Anisotropic RKKY interactions mediated by $j=3/2$ quasiparticles in half-Heusler topological semimetal

Abstract

We theoretically explore the RKKY interaction mediated by spin-3/2 quasiparticles in half-Heusler topological semimetals in quasi-two-dimensional geometries. We find that while the Kohn-Luttinger terms gives rise to generalized Heisenberg coupling of the form ${\mathcal{H}}_{\mathrm{RKKY}}\propto {\sigma }_{1,i}{\mathcal{I}}_{ij}{\sigma }_{2,j}$ with a symmetric matrix ${\mathcal{I}}_{ij}$, addition of small antisymmetric linear spin-orbit coupling term leads to Dzyaloshinskii-Moriya (DM) coupling with an antisymmetric matrix ${\mathcal{I}}_{ij}^{\prime }$. We demonstrate that besides the oscillatory dependence on the distance, all coupling strengths strongly depend on the relative orientation of the two impurities with respect to the lattice. This yields a strongly anisotropic behavior for ${\mathcal{I}}_{ij}$ such that by only rotating one impurity around another at a constant distance, we can see further oscillations of the RKKY couplings. This unprecedented effect is unique to our system which combines spin-orbit coupling with strongly anisotropic Fermi surfaces. We further find that all of the RKKY terms have two common features: a tetragonal warping in their map of spatial variations, and a complex beating pattern. Intriguingly, all these features survive in all dopings and we see them in both electron- and hole-doped cases. In addition, due to the lower dimensionality combined with the effects of different spin-orbit couplings, we see that only one symmetric off-diagonal term, ${\mathcal{I}}_{xy}$ and two DM components ${\mathcal{I}}_{xz}^{\prime }$ and ${\mathcal{I}}_{yz}^{\prime }$ are nonvanishing, while the remaining three off-diagonal components are identically zero. This manifests another drastic difference of RKKY interaction in half-Heusler topological semimetals compared to the electronic systems with spin-1/2 effective description.

arXiv comment12 pages, 4 figures

References in corpus (50)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• First observation of Spin-Momentum Helical Locking in Bi2Se3 and Bi2Te3, demonstration of Topological-Order at 300K and a realization of topological-transport-regime
• Dilute ferromagnetic semiconductors: Physics and spintronic structures
• Tunable Multifunctional Topological Insulators in Ternary Heusler Compounds
• A new platform for topological quantum phenomena : Topological Insulator states in thermoelectric Heusler-related ternary compounds
• Magnetic impurities on the surface of a topological insulator
• Topological Superconductivity and Majorana Fermions in RKKY Systems
• Topological superconducting phase in helical Shiba chains
• The development of ferromagnetism in the doped topological insulator Bi2-xMnxTe3
• Interplay between classical magnetic moments and superconductivity in quantum one-dimensional conductors: toward a self-sustained topological Majorana phase
• Half-Heusler Compounds as a New Class of Three-Dimensional Topological Insulators
• Heusler, Weyl, and Berry
• Electrically controllable surface magnetism on the surface of topological insulator
• Superconductivity in the topological semimetal YPtBi
• RKKY Interaction in Graphene from Lattice Green's Function
• Ordering of magnetic impurities and tunable electronic properties of topological insulators
• RKKY coupling in graphene
• Twisted exchange interaction between localized spins embedded in a one- or two-dimensional electron gas with Rashba spin-orbit coupling
• Superconductivity in the noncentrosymmetric half-Heusler compound LuPtBi : A possible topological superconductor
• Beyond Triplet: Unconventional Superconductivity in a Spin-3/2 Topological Semimetal
• RKKY Interaction in Graphene Calculated Following Ruderman and Kittel
• RKKY interaction in graphene
• Pairing of j=3/2 fermions in half-Heusler superconductors
• Majorana states in helical Shiba chains and ladders
• RKKY interaction of magnetic impurities in Dirac and Weyl semimetals
• Indirect RKKY interaction in any dimensionality
• Helical order in one-dimensional magnetic atom chains and possible emergence of Majorana bound states
• Superconductivity in three-dimensional spin-orbit coupled semimetals
• RKKY interaction in carbon nanotubes and graphene nanoribbons
• Topological superconductivity of spin-3/2 carriers in a three-dimensional doped Luttinger semimetal
• Pairing states of spin-3/2 fermions: Symmetry-enforced topological gap functions
• Inflated nodes and surface states in superconducting half-Heusler compounds
• Ruderman-Kittel-Kasuya-Yosida interaction in Weyl semimetals
• Magnetic Ordering of Nuclear Spins in an Interacting 2D Electron Gas
• RKKY interaction in three-dimensional electron gases with linear spin-orbit coupling
• Low-energy theory and RKKY interaction for interacting quantum wires with Rashba spin-orbit coupling
• Fingerprints of tilted Dirac cones on the RKKY exchange interaction in 8-Pmmn Borophene
• RKKY interaction in SDW phase of iron-based superconductors
• Electrically-controllable RKKY interaction in semiconductor quantum wires
• Evolution of the multiband RKKY interaction: Application to iron pnictides and chalcogenides
• Interface symmetry and spin control in topological insulator-semiconductor heterostructures
• Interlayer RKKY Coupling in Bulk Rashba Semiconductors under Topological Phase Transition
• Exporting superconductivity across the gap: Proximity effect for semiconductor valence-band states due to contact with a simple-metal superconductor
• RKKY interaction induced by two-dimensional hole gases
• RKKY interaction in Mn-doped 4 $\times$ 4 Luttinger systems

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