Superconductivity enhancement on a topological insulator surface by antiferromagnetic squeezed magnons Eirik Erlandsen, Akashdeep Kamra, Arne Brataas, and Asle Sudbø ∗ Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway We study magnon-mediated superconductivity in a heterostructure consisting of a topological insulator and an antiferromagnetic insulator on a bipartite lattice. Our main finding is that one may significantly enhance magnon-mediated superconductivity on the surface of the topological insulator by coupling to only one of the two antiferromagnetic sublattices. Such a sublattice symmetry-breaking coupling considerably strengthens the effective attractive interaction between gapless helical fermions, living on the surface of the topological insulator, compared to the case where the topological insulator couples symmetrically to both sublattices. We provide a general physical picture of this mechanism based on the notion of squeezed bosonic eigenmodes. We also contrast our results to the analogous case of an antiferromagnetic insulator coupled to a normal metal. Introduction. – Hybrids comprised of a magnetic in- sulator coupled to a conducting layer allow for inter- conversion between magnonic and electronic spin cur- rents [1–11]. Spin Hall effect [12, 13] in the conductor has further been exploited to electrically control and de- tect the magnonic spin currents [14], thereby enabling their integration with conventional electronics. The spin- momentum locking in the surface states of a topological insulator (TI) provides a strong chirality [15] and thus, a potentially superior alternative [16] to a spin Hall con- ductor employed towards spin-charge coupling in these hybrids. The ensuing newly gained control over spin currents has instigated a wide range of magnon trans- port based concepts and devices [5, 8, 9, 17–20]. Con- versely, magnons in the magnet can mediate electron- electron attraction in the conducting layer. The result- ing magnon-mediated superconductivity has been inves- tigated both theoretically, in normal metals [21] as well as TIs [22, 23], and experimentally [24]. Interest in antiferromagnets (AFMs) has recently been invigorated [25–27] due to their distinct advantages over ferromagnets (FMs), such as minimization of stray fields, sensitivity to external magnetic noise, and low-energy magnons. The demonstration of electrically-accessible memory cells based on AFMs [28, 29] and spin trans- port across micrometers [20] corroborates their high ap- plication potential. Furthermore, their two-sublattice na- ture allows for unique phenomena [30, 31], such as topo- logical spintronics [32] and strong quantum fluctuations, not accommodated by FMs. AFMs with uncompen- sated interfaces, proven instrumental in exchange bias- ing [33–39] FMs for contemporary memory technology, have been predicted to amplify spin transfer to an adja- cent conductor [40]. Recently, a theoretical proposal for proximity-inducing spin splitting in a superconductor us- ing an uncompensated AFM, along with an experimen- tal feasibility study based on existing literature, has also been put forward [41]. Within the standard theory of boson-mediated super- conductivity [42, 43], the superconducting critical tem- perature T c is determined by an energy scale set by some high-frequency cutoff ω c on the boson-spectrum, the interaction of electrons to these bosons, and the single-particle electronic density of states on the Fermi- surface. The latter two combine to an effective di- mensionless coupling constant λ. In the simplest case, T c = ω c exp ( −1/λ ) . An enhancement of electron- phonon coupling, possibly in a feedback loop involving strong correlation effects, typically results in an enhance- ment of Tc [44]. In the context of magnon-mediated superconductivity, an amplification of electron-magnon coupling should result in an analogous enhancement of T c . In this Letter, we theoretically demonstrate a dras- tically increased, attractive, magnon-mediated electron- electron interaction, exploiting the two-sublattice nature of, and squeezing-mediated strong quantum fluctuations in, an AFM [45]. We study the case where a TI can couple either equally or differently to the two sublattices of an AFM insulator (AFMI), as depicted in Fig. 2, and find a significant enhancement of the attractive interac- tion in the latter case. This enhancement appears through magnon coherence factors acting constructively, instead of destructively as they do in the case of equal coupling to both sublattices. These magnon coherence factors, u k FIG. 1. Representation of a spin-up antiferromagnetic squeezed magnon. The squeezed excitation is a coherent superposition of states with N+1 spin-up and N spin-down magnons. Each of the constituent states possesses unit net spin, but varies in its spin content on each sublattice thereby resulting in strong quantum fluctuations. arXiv:1903.01470v1 [cond-mat.supr-con] 4 Mar 2019