We predict a new mechanism of surface plasmon amplification in graphene-insulator-graphene van der Waals heterostructures. The amplification occurs upon the stimulated interlayer electron tunneling accompanied by the emission of a coherent plasmon. The quantum-mechanical calculations of the non-local high-frequency tunnel conductivity show that a relative smallness of the tunneling exponent can be compensated by a strong resonance due to the enhanced tunneling between electron states with collinear momenta in the neighboring graphene layers. With the optimal selection of the barrier layer, the surface plasmon gain due to the inelastic tunneling can compensate or even exceed the loss due to both Drude and interband absorption. The tunneling emission of the surface plasmons is robust against a slight twist of the graphene layers and might explain the electroluminescence from the tunnel-coupled graphene layers observed in the recent experiments.The ultrarelativistic nature of electrons in graphene gives rise to the uncommon properties of their collective excitations -surface plasmons [1][2][3]. The deep subwavelength confinement [3], the unconventional density dependence of frequency [4,5], and the absence of Landau damping [4] are probably the most well-known features of plasmons in graphene-based heterostructures. Among more sophisticated predictions there stand the existence of weakly damped transverse electric plasmons [6] and quasi-neutral electron-hole sound waves near the neutrality point [7,8]. Some peculiar types of plasmons can be excited in the graphene p − n junctions [9], field-effect transistors [10,11], optoelectronic modulators [12], and nanomechanical resonators [13] engaging for the improved device performance at the terahertz frequencies.Unfortunately, the experimental studies of graphene plasmons are yet unable to confirm or refute many of these predictions. To achieve an extreme plasmon confinement, one has to sacrifice their propagation length. The latter is of the order of several micrometers at the infrared frequencies [14,15] and is limited by the interband absorption in intrinsic samples and somewhat lower Drude absorption in the doped ones [16]. The experimentally reported quality factors of graphene plasmons reach only five for graphene on SiO 2 [14, 15], and 25 for graphene encapsulated in hexagonal boron nitride [17] at room temperature. In the latter case, the damping is due to the scattering by the intrinsic acoustic phonons [16] and can be suppressed only by lowering the temperature.Instead of reducing the plasmon loss, it is possible to overcome the damping by introducing the gain medium which can replenish the energy being dissipated upon scattering. This idea has stimulated the re-examination of various 'classical' plasma instabilities in graphene, including the beam and resistive instabilities [18], Dyakonov-Shur self-excitation [10,11], and generation due to the negative differential conductance [19]. On the other hand, the plasmon gain can be provided by the photogenerated ele...

An inhomogeneous magnetic exchange field at a superconductor/ferromagnet interface converts spin-singlet Cooper pairs to a spin-polarized triplet state. Although the decay envelope of triplet pairs within ferromagnetic materials is well studied, little is known about their decay in nonmagnetic metals and superconductors and, in particular, in the presence of spin-orbit coupling (SOC). Here, we investigate devices in which singlet and triplet supercurrents propagate into the s-wave superconductor Nb. In the normal state of Nb, triplet supercurrents decay over a distance of 5 nm, which is an order of magnitude smaller than the decay of spin-singlet pairs due to the SOC. In the superconducting state of Nb, triplet supercurrents are not able to couple with the singlet wave function and are thus blocked by the absence of available equilibrium states in the singlet gap. The results offer insight into the dynamics between s-wave singlet and s-wave triplet states.

No abstract