Superparamagnetism-induced mesoscopic electron focusing in topological insulators

Abstract

1 arXiv:1602.03902v1 [cond-mat.mes-hall] 11 Feb 2016 AbstractThe particle-wave duality sets a fundamental correspondence between optics and quantum mechanics. Within this framework, the propagation of quasiparticles can give rise to superposition phenomena which, like for electromagnetic waves, can be described by the Huygens principle. However, the utilization of this principle by means of propagation and manipulation of quantum information is limited by the required coherence in time and space. Here we show that in topological insulators, which in their pristine form are characterized by opposite propagation directions for the two quasiparticles spin channels, mesoscopic focusing of coherent charge density oscillations can be obtained at large nested segments of constant-energy contours by magnetic surface doping. Our findings provide evidence of strongly anisotropic Dirac fermion-mediated interactions. Even more remarkably, the validity of our findings goes beyond topological insulators but applies for systems with spin-orbit-lifted degeneracy in general. It demonstrates how spin information can be transmitted over long distances, allowing the design of experiments and devices based on coherent quantum effects in this fascinating class of materials. 2Coherence is a general property of waves as it describes the capability of keeping a welldefined phase relation while propagating in space and time. Because of the particle-wave duality, which lays at the very foundations of quantum mechanics, the same concept can also be applied to quasiparticles in solids. Quantum coherence is of fundamental importance since it sets the limits up to which information can be transmitted and processed with high fidelity. With the invention of the scanning tunneling microscope it became possible to visualize coherent phenomena in real space by imaging the standing wave pattern produced by scattering events around individual atomic-scale defects [1]. In analogy with electromagnetic waves these results can be interpreted within the Huygens principle. It describes the interference pattern which results from the superposition of waves propagating along all different paths and can be theoretically elegantly expressed by using the quantum-mechanical propagator.The further development of atomic-scale manipulation techniques allowed to engineer these properties at the atomic scale. This capability was used for the creation of exotic effects such as quantum mirages [2], for the extraction of the phase of electron wave functions to analyze how propagating waves in solids are influenced by the periodic potential of the crystal lattice. In particular, it has been shown that the propagation of quasiparticle waves can become anisotropic when the shape of a constant-energy cut (CEC) deviates from an isotropic contour. In analogy to optics, focussing and defocussing lead to an enhanced intensity along certain crystallographic directions and to partial or even complete suppression along others, respectively [5]. However, despite its relevance in s...

Towards microscopic control of the magnetic exchange coupling at the surface of a topological insulator

“…This happens because the synergistic effect of electron-doping by the magnetic adatoms and exchange interaction among them enhances, only in a restricted Mn coverage range, the ferromagnetic exchange mediated by the topological state, thus stabilizing a large effective magnetization. This, in turn, is one of the necessary conditions, together with the characteristic hexagonal warping of the constant energy contours of topological insulators, to achieve the transmission of spin information over long distances, as previously observed [35]. In the case of Co, on the other hand, the AFM exchange mechanisms dominating in the coverage range of predominantly individual adatoms lead to low effective moments, unable to open intense backscattering channels [40].…”

“…We find that the oscillation periods in the GM and GK directions are compatible with the back-scattering vectors q 1 and q 2 , respectively, on the Fermi surface, shown in figure 1(d). A third vector q 3 in the GM-direction, connecting the Fermi surface snowflake tip-to-tip, is expected to play only a minor role because of the large curvature of the tip (flat segments of the Fermi surface produce longer-reaching coherent waves and thus longer-reaching interactions [35]).…”

“…The topological insulator Bi 2 Te 3 shows furthermore a particularly strong hexagonal warping of its topological surface state [34]. This causes a focusing effect [35] which can be exploited to enhance the interaction strength at large distances in certain crystallographic directions. Moreover, avoiding doping of the bulk potentially facilitates the realization of bulk insulating samples, which is one of the major challenges TI materials face on their way towards technological application.…”

Electron refraction at lateral atomic interfaces

“…20 Moreover, our model system is fully metallic, and hence, inelastic contributions from the underlying substrate would potentially screen surface effects, adding up to the strong scattering of surface electrons by defects that are commonly present even in well-cleaned surfaces. In this context, topological insulators seem to fulfill all SSNE prerequisites, 26 being insulators and hosting spin-polarized robust surface states. Research in 2D and 3 D topological insulators is rapidly progressing, and hence, a variety of featured CESs that match different analogues of optics phenomena could be explored.…”

The focusing effect of electron flow and negative refraction in three-dimensional topological insulators

“…One is the opposite dispersions in the conduction band and valence band, the other is the nearly transparent PNJ. In principle, besides massless Dirac fermions, [10,11] all gapless semi-metals and topological materials [12,13] described by the quadratic massive Dirac equation in 2D or beyond 2D, such as the 3D topological insulator (TI), are expected to have the same effect. Considering the helical resolved characteristics of the TI materials, the focusing effect in TIs can have great potential in the applications of helicity-based electronic optics [12].…”