RKKY coupling in Weyl semimetal thin films

Abstract

We consider the effective coupling between impurity spins on surfaces of a thin-film Weyl semimetal within Ruderman-Kittel-Kasuya-Yoshida (RKKY) theory. If the spins are on the same surface, their coupling reflects the anisotropy and the spin-momentum locking of the Fermi arcs. By contrast when the spins are on opposite surfaces, their coupling is mediated by the Fermi arcs as well as by bulk states. In this case the coupling is both surprisingly strong and strongly thickness dependent, with a maximum at an optimum thickness. We demonstrate our results using analytical solutions of states in the thin-film geometry, as well using a two-surface recursive Green's function analysis of the tight-binding model.

Signatures of interfacial topological chiral modes via RKKY exchange interaction in Dirac and Weyl systems

“…In recent times, a few proposals have been put forwarded to extract the contributions of the Fermi arcs which appear across the interface between the WSM and vacuum via RKKY exchange interaction [48,76]. The contributions of the bulk states are inevitably present in those studies when the impurities are located at two opposite surfaces.…”

“…It is an indirect exchange interaction mediated by the conduction electrons of the host material and already investigated extensively in different Dirac materials [33][34][35][36][37][38][39], topological insulators [40], etc. RKKY exchange interaction has also been proposed to determine the magnetic ordering in spin glasses [41] and alloys [42] and to probe topological phase in silicene [43], edge states of graphene nanoribbon [44] and 2D topological insulators [45], decoupled edge modes in phosphorene [46], order of tilting in the spectrum of borophene [47] and the Fermi arc in WSM thin films [48], etc. Several experimental methods like single-atomic magnetometry and magnetotransport measurement based on angle-resolved photoemission spectroscopy (ARPES) are used to capture this exchange interaction [49][50][51].…”

Dipolar optical plasmon in thin-film Weyl semimetals

“…If one retains one block each of the form H η=+ and H η=− , which are time-reversal partners, together they serve as a four band model for a DSM. For a slab geometry with a finite thickness L along the z direction, the electronic states from these Hamiltonians can be obtained by imposing appropriate boundary conditions on the surfaces [20] (see details in the Appendix). The resulting energy bands are indexed by n = ±1, ±2 • • • (± for positive and negative energy bands), for each η sector.…”

“…The WSM/DSM slab is confined between z = 0 and z = L. Following ref. 20 of the main text, we infinite mass boundary conditions by taking the Hamiltonian of the vacuum to be same as Eq. (A26), except for the mass term, whose form is taken to be M vac η = ηm 0 , with m 0 → ∞.…”

“…In contrast to thick systems, where electrons on different surfaces have negligible influence on one another, geometries of these systems with large surface-to-volume ratios, specifically slabs, offer a platform in which the surface states are influential and induce novel properties. For a thin-film geometry, which is the primary focus of our work, FA states of opposite surfaces can no longer be treated individually and the low-energy Fermi surface, in the two dimension, interpolates states predominantly supported by the two surfaces and the bulk [20]. This intertwining of surface and bulk states raises questions on the nature of the collective modes that these materials can support, how they differ between Dirac and the Weyl semimetals, and how both differ from analogous conventional conducting systems.…”