Surface Of Three-dimensional Topological Insulator Research Articles

Nambu-Eliashberg theory for multiscale quantum criticality: Application to ferromagnetic quantum criticality in the surface of three-dimensional topological insulators

We develop an Eliashberg theory for multi-scale quantum criticality, considering ferromagnetic quantum criticality in the surface of three dimensional topological insulators. Although an analysis based on the random phase approximation has been performed for multi-scale quantum criticality, an extension to an Eliashberg framework was claimed to be far from triviality in respect that the self-energy correction beyond the random phase approximation, which originates from scattering with $z = 3$ longitudinal fluctuations, changes the dynamical exponent $z = 2$ in the transverse mode, explicitly demonstrated in nematic quantum criticality. A novel ingredient of the present study is to introduce an anomalous self-energy associated with the spin-flip channel. Such an anomalous self-energy turns out to be essential for self-consistency of the Eliashberg framework in the multi-scale quantum critical point because this off diagonal self-energy cancels the normal self-energy exactly in the low energy limit, preserving the dynamics of both $z = 3$ longitudinal and $z = 2$ transverse modes. This multi-scale quantum criticality is consistent with that in a perturbative analysis for the nematic quantum critical point, where a vertex correction in the fermion bubble diagram cancels a singular contribution due to the self-energy correction, maintaining the $z = 2$ transverse mode. We also claim that this off diagonal self-energy gives rise to an artificial electric field in the energy-momentum space in addition to the Berry curvature. We discuss the role of such an anomalous self-energy in the anomalous Hall conductivity.

Electrically Controllable Surface Magnetism on the Surface of Topological Insulators

We study theoretically the RKKY interaction between magnetic impurities on the surface of three-dimensional topological insulators, mediated by the helical Dirac electrons. Exact analytical expression shows that the RKKY interaction consists of the Heisenberg-like, Ising-like, and Dzyaloshinskii-Moriya (DM)-like terms. It provides us a new way to control surface magnetism electrically. The gap opened by doped magnetic ions can lead to a short-range Bloembergen-Rowland interaction. The competition among the Heisenberg, Ising, and DM terms leads to rich spin configurations and an anomalous Hall effect on different lattices.

Kondo spin screening cloud in two-dimensional electron gas with spin–orbit couplings

A spin-1/2 Anderson impurity in a semiconductor quantum well with Rashba and Dresselhausspin–orbit couplings is studied by using a variational wavefunction method. The localmagnetic moment is found to be quenched at low temperatures. The spin–spincorrelations of the impurity and the conduction electron density show anisotropy inboth spatial and spin spaces, which interpolates the Kondo spin screenings of aconventional metal and of a surface of three-dimensional topological insulators.

Impurity-induced states on the surface of three-dimensional topological insulators

We calculate the modification of the local electronic structure caused by a single local impurity on the surface of a three-dimensional topological insulator. We find that the local density of states around the Dirac point of the electronic spectrum at the surface is significantly disrupted near the impurity by the creation of low-energy resonance state(s)---however, this is not sufficient to (locally) destroy the Dirac point. We also calculate the nontrivial spin textures created near the magnetic impurities and discover anisotropic Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling between them.

Manipulation of the Majorana Fermion, Andreev Reflection, and Josephson Current on Topological Insulators

We study theoretically the transport properties of a normal metal (N)/ferromagnet insulator (FI)/superconductor (S) junction and a S/FI/S junction formed on the surface of a three-dimensional topological insulator, where the chiral Majorana mode exists at the FI/S interface. We find the chiral Majorana mode generated in N/FI/S and S/FI/S junctions is very sensitively controlled by the direction of the magnetization m in the FI region. In particular, the current-phase relation of the Josephson current in S/FI/S junctions has a phase shift of neither 0 nor pi that can be tuned continuously by the component of m perpendicular to the interface.