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An exact solution of the collisionless time-dependent Vlasov equation is found. For the first time in a century, an analytical solution to the one-dimensional time-dependent Vlasov–Boltzmann equation has been found. It has been found that instead of the widely discussed damping, waves are subject to instability. By means of this solution, the behavior of the Langmuir waves in the nonlinear stage is considered. A symmetry method is found that allows us to establish the dependence on time of the desired quantity based on the dependence on the previous time. The analysis is restricted by the consideration of the first nonlinear approximation—keeping the second power of the electric strength. It is shown that in general the waves with finite amplitudes are not subjected to the damping. Conditions have been found under which waves can be unstable.

Hot carriers in plasmonic nanostructures, generated via plasmon decay, play key roles in applications such as photocatalysis and in photodetectors that circumvent bandgap limitations. However, direct experimental quantification of steady-state energy distributions of hot carriers in nanostructures has so far been lacking. We present transport measurements from single-molecule junctions, created by trapping suitably chosen single molecules between an ultrathin gold film supporting surface plasmon polaritons and a scanning probe tip, that can provide quantification of plasmonic hot-carrier distributions. Our results show that Landau damping is the dominant physical mechanism of hot-carrier generation in nanoscale systems with strong confinement. The technique developed in this work will enable quantification of plasmonic hot-carrier distributions in nanophotonic and plasmonic devices.

The development of nanophotonic technology is reliant on the ability to confine light to spatial dimensions much less than the wavelength of the light itself. Typically, however, in metal plasmonic approaches, there is a trade-off between confinement and losses. Alcaraz Iranzo et al. fabricated heterostructures comprising monolayers of graphene and hexagonal boron nitride (hBN) and an array of metallic rods. The light was confined vertically (as propagating plasmons) between the metal and the graphene, even when the insulating hBN spacer was just a single monolayer. Such heterostructures should provide a powerful and versatile platform for nanophotonics. Science , this issue p. 291 A heterostructure design confines light to a single atomic layer. The ability to confine light into tiny spatial dimensions is important for applications such as microscopy, sensing, and nanoscale lasers. Although plasmons offer an appealing avenue to confine light, Landau damping in metals imposes a trade-off between optical field confinement and losses. We show that a graphene-insulator-metal heterostructure can overcome that trade-off, and demonstrate plasmon confinement down to the ultimate limit of the length scale of one atom. This is achieved through far-field excitation of plasmon modes squeezed into an atomically thin hexagonal boron nitride dielectric spacer between graphene and metal rods. A theoretical model that takes into account the nonlocal optical response of both graphene and metal is used to describe the results. These ultraconfined plasmonic modes, addressed with far-field light excitation, enable a route to new regimes of ultrastrong light-matter interactions.

Surface plasmons in 2-dimensional electron systems with narrow Bloch bands feature an interesting regime in which Landau damping (dissipation via electron–hole pair excitation) is completely quenched. This surprising behavior is made possible by strong coupling in narrow-band systems characterized by large values of the “fine structure” constant α = e²/ħκVF . Dissipation quenching occurs when dispersing plasmon modes rise above the particle–hole continuum, extending into the forbidden energy gap that is free from particle–hole excitations. The effect is predicted to be prominent in moiré graphene, where at magic twist-angle values, flat bands feature α ≫ 1. The extinction of Landau damping enhances spatial optical coherence. Speckle-like interference, arising in the presence of disorder scattering, can serve as a telltale signature of undamped plasmons directly accessible in near-field imaging experiments.

Does overall thermal equilibrium exist between ions and electrons in a weakly collisional, magnetized, turbulent plasma? And, if not, how is thermal energy partitioned between ions and electrons? This is a fundamental question in plasma physics, the answer to which is also crucial for predicting the properties of far-distant astronomical objects such as accretion disks around black holes. In the context of disks, this question was posed nearly two decades ago and has since generated a sizeable literature. Here we provide the answer for the case in which energy is injected into the plasma via Alfvénic turbulence: Collisionless turbulent heating typically acts to disequilibrate the ion and electron temperatures. Numerical simulations using a hybrid fluid-gyrokinetic model indicate that the ion–electron heating-rate ratio is an increasing function of the thermal-to-magnetic energy ratio, β i: It ranges from ∼0:05 at β i = 0:1 to at least 30 for β i ≳ 10. This energy partition is approximately insensitive to the ion-to-electron temperature ratio T i/T e. Thus, in the absence of other equilibrating mechanisms, a collisionless plasma system heated via Alfvénic turbulence will tend toward a nonequilibrium state in which one of the species is significantly hotter than the other, i.e., hotter ions at high β i and hotter electrons at low β i. Spectra of electromagnetic fields and the ion distribution function in 5D phase space exhibit an interesting new magnetically dominated regime at high β i and a tendency for the ion heating to be mediated by nonlinear phase mixing (“entropy cascade”) when β i ≲ 1 and by linear phase mixing (Landau damping) when β i ≫ 1.

It is an long-standing goal to produce a photonic quantum Hall effect, analogous to the well-known quantum Hall effect for electrons; now an artificial magnetic field for a continuum of photons has been produced, making it possible to observe photonic Landau levels in a photonic quantum Hall material. A magnetic field for light Employing topological effects in the design of optical devices and materials offers exciting new directions in applications and fundamental research. It is an outstanding goal to produce a photonic quantum Hall effect, with topologically protected photonic edge states, analogous to the well-known quantum Hall effect for electrons. In previous topological photonic approaches, photons were restricted to lattices of waveguides. To realize an artificial magnetic field for a continuum of photons, Nathan Schine et al . make a carefully designed trap for photons, using four mirrors so that photons are subject to a Coriolis force equivalent to a Lorentz force as if produced by a magnetic field. The approach made it possible to observe photonic Landau levels in a photonic quantum Hall material. Synthetic photonic materials are an emerging platform for exploring the interface between microscopic quantum dynamics and macroscopic material properties 1 , 2 , 3 , 4 , 5 . Photons experiencing a Lorentz force develop handedness, providing opportunities to study quantum Hall physics and topological quantum science 6 , 7 , 8 . Here we present an experimental realization of a magnetic field for continuum photons. We trap optical photons in a multimode ring resonator to make a two-dimensional gas of massive bosons, and then employ a non-planar geometry to induce an image rotation on each round-trip 9 . This results in photonic Coriolis/Lorentz and centrifugal forces and so realizes the Fock–Darwin Hamiltonian for photons in a magnetic field and harmonic trap 10 . Using spatial- and energy-resolved spectroscopy, we track the resulting photonic eigenstates as radial trapping is reduced, finally observing a photonic Landau level at degeneracy. To circumvent the challenge of trap instability at the centrifugal limit 10 , 11 , we constrain the photons to move on a cone. Spectroscopic probes demonstrate flat space (zero curvature) away from the cone tip. At the cone tip, we observe that spatial curvature increases the local density of states, and we measure fractional state number excess consistent with the Wen–Zee theory, providing an experimental test of this theory of electrons in both a magnetic field and curved space 12 , 13 , 14 , 15 . This work opens the door to exploration of the interplay of geometry and topology, and in conjunction with Rydberg electromagnetically induced transparency, enables studies of photonic fractional quantum Hall fluids 16 , 17 and direct detection of anyons 18 , 19 .

Plasmon–emitter interactions are of central importance in modern nanoplasmonics and are generally maximal at short emitter–surface separations. However, when the separation falls below 10–20 nm, the classical theory deteriorates progressively due to its neglect of quantum effects such as nonlocality, electronic spill-out, and Landau damping. Here we show how this neglect can be remedied in a unified theoretical treatment of mesoscopic electrodynamics incorporating Feibelman d -parameters. Our approach incorporates nonclassical resonance shifts and surface-enabled Landau damping—a nonlocal damping effect—which have a dramatic impact on the amplitude and spectral distribution of plasmon–emitter interactions. We consider a broad array of plasmon–emitter interactions ranging from dipolar and multipolar spontaneous emission enhancement, to plasmon-assisted energy transfer and enhancement of two-photon transitions. The formalism gives a complete account of both plasmons and plasmon–emitter interactions at the nanoscale, constituting a simple yet rigorous platform to include nonclassical effects in plasmon-enabled nanophotonic phenomena. Plasmonic enhancements of light–matter interactions are generally maximal at short emitter–surface separations. Here, the authors investigate the impact of nonlocality, spill-out, and surface-assisted Landau damping at nanoscale separations using a mesoscopic electrodynamic framework.

How turbulent energy is dissipated in weakly collisional space and astrophysical plasmas is a major open question. Here, we present the application of a field-particle correlation technique to directly measure the transfer of energy between the turbulent electromagnetic field and electrons in the Earth’s magnetosheath, the region of solar wind downstream of the Earth’s bow shock. The measurement of the secular energy transfer from the parallel electric field as a function of electron velocity shows a signature consistent with Landau damping. This signature is coherent over time, close to the predicted resonant velocity, similar to that seen in kinetic Alfven turbulence simulations, and disappears under phase randomisation. This suggests that electron Landau damping could play a significant role in turbulent plasma heating, and that the technique is a valuable tool for determining the particle energisation processes operating in space and astrophysical plasmas Various physical mechanisms are proposed to explain the heating observed in turbulent astrophysical plasmas. Here, Chen et al. find a signature consistent with one of these mechanisms, electron Landau damping, by applying a field-particle correlation technique to in situ spacecraft data of turbulence in the Earth’s magnetosheath.

In strongly correlated materials, quasiparticle excitations can carry fractional quantum numbers. An intriguing possibility is the formation of fractionalized, charge-neutral fermions—for example, spinons 1 and fermionic excitons 2 , 3 —that result in neutral Fermi surfaces and Landau quantization 4 , 5 in an insulator. Although previous experiments in quantum spin liquids 1 , topological Kondo insulators 6 – 8 and quantum Hall systems 3 , 9 have hinted at charge-neutral Fermi surfaces, evidence for their existence remains inconclusive. Here we report experimental observation of Landau quantization in a two-dimensional insulator, monolayer tungsten ditelluride (WTe 2 ), a large-gap topological insulator 10 – 13 . Using a detection scheme that avoids edge contributions, we find large quantum oscillations in the material’s magnetoresistance, with an onset field as small as about 0.5 tesla. Despite the huge resistance, the oscillation profile, which exhibits many periods, mimics the Shubnikov–de Haas oscillations in metals. At ultralow temperatures, the observed oscillations evolve into discrete peaks near 1.6 tesla, above which the Landau quantized regime is fully developed. Such a low onset field of quantization is comparable to the behaviour of high-mobility conventional two-dimensional electron gases. Our experiments call for further investigation of the unusual ground state of the WTe 2 monolayer, including the influence of device components and the possible existence of mobile fermions and charge-neutral Fermi surfaces inside its insulating gap. Pronounced quantum oscillations in magnetoresistance, a phenomenon that was only expected in metals with highly mobile carriers, are observed in the strongly insulating state of two-dimensional WTe 2 .

Graphene, a unique two-dimensional material comprising carbon in a honeycomb lattice1, has brought breakthroughs across electronics, mechanics and thermal transport, driven by the quasiparticle Dirac fermions obeying a linear dispersion2,3. Here, we demonstrate a counter-pumped all-optical difference frequency process to coherently generate and control terahertz plasmons in atomic-layer graphene with octave-level tunability and high efficiency. We leverage the inherent surface asymmetry of graphene for strong second-order nonlinear polarizability4,5, which, together with tight plasmon field confinement, enables a robust difference frequency signal at terahertz frequencies. The counter-pumped resonant process on graphene uniquely achieves both energy and momentum conservation. Consequently, we demonstrate a dual-layer graphene heterostructure with terahertz charge- and gate-tunability over an octave, from 4.7 THz to 9.4 THz, bounded only by the pump amplifier optical bandwidth. Theoretical modelling supports our single-volt-level gate tuning and optical-bandwidth-bounded 4.7 THz phase-matching measurements through the random phase approximation, with phonon coupling, saturable absorption and below the Landau damping, to predict and understand graphene plasmon physics.