We investigate the effect of spin-orbit coupling on the behavior of magnetic impurity at the edge of a zigzag graphene ribbon by means of quantum Monte Carlo simulations. A peculiar interplay of Kane-Mele type spin-orbit and impurity-host coupling is found to affect local properties such as the impurity magnetic moment and spectral densities. The special helical nature of the topological insulator on the edge is found to affect nonlocal quantities, such as the two-particle and spin-spin correlation functions linking electrons on the impurity with those in the conduction band.
Based on the first-principles calculations and theoretical analysis, we investigate the electronic structures, topological phase transition (TPT) and topological properties of layered magnetic compound MnSb2Te4. It has the similar crystal and magnetic structure as the magnetic topological insulator MnBi2Te4. We find that when the spin-orbit coupling (SOC) is considered, the band structure of MnSb2Te4 in antiferromagnetic (AFM) state has no band inversion at {Gamma}. This is due to the SOC strength of Sb is less than that of Bi. The band inversion can be realized by increasing the SOC of Sb by 0.3 times, which drives MnSb2Te4 from a trivial AFM insulator to an AFM topological insulator (TI) or axion insulator. Uniaxial compressive strain along the layer stacking direction is another way to control the band inversion. The interlayer distance shorten by 5% is needed to drive the similar TPT. For the ferromagnetic (FM) MnSb2Te4 with experimental crystal structure, it is a normal FM insulator. The band inversion can happen when SOC is enhanced by 0.1 times or the interlayer distance is decreased by more than 1%. Thus, FM MnSb2Te4 can be tuned to be the simplest type-I Weyl semimetal with only one pair of Weyl nodes on the three-fold rotational axis. These two Weyl nodes are projected onto (1-10) surface with one Fermi arc connecting them.
Whereas there exists considerable evidence for the conversion of singlet Cooper pairs into triplet Cooper pairs in the presence of inhomogeneous magnetic fields, recent theoretical proposals have suggested an alternative way to exert control over triplet generation: intrinsic spin-orbit coupling in a homogeneous ferromagnet coupled to a superconductor. Here, we proximity-couple Nb to an asymmetric Pt/Co/Pt trilayer, which acts as an effective spin-orbit coupled ferromagnet owing to structural inversion asymmetry. Unconventional modulation of the superconducting critical temperature as a function of in-plane and out-of- plane applied magnetic fields suggests the presence of triplets that can be controlled by the magnetic orientation of a single homogeneous ferromagnet. Our studies demonstrate for the first time an active role of spin-orbit coupling in controlling the triplets -- an important step towards the realization of novel superconducting spintronic devices.
By using the cluster perturbation theory, we investigate the effects of the local electron-phonon interaction in the quantum spin Hall topological insulator described by the half-filled Kane-Mele model on an honeycomb lattice. Starting from the topological non trivial phase, where the minimal gap is located at the two inequivalent Dirac points of the Graphene, $text{K}$ and $text{K}$, we show that the coupling with quantum phonons induces a topological-trivial quantum phase transition through a gap closing and reopening in the $text{M}$ point of the Brillouin zone. The average number of fermions in this point turns out to be a direct indicator of the quantum transition pointing out a strong hybridization between the two bare quasiparticle bands of the Kane-Mele model. By increasing the strength of charge-lattice coupling, the phonon Greens propagator displays a two peak structure: the one located at the lowest energy exhibits a softening that is maximum around the topological transition. Numerical simulations provide also evidence of several kinks in the quasiparticle dispersion caused by the coupling of the electrons with the bosonic lattice mode.
Quantum states induced by single-atomic-impurities are the current frontier of material and information science. Recently the spin-orbit coupled correlated kagome magnets are emerging as a new class of topological quantum materials, although the effect of single-atomic impurities remains unexplored. Here we use state-of-the-art scanning tunneling microscopy/spectroscopy (STM/S) to study the atomic indium impurity in a topological kagome magnet Co3Sn2S2, which is designed to support the spin-orbit quantum state. We find each impurity features a strongly localized bound state. Our systematic magnetization-polarized tunneling probe reveals its spin-down polarized nature with an unusual moment of -5uB, indicative of additional orbital magnetization. As the separation between two impurities progressively shrinks, their respective bound states interact and form quantized molecular orbital states. The molecular orbital of three neighboring impurities further exhibits an intriguing splitting owing to the combination of geometry, magnetism, and spin-orbit coupling, analogous to the splitting of the topological Weyl fermion line12,19. Our work demonstrates the quantum-level interplay between magnetism and spin-orbit coupling at an individual atomic impurity, which provides insights into the emergent impurity behavior in a topological kagome magnet and the potential of spin-orbit quantum impurities for information science.
Recent theoretical studies of topologically nontrivial electronic states in Kondo insulators have pointed to the importance of spin-orbit coupling (SOC) for stabilizing these states. However, systematic experimental studies that tune the SOC parameter $lambda_{rm{SOC}}$ in Kondo insulators remain elusive. The main reason is that variations of (chemical) pressure or doping strongly influence the Kondo coupling $J_{text{K}}$ and the chemical potential $mu$ -- both essential parameters determining the ground state of the material -- and thus possible $lambda_{rm{SOC}}$ tuning effects have remained unnoticed. Here we present the successful growth of the substitution series Ce$_3$Bi$_4$(Pt$_{1-x}$Pd$_x$)$_3$ ($0 le x le 1$) of the archetypal (noncentrosymmetric) Kondo insulator Ce$_3$Bi$_4$Pt$_3$. The Pt-Pd substitution is isostructural, isoelectronic, and isosize, and therefore likely to leave $J_{text{K}}$ and $mu$ essentially unchanged. By contrast, the large mass difference between the $5d$ element Pt and the $4d$ element Pd leads to a large difference in $lambda_{rm{SOC}}$, which thus is the dominating tuning parameter in the series. Surprisingly, with increasing $x$ (decreasing $lambda_{rm{SOC}}$), we observe a Kondo insulator to semimetal transition, demonstrating an unprecedented drastic influence of the SOC. The fully substituted end compound Ce$_3$Bi$_4$Pd$_3$ shows thermodynamic signatures of a recently predicted Weyl-Kondo semimetal.
F. M. Hu
,T. O. Wehling
,J. E. Gubernatis
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(2013)
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"Magnetic Impurity Affected by Spin-Orbit Coupling: Behavior near a Topological Phase Transition"
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Feiming Hu
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