RKKY interaction on surfaces of topological insulators with superconducting proximity effect

Abstract

We consider the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities on the surface of a three-dimensional topological insulator with proximity induced superconductivity. A superconductor placed on the top of the topological insulator induces a gap in the surface electron states and gives rise to a long-ranged in-plane antiferromagnetic RKKY interaction. This interaction is frustrated due to strong spin-orbit coupling, decays as 1/r for r < ξ, where r is the distance between two magnetic impurities and ξ the superconducting coherence length, and dominates over the ferromagnetic and Dzyaloshinskii-Moriya type interactions for r > ξ. We find the condition for the Yu-Shiba-Rusinov intragap states that are bound to the magnetic impurities. Motivated by the intense research on the interplay of topological insulators (TI), magnetism, [10][11][12][13][14][15][16][17][18], and superconductivity [1,19,20], we study here the RKKY interaction between magnetic impurities (localized spins) on the surface of a three-dimensional TI with proximity induced superconductivity, see Fig. 1. The effect of strong spin-orbit interaction at the surface of a TI on the RKKY interaction without superconductivity is well-studied theoretically [10][11][12][13][14][15]. If the system is at the charge neutrality point, i.e., the chemical potential is at the Dirac point, it is predicted that the localized spins can form a ferromagnetic order with magnetization pointing normal to the surface of the TI, if the out-of-plane anisotropy of the RKKY interaction is stronger than the in-plane one. Out-of-plane ferromagnetic order breaks time-reversal symmetry and opens energy band gaps in the surface states. On the other hand, the in-plane interaction is frustrated. It may result in a spin-glass state [21,22] if the in-plane anisotropy is stronger than the out-of plane one [14].The effect of magnetic impurities deposited on the surface of a TI on the band gap and the resulting magnetic order is under experimental debate [23][24][25][26][27][28][29][30]. Alternatively, the locally induced electronic spin density can be measured by NV-center atomic force microscope tips, allowing one to experimentally probe the spin-spin correlations independently of the magnetic impurities on the surface [31]. The method of spin-polarized scanning tunneling microscope for probing the surface magnetic properties of TI is well established experimentally [30].In the present paper, we consider an s-wave superconductor placed on the surface of a three-dimensional TI. The proximity effect can lead to a gap in the density

RKKY interaction on the surface of three-dimensional Dirac semimetals

“…At low chemical potentials, such that |µx|/v < 1, the RKKY interaction has a negative sign, and thus favors a ferromagnetic alignment of spins. This result is reminiscent of the interaction between two magnetic impurities on the surface of a topological insulator [8][9][10][11][12][13][14][15].…”

“…Since the mid-twentieth century it has been understood that localized spins in metals can interact by means of the Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism [1][2][3]. This indirect exchange coupling is mediated by the conduction electrons and has been investigated in materials of different nature such as disordered metals [4], superconductors [5][6][7], topological insulators [8][9][10][11][12][13][14][15], graphene [16][17][18][19][20], carbon nanotubes [21,22], and semiconducting wires [23].…”

Anisotropic ferroelectric distortion effects on the RKKY interaction in topological crystalline insulators

“…Based on a self-consistent calculation on the surface spectrum of TIs, the structure of RKKY interaction is preserved in the presence of the gap induced by exchange field of magnetic impurities, nevertheless, its strength is considerably suppressed 45 . It should be mentioned that the RKKY interaction is also calculated inside the gap energies of TI induced by proximity of a superconductor on top of TI surface 46 . Furthermore, RKKY interaction is relevant in the presence of local gaps induced by doped magnetic impurities on the surface of TI 47 .…”

Non-Hermitian indirect exchange interaction in a topological insulator coupled to a ferromagnetic metal

“…Indirect exchange interaction between magnetic impurities mediated by carriers of host material, known as Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction 32 – 34 has been investigated in systems having definite chirality, such as graphene 35 – 44 , 3D topological insulators 45 – 47 , topological crystalline insulators 48 , 49 , and Weyl quasi-particles 50 , 51 . The effects of superconducting correlations 52 , temperature, and Zeeman field 53 on the RKKY interaction have also been explored in topological insulators. However, the study is still lacking as far as the signature of non-hermiticity in magnetic indirect interaction is concerned.…”