spin-wave excitation near an edge. Interestingly, we obtain a single branch of relativistic ferromagnetic magnon near the zigzag edge of graphene due to the presence of the open boundary. Note that magnons in antiferomagnets appear in pairs, while the single branch magnon in ferromagnets does not have relativistic dispersion. Thus, the magnon near the zigzag edge of graphene is a hybrid of both, signaling its intrinsic property as a boundary excitation that must be embedded in a higher dimensional bulk system.

In the end, we will focus on the electronic properties in graphene with a point defect. It is generally believed that a point defect in graphene gives rise to an impurity state at zero energy and causes a sharp peak in the local density of states near the defect site. We revisit the defect problem in graphene and find the general consensus incorrect. By both analytic and numeric methods, we show that the contribution to the local density of states from the impurity state vanishes in the thermodynamic limit. Instead, the pronounced peak of the zero-bias anomaly is a power-law singularity $1/|E|$ from infinite resonant peaks in the low-energy regime induced by the defect. Our finding shows that the peak shall be viewed as a collective phenomenon rather than a single impurity state in previous studies.

關鍵字

邊界 ； 磁性 ； 奈米碳片

並列摘要

無資料

並列關鍵字

edge ； impurity ； graphene ； magnetism

參考文獻

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