Proximity effect and p-wave superconductivity in s-wave superconductor/helimagnet heterostructures

TL;DR

This work analyzes proximity effects in atomically thin SC/HM bilayers where helimagnetism preserves superconductivity and induces $p$-wave triplet correlations. Using a 2D tight-binding model and Green's function techniques, the authors quantify the self-consistent suppression of $s$-wave superconductivity, the structure of proximity-induced $p$-wave triplets, and the emergence of a dissipationless spin current carried by these triplets. They show that an effective SC+HM description with a small, nonmonotonic $h_{ m eff}$ and a Dynes-like $oldGamma$ can capture the triplet physics, though full suppression and leakage into the HM limit the achievable triplet amplitude. Conical magnets can host sizable transport spin currents, with the current enhanced by increasing conicity up to a point, offering a tunable platform for low-dissipation spintronics despite intrinsic limits set by Fermi-surface mismatch.

Abstract

It is known that in contrast to homogeneous ferromagnetism helical magnetism is compatible with superconductivity and causes only weak suppressive effect on superconducting critical temperature. Despite this fact it induces p-wave triplet superconducting correlations in homogeneous superconducting systems with intrinsic helical magnetism. The combination of these two facts indicates a high potential for the application of such systems in disspationless spintronics. For this reason here we investigate the proximity effect in atomically thin superconductor/helical (conical) magnet heterostructures (SC/HM). It is shown that in SC/HM heterostructures the strength of the proximity effect and, in particular, amplitude of p-wave triplet superconductivity and the degree of superconductivity suppression are complex functions of the magnet exchange field and filling factors of the magnet and the superconductor. Further we demonstrate that $p$-wave correlations ensure transport spin supercurrent flow in the SC/HM heterostructure with conical magnets and unveil the physical relationship between the transport spin supercurrent, degree of the magnet conicity and internal structure of p-wave correlations in the momentum space.

Figures (11)

• Figure 1: Sketch of the superconductor/helical magnet (SC/HM) bilayer (a) and the superconductor/conical magnet bilayer (b). The SC and HM layers are assumed to be 2D. The spatial distribution of the magnetization in one magnetic unit cell, containing 4 sites, is shown by black arrows. The HM magnetization is assumed to be homogeneous along the $y$-direction.
• Figure 2: Dependence of the superconducting order parameter in SC/HM bilayer on the helical exchange field $h_\perp = h$ of the HM layer. The magnetization component $h_x$ along the helix axis is assumed to be zero. $\Delta_0$ is the superconducting order parameter of the isolated SC film at temperature $T$. $t_S=70\Delta_0$, $t_M=1.25t_S$, $\mu_S=0.33t_S$, $T=0.35\Delta_0$, $t_{SM}=1.2\Delta_0$.
• Figure 3: Dependence of the superconducting order parameter on the internal helical exchange field $h_{\rm{int}}$ calculated in the framework of the effective homogeneous SC+HM model. The parameters of the hopping hamiltonian describing the SC+HM model correspond to the parameters of the superconducting layer of the SC/HM heterostructure from Fig. \ref{['fig:Delta_h']}$t_{SC+HM} = t_S = 70 \Delta_0$, $\mu_{SC+HM} = \mu_S = 0.33 t_S$, $T=0.35\Delta_0$. Parameters $t_M$, $\mu_M$ and $t_{SM}$ are not applicable in this case.
• Figure 4: Dependence of the effective exchange field $h_{\rm{eff}}$, which is appropriate for description of the the SC/HM heterostructure in the framework of the SC+HM model on the true exchange field $h$ in the magnetic layer of the SC/HM heterostructure. Parameters are the same as in Fig. \ref{['fig:Delta_h']}.
• Figure 5: Dependence of the effective exchange field $h_{\rm{eff}}$, which is appropriate for description of the the SC/FM heterostructure in the framework of the SC+FM model on the true exchange field $h$ of the FM layer. Parameters are the same as in Fig. \ref{['fig:Delta_h']}.