ReviewQuantum Materials

Polaritons in van der Waals materials

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Science  14 Oct 2016:
Vol. 354, Issue 6309, aag1992
DOI: 10.1126/science.aag1992

Structured Abstract

BACKGROUND

Light trapped at the nanoscale, deep below the optical wavelength, exhibits an increase in the associated electric field strength, which results in enhanced light-matter interaction. This leads to strong nonlinearities, large photonic forces, and enhanced emission and absorption probabilities. A practical approach toward nanoscale light trapping and manipulation is offered by interfaces separating media with permittivities of opposite signs. Such interfaces sustain hybrid light-matter modes involving collective oscillations of polarization charges in matter, hence the term polaritons. Surface plasmon polaritons, supported by electrons in metals, constitute a most-studied prominent example. Yet there are many other varieties of polaritons, including those formed by atomic vibrations in polar insulators, excitons in semiconductors, Cooper pairs in superconductors, and spin resonances in (anti)ferromagnets. Together, they span a broad region of the electromagnetic spectrum, ranging from microwave to ultraviolet wavelengths. We discuss polaritons in van der Waals (vdW) materials: layered systems in which individual atomic planes are bonded by weak vdW attraction (see the figure). This class of quantum materials includes graphene and other two-dimensional crystals. In artificial structures assembled from dissimilar vdW atomic layers, polaritons associated with different constituents can interact to produce unique optical effects by design.

ADVANCES

vdW materials host a full suite of different polaritonic modes with the highest degree of confinement among all known materials. Advanced near-field imaging methods allow the polaritonic waves to be launched and visualized as they travel along vdW layers or through multilayered heterostructures. Spectroscopic and nanoimaging experiments have identified multiple routes toward manipulation of nano-optical phenomena endowed by polaritons. A virtue of polaritons in vdW systems is their electrical tunability. Furthermore, in heterostructures assembled from dissimilar vdW layers, different brands of polaritons interact with each other, thus enabling unparalleled control of polaritonic response at the level of single atomic planes. New optoelectronic device concepts aimed at the detection, harvesting, emission, propagation, and modulation of light are becoming feasible as a result of combined synthesis, nanofabrication, and modeling of vdW systems. The extreme anisotropy of vdW systems leading to opposite signs of the in-plane and out-of-plane permittivities of the same layered crystal enables efficient polaritonic waveguides, which are instrumental for subdiffractional focusing and imaging. In addition to near-field optical probes facilitating nanoimaging, coupling to polaritons can be accomplished via electrical excitation and nonlinear wave mixing.

OUTLOOK

Potential outcomes of polariton exploration in vdW heterostructures go beyond nano-optical technologies. In particular, images of polaritonic standing and traveling waves contain rich insights into quantum phenomena occurring in the host material supporting polaritons. This line of inquiry into fundamental physics through polaritonic observations constitutes an approach toward optics-based materials research. In particular, the strong spatial confinement exhibited by vdW polaritons involves large optical-field gradients—or equivalently, large momenta—which allows regions of the dispersion relations of electrons, phonons, and other condensed-matter excitations to be accessed beyond what is currently possible with conventional optics. Additionally, polaritons created by short and intense laser pulses add femtosecond resolution to the study of these phenomena. Alongside future advances in the understanding of the physics and interactions of vdW polaritons, solutions to application challenges may be anticipated in areas such as loss compensation, nanoscale lasing, quantum optics, and nanomanipulation. The field of vdW polaritonics is ripe for exploring genuinely unique physical scenarios and exploiting these new phenomena in technology.

Polaritons in van der Waals (vdW) materials.

Polaritons—a hybrid of light-matter oscillations—can originate in different physical phenomena: conduction electrons in graphene and topological insulators (surface plasmon polaritons), infrared-active phonons in boron nitride (phonon polaritons), excitons in dichalcogenide materials (exciton polaritons), superfluidity in FeSe- and Cu-based superconductors with high critical temperature Tc (Cooper-pair polaritons), and magnetic resonances (magnon polaritons). The family of vdW materials supports all of these polaritons. The matter oscillation component results in negative permittivity (εB < 0) of the polaritonic material, giving rise to optical-field confinement at the interface with a positive-permittivity (εA > 0) environment. vdW polaritons exhibit strong confinement, as defined by the ratio of incident light wavelength λ0 to polariton wavelength λp.

van der Waals (vdW) materials consist of individual atomic planes bonded by weak vdW attraction. They display nearly all optical phenomena found in solids, including plasmonic oscillations of free electrons characteristic of metals, light emission/lasing and excitons encountered in semiconductors, and intense phonon resonances typical of insulators. These phenomena are embodied in confined light-matter hybrid modes termed polaritons—excitations of polarizable media, which are classified according to the origin of the polarization. The most studied varieties are plasmon, phonon, and exciton polaritons. In vdW materials, polaritons exhibit extraordinary properties that are directly affected by dimensionality and topology, as revealed by state-of-the-art imaging of polaritonic waves. vdW heterostructures provide unprecedented control over the polaritonic response, enabling new quantum phenomena and nanophotonics applications.

Atomically thin two-dimensional (2D) crystalline layers constitute the elemental building blocks of van der Waals (vdW) materials. Exfoliated atomic layers are structurally robust and amenable to assembly to produce complex heterostructures. These materials support a variety of polaritons associated with oscillations of conduction electrons, phonons, and excitons, as well as their hybrids (e.g., plasmon-phonon polaritons). A number of vdW materials display extraordinary quantum phenomena: high–critical temperature (Tc) superconductivity, exotic magnetism, topologically protected states, strong Coulomb interactions, and non–Fermi-liquid behavior. All of these properties permeate the polaritonic response of vdW systems.

In the ongoing quest for exploration of polaritons, scanning optical near-field imaging (Fig. 1) has had an exceptional impact. This technique uses the sharp tip of an atomic force microscope (AFM) as an optical antenna (1, 2), allowing one to detect how incident light of free-space wavelength λ0 is scattered at the apex of the tip in the proximity of the studied specimen (Fig. 1A). The obtained signal is governed by the local electric field of the polariton wave launched by the tip, rendering nanometer spatial resolution as the tip is raster-scanned over the sample. The principal characteristics of polaritons, including wavelength λp, confinement ratio λ0p, and quality factor Q (Table 1), reveal that vdW polaritons are simultaneously compact and long-lived. The polariton wavelength can often be tuned with various methods, of which electrical gating is of paramount importance. These characteristics render vdW polaritons complementary and sometimes superior to those observed in more conventional materials (3, 4).

Fig. 1 Polaritons in vdW materials visualized through near-field nanoimaging.

(A) Dirac plasmons in graphene (20, 21). [Reproduced from (20)] (B) Edge plasmons at the boundary of a graphene nanoresonator (64, 65). [Reproduced, with permission, from (65)] (C) One-dimensional plasmons in a carbon nanotube (30). [Reproduced, with permission, from (30)] (D) Superlattice plasmons in graphene–h-BN moiré superlattices (24). [Reproduced from (24)] (E) Hybrid plasmon-phonon polaritons in graphene on h-BN (60). [Reproduced from (60)] (F) Exciton polaritons (45) in WSe2. [Reproduced, with permission, from (45)] (G) Hyperbolic phonon polaritons in a h-BN slab (102), propagating as guided waves (schematic line).

Table 1 Characteristics of polaritons in vdW materials.

Tunability methods marked with asterisks indicate already demonstrated results. All experimental entries are obtained under ambient conditions, except for Cooper-pair plasmons at T = 5 K. SPP, surface plasmon polariton; DE, dielectric environment; N/A, not available.

View this table:

A major challenge of polariton imaging and spectroscopy stems from the large momentum mismatch with free-space photons. However, experimentalists are becoming increasingly adept at overcoming this difficulty. Figure 2 displays various coupling schemes. Coherent launchers (Fig. 2, A to C) have relatively small coupling cross sections, although they can be enhanced through optical antennas, including AFM tips (Fig. 2C) and metal bars or disks (5). Incoherent launchers (Fig. 2, D to F) can reach order-unity efficiency; in particular, electron beams (Fig. 2D) eventually will enable an impressive combination of energy and space resolution (6).

Fig. 2 Launching and visualizing polaritons.

(A to F) Excitation and probing of vdW polaritons (blue arrows) can be achieved using (A) periodic structures (110112), (B) nonlinear wave mixing (95), (C) antenna-like nanotips (20, 21), (D) electron beams (113), (E) quantum dots and localized emitters (114, 115), and (F) electron tunneling (116). Polaritons produced by processes shown in (A) to (C) maintain phase coherence with respect to the external illumination, in contrast to mechanisms shown in (D) to (F), which are inelastic. A variant of (A) has been proposed that relies on surface acoustic wave modulation (117, 118). Sample edges (64, 65) also provide additional momentum to mediate light-polariton coupling. Localized polaritons confined to nanoislands can be resonantly excited by incident light. Radiative outcoupling of polaritons can be visualized by reversing the arrows in (A) to (C).

Primer on polaritons

Polariton dispersion in thin layers

When the sample thickness d is much smaller than the wavelength λp of polaritons, only the in-plane optical response of the material is important. In this thin-film limit, one findsEmbedded Image (1)where εa is the permittivity of the environment, σ is the in-plane conductivity, ω is the frequency, and kp is the in-plane polariton wave vector. The field of the polariton wave decreases exponentially away from the interface over a characteristic distance ~λp/2π. It is common to describe σ in Eq. 1 as the sum

Embedded Image (2)The first (Drude) and the second (Lorentz) terms represent the contribution of free (f) and bound (b) charges, respectively. The latter can also account for optical phonons. Different vdW materials can be modeled with a suitable choice of parameters in Eq. 2: the spectral weights Sf and Sb, the exciton/phonon frequency ωb, and the phenomenological relaxation times τf and τb (related to Q in Table 1 by τ = Q/ω).

The spectral weights in Eq. 2, and therefore the polariton wavelengths of vdW materials, are often tunable. In graphene, Sf scales with the Fermi energy EF according to Sf ~ (e/ħ)2EF (where e is the charge on the electron and ħ is the Planck constant divided by 2π) (7); the value of Sf can be controlled via electrical gating, doping, and photoexcitation. In insulators, where Sb ~ (e2/ħ)fωb, the dimensionless parameter f scales linearly with the number N of atomic layers. In particular, fph ~ Embedded Image << 1 for optical phonons and fex ~ N(D/eaex)2 for excitons. Here, m, M, aex, and D are the electron mass, the atomic mass, the exciton Bohr radius, and the exciton transition dipole, respectively. In superconductors, the total Drude weight is constant but is split between normal- and super-current components, with a relative weight depending on temperature. When applied to graphene, Eqs. 1 and 2 readily explain why the surface plasmon polariton (SPP) confinement ratio λ0p = (εa/α)(ħω/2EF) >> 1 can be extraordinarily high (8): λ0p scales with the inverse of the fine-structure constant α ≈ 1/137. However, a stronger confinement is accompanied by larger damping rate Embedded Image [which also increases with ω (9, 10)].

Polariton dispersion in slabs and heterostructures

For highly confined polaritons (or thicker samples), the condition λp >> d may not hold, so the polariton dispersion becomes more intricate (Fig. 3). Both the in- and out-of-plane responses need to be considered, and it is more convenient to use the permittivity tensor, whose in-plane component ε relates to σ(ω) as ε = 1 + (4πiσ/ωd), whereas the out-of-plane component ε may differ from ε in both magnitude and sign because of the strong anisotropy of vdW materials (Fig. 3, E and F). Additional complications arise if the sample is a heterostructure made of dissimilar vdW materials (metals, insulators, or semiconductors). These more complex dispersions can be dissected into simpler elements (11, 12) as in Fig. 3, A to G.

Fig. 3 Polariton dispersions.

(A) Bulk conductors (metals or doped semiconductors). (B) Thin conducting films. (C) Isotropic polar dielectrics. (D) Thin polar dielectric slabs. (E) Type II hyperbolic materials. (F) Thin slab of a type II hyperbolic material with its optical axis normal to the surfaces. (G) Graphene–h-BN heterostructures (10). The horizontal axis is the transverse wave vector in (E) and the 3D bulk or in-plane wave vector in the other plots, depending on the mode. [Adapted from (10)]

SPPs are supported by materials that possess mobile charges: metals, doped semiconductors, and superconductors. We find three types of electromagnetic modes in these materials (Fig. 3A): two in the bulk (photon and plasmon) and one confined at the surface (lower curve, representing the TM-polarized SPP). The transverse upper branch also starts at frequency ωp and disperses upward at higher wave vector k. This behavior results from level repulsion between the photon (dashed line in Fig. 3A) and the zero-frequency (Drude) resonance of the conductor. The high-k SPP is often referred to as a surface plasmon (SP). Its dispersion asymptotically approaches ωSP = Embedded Image.

The SPPs at the surfaces of a thin conducting film of thickness d << cp split into two branches of opposite symmetry. The lower, symmetric branch corresponds to the thin-film plasmons (Eq. 1 and Fig. 3B). For k >> 1/d, both of these branches are localized to the film surfaces and are nearly degenerate. A set of guided waves above the bulk plasmon frequency ωp may also exist between the light lines of vacuum and the material (tilted dashed lines in Fig. 3B) for films with high-frequency permittivity larger than unity.

Phonon and exciton polaritons in dielectrics

A typical bulk dielectric exhibits three modes: two transverse optical branches of phonon polaritons (PhPs) ωTO, generated by hybridization of a photon (dashed line in Fig. 3C) and a TO phonon; and one longitudinal phonon ωLO, analogous to the bulk plasmon in a metal. In a semi-infinite dielectric, a surface phonon polariton (SPhP) emerges inside the bulk stop band ωTO < ω < ωLO. In thin slabs (Fig. 3D), the PhP branches split into guided modes while the SPhP generates symmetric and antisymmetric modes similar to SPPs in metal films. The mode structure of exciton polaritons in semiconductors is similar to that of phonon polaritons in dielectrics, except that the role of ωTO is played by the exciton energy and the dispersion at large momenta is quadratic: ω(k) = ωTO + (ħk2/2mex), where mex is the exciton mass. The ωLOTO gap in excitonic systems is referred to as the Rabi splitting.

Hyperbolic media and waveguide modes

Hyperbolic materials exhibit permittivities of opposite signs along different directions. In particular, type II hyperbolic materials possess positive ε|| and negative ε. In anisotropic polar dielectrics, this regime may be realized within stop bands. Hyperbolicity leads to birefringence, with the dispersion relations of the ordinary and extraordinary rays given by ω2/c2 = Embedded Image and ω2/c2 = Embedded Image, respectively. The extraordinary rays have peculiar isofrequency open surfaces, shaped as single-sheet hyperboloids (1315). When projected on the ω-k plane, the hyperboloids fill a continuous region (orange fringes in Fig. 3E). The transverse k and axial k momenta of these extraordinary polaritons can be very large, being limited only by the atomic structure of the material.

Polaritons can only propagate at angles θ or π – θ with respect to the optical axis satisfying the relation tan θ = |ε|1/2. This implies that the polariton can be focused into narrow beams that do not spread laterally as they propagate through the material (see below). A thin slab with surfaces normal to the optical axis supports weakly confined surface modes that evolve into the principal branch of the guided waves as k increases (Fig. 3F). This is accompanied by numerous higher-order branches (Fig. 3F) that arise from splitting of the extraordinary ray continuum in Fig. 3E. The group velocity can be negative in a hyperbolic material, as demonstrated by direct imaging (16, 17). Hyperbolic electrodynamics is ubiquitous in vdW materials and originates not only in the phonon modes (Fig. 3, E and F) but also in a highly anisotropic electronic response.

Plasmon-phonon polaritons are more complex modes involving the hybridization of the corresponding elemental excitations in heterostructures. For example, in graphene supported by hexagonal boron nitride (h-BN) (18, 60) (Fig. 3E), the hyperbolic guided waves (1315) appear in the two bands marked type I and type II. Outside these bands, one finds SPP and SP branches similar to those in Fig. 3B. The slope of the SP dispersion—the group velocity νg—is much smaller than c: The light cone is nearly vertical (and hence invisible) in Fig. 3G. Additionally, νg nearly everywhere exceeds the Fermi velocity and the plasmon does not overlap the electron-hole pair continuum (green region in Fig. 3G), so Landau damping is prevented.

New physics revealed by polaritonic observations

Polaritons in vdW materials provide unique opportunities for exploring electronic phenomena and lattice dynamics. In particular, polaritonic images grant us access into regions of the dispersion relations of various excitations beyond what is attainable with conventional optics.

Interactions and many-body effects

The decay rate and wavelength of plasmonic and polaritonic waves (Fig. 1) are determined by the complex optical conductivity σ(k, ω) of the medium that supports these waves. It is thus possible to reconstruct σ(k, ω) from polaritonic images, which contain information on both electronic and lattice dynamics (10, 1921). Specifically, the periodicity of plasmonic waves in graphene (Fig. 1A) is determined by the imaginary part of the conductivity, whereas the rate at which these waves decay into the interior of the samples is governed by Re σ/Im σ. The plasmon propagation length ~(Im σ/Re σ)λp has been shown to reach ~1 μm (i.e., tens of plasmon wavelengths) in high-mobility encapsulated graphene (10, 19). The corresponding lifetime, ~500 fs, is only weakly dependent on gate voltage or probing photon frequency from the terahertz to mid-infrared regimes (22). This result is consistent with the dominant role of acoustic phonons in scattering processes (9), a conjecture further supported by theoretical analysis of the ω and k dependence of the plasmon scattering rate τ–1 = (Re σ/Im σ)ω (Fig. 4A). Data on interactions among electrons, phonons, and plasmons in other vdW systems are fragmentary, but implications of these interfacial effects may be quite spectacular. For example, coupling between electrons in monolayer FeSe and phonons in SrTiO3 appears as a viable mechanism for high-temperature superconductivity in FeSe/SrTiO3 heterostructures (23).

Fig. 4 Spectroscopy and imaging of polaritons enable a new line of inquiry into the fundamental physics of the media supporting polaritonic behavior.

(A) Scattering rate τ–1(k, ω) for Dirac plasmons in monolayer graphene calculated (9) for three selected values of the in-plane wave vector k. Shaded areas correspond to stop bands. [Reproduced, with permission, from (9)] (B) Photoexcitation of semi-infinite monolayer graphene with intense femtosecond pulses increases electronic temperature and enhances the spectral weight available for surface plasmons. Hyperspectral images (19) of the photoinduced change in the scattering amplitude Δs(ω, x) reveal the dispersion of photoinduced plasmons (red traces). A vertical line indicates the edge of the graphene sample. Dashed lines are theoretical fits. [Reproduced from (19)] (C) Nano-infrared contrast produced by plasmonic reflections at topological domain boundaries in bilayer graphene (27). [Reproduced, with permission, from (27)] (D) Exciton-photon coupling in a MoSe2 double quantum-well heterostructure showing an anticrossing between the neutral exciton and discrete cavity modes at 4.2 K. Top: A fit to the peak position as a function of detuning yields a Rabi splitting of 29 meV. Bottom: The upper and lower polariton branches (UPB and LPB) are well resolved spectrally (43). [Reproduced from (43)]

Polaritonic probe of the electronic structure and inhomogeneities

Equations 1 and 2 establish that images of polaritonic waves in a given medium encode the optical conductivity, and hence the fundamental information about intraband, interband, and excitonic effects within that medium. For example, the analysis of plasmonic reflections and standing waves has been used to decipher the electronic structure of moiré superlattices formed at the interface of slightly mismatched hexagonal lattices of graphene and h-BN (24). Moiré patterns are periodic superlattice structures that appear when two crystals with a small lattice mismatch are superimposed. Moiré superlattices reveal the energy gap in the otherwise gapless electronic structure of graphene and therefore modify the conductivity σ(k, ω). The boundary between plain and superlattice graphene is thus associated with an abrupt change of the electronic conductivity—a property that prompts plasmonic reflections (Fig. 1D). The magnitude of the moiré-induced energy gap is inferred from a systematic analysis of these plasmonic patterns collected at different wavelengths for specimens with different doping. Plasmonic reflections also occur at other forms of electronic discontinuities, including grain boundaries in extended graphene films (25, 26), stacking domains (Fig. 4C) in bilayer graphene (27), and nanometer-scale local gates (28, 29). In particular, a carbon nanotube (CNT) gate acts as a perturbation produced by a line of charge, which introduces 1D-bound states in an adjacent graphene layer. In a related context, plasmons imaged in CNTs (Fig. 1C) are found to exhibit approximately doping- and frequency-independent (quantized) group velocity, which is a consequence of the 1D nature of these materials (30). We note that 1D phonon polaritons are also observed in BN nanotubes (31).

Polaritons far and away from equilibrium

When subjected to photoexcitation by short and intense optical pulses, vdW polaritons can radically change their properties (32). Hyperspectral near-field imaging of graphene under intense optical pumping (19) (Fig. 4B) uncovers the emergence of mid-infrared plasmons in a specimen that shows no such modes in equilibrium because of its low Drude spectral weight Sf (Eq. 1). This effect is driven by thermal smearing of conduction electrons, which produces a boost in SfkBT (where kB is the Boltzmann constant); the electron temperatures can be as high as T = 5000 K (33). Ultrafast heating of electrons and plasmons may realize a regime in which the dynamics of an approximately equal number of electrons and holes in graphene resembles the behavior of viscous liquids described by relativistic hydrodynamics (34, 35). Several theoretical works have discussed plasmon amplification in vdW materials (36, 37) under photoexcitation, followed by a recent experimental report (38). Apart from probing inherent nonlinearities of the materials (39), an experimental implementation of these ideas may uncover pathways for mitigating or eliminating electronic losses in the plasmonic or polaritonic response. An alternative route for loss compensation consists of fulfilling the optical gain condition Re σ(ω) < 0 by means of population inversion, an effect recently demonstrated (40) in the frequency range of excitonic transitions in WS2.

High-temperature exciton polaritons

Atomically thin transition metal dichalcogenides (TMDs), including MoS2 and MoSe2, exhibit strong many-body effects due to their high effective carrier masses and low dielectric permittivities. Monolayers of TMDs are direct-gap semiconductors that host excitons with binding energies from 0.4 to 0.9 eV (41, 42). When integrated in an optical cavity, TMDs may form exciton polaritons, provided that the cavity-enhanced exciton-photon coupling (i.e., the Rabi frequency) exceeds the exciton decay rate (on the order of tens of meV). A realization of this regime was recently reported in a MoSe2-based heterostructure (Fig. 4D) at 4.2 K (43) with a Rabi frequency of 29 meV and a clearly resolved avoided crossing of exciton and photon dispersions. Similar results were obtained for MoS2 (44). The lower-k part of the exciton polariton–guided waves (Fig. 1F) has been imaged in thin WSe2 crystals under ambient conditions (45), in a regime where these propagating modes have a dominant photon character (Fig. 1F).

A challenge for future nanoimaging experiments is to probe the strongly confined, large-k part of the exciton polariton branches. The exciton and exciton polariton propagation lengths are expected to be greatly enhanced if they form condensates, which are also predicted to occur in TMDs near room temperature (46), more than one order of magnitude higher than in conventional inorganic semiconductors. The interaction of exciton polariton condensates with a two-dimensional electron system of vdW materials may enable a new pathway toward high-temperature superconductivity (47, 48). Diverse polaritonic phenomena of excitonic origin may also be anticipated in CNTs, in view of the strong excitonic dipole activity of these 1D systems (49, 50).

Spatial dispersion

Nonlocal effects in the conductivity become relevant when the polariton wavelength is comparable with the Fermi wavelength λF. These phenomena remain largely unexplored in vdW materials. Nonlocal effects are typically investigated using momentum-resolved methods such as electron energy-loss spectroscopy, but they appear to be within reach for nano-optics techniques in view of the large values of λF in vdW layers. Nanoimaging and nanospectroscopy experiments allow one to determine the nonlocal conductivity (10, 51) σ(kp, ω). Future nano-infrared measurements may provide additional insight into other momentum-dependent electronic phenomena (52).

Topological polaritonics

Topological order and Berry phases are playing a prominent role in the understanding of electronic properties of vdW solids such as chirality and anomalous Hall conductivity. These intriguing properties have implications in photonics and polaritonics (53, 54). For example, in gapped (bilayer) graphene or TMDs, the anomalous Hall conductivities of the two valleys cancel each another in equilibrium. This cancellation can be removed through pumping with circularly polarized light, leading to a chiral polaritonic response (55, 56). Among many fascinating predictions exploring the roles of topology and chirality in polariton propagation, we mention those of chiral edge modes of plasmonic and excitonic origin (57). Recent observations of edge plasmons in graphene nanoribbons (Fig. 1B) fulfill the preconditions for exploring topological properties via polaritons.

Tailoring polaritonic characteristics specific to vdW materials

Stacking

Restacking of exfoliated and/or epitaxial vdW layers yields vertical heterostructures in which electromagnetic coupling between polaritonic modes of proximal planes gives rise to new optical properties beyond those of the individual constituents. For example, mid-infrared plasmons in graphene hybridize with phonon polaritons of an underlying polar substrate (18, 51, 58, 59). Hyperbolic polaritons observed in graphene–h-BN stacks (60) inherit electrostatic tunability from graphene and long propagation lengths from phonons in h-BN. Changes in electronic structure produced by interlayer interaction can further give rise to modified polaritonic response—for example, in rotationally aligned graphene–h-BN stacks, where the formation of long-period moiré superlattices modifies the dispersion and lifetime of composite plasmon polaritons (24). Finally, chiral twisted stacks may exhibit optical gyrotropy (61, 62).

Nanostructuring

Nanostructuring is commonly used to produce systems with reduced dimensionality, including stripes, discs, and nanocones of h-BN (63). Both artificial and natural boundaries of vdW samples harbor 1D polaritonic edge modes that reveal a dispersion distinct from that of “bulk” polaritons in the interior of vdW crystals (64, 65). Similarly, 1D modes are likely to occur at domain walls, lateral Josephson junctions, and p-n junctions.

Controls

Unlike conventional plasmonic media, vdW materials are amenable to active tuning of their polaritonic properties via chemical doping and gating. Graphene is a paramount example of this tunability. Additionally, doping of vdW semiconductors such as black phosphorus (66) affects the interplay between spectrally overlapping intra- and interband responses, which has an impact on their hyperbolic behavior (67). Persistent switching of optical properties can be realized in vdW/ferroelectric multilayers and by manipulating defects in h-BN layers (68). Optical pumping provides a mechanism of ultrafast control (40, 69, 70). Also, both strain and photoexcitation with circularly polarized light lift the valley degeneracy in vdW materials such as bilayer graphene and TMDs (71), enabling one to explore valley-selective phenomena. An expanding list of polaritonic “control knobs” includes population inversion (40), n- and p-type doping of graphene upon photoexcitation (69), magnetic fields applied to graphene (72), and strain engineering of excitons in WSe2 (73).

Impending applications

The unusual optical properties displayed by vdW materials offer exciting opportunities for technological applications (74).

Light trafficking

Polariton nanoimaging experiments in vdW materials (Fig. 1) revealed that these ultracompact light-matter modes are capable of carrying optical signals over many micrometers in some cases. Furthermore, the propagation, reflection, and refraction of polaritons can be readily controlled by heterostructuring or through stimuli such as electrical gating (20, 21). Thus it is feasible to implement transformational polaritonics (75), polaritonic transistors, and integrated nanophotonic circuits using vdW systems. In heterostructures combining chiral and hyperbolic layers, it may be possible to produce polaritons topologically protected from backscattering, which could lead to protected unidirectional propagation and robustness against disorder (53, 76).

Electro-optical modulators

Integration of vdW materials with semiconductor photonics is equally appealing. Early demonstrations (Fig. 5B) include quantum-cascade lasers with tunable emission characteristics (77, 78) and electrically controlled modulators (7981). The extreme reduction of the polariton wavelength in vdW materials should enable the design of ultrasmall spectrometers on a chip, with spectral resolution achieved through using different structures with polaritonic resonances covering a dense and broad set of frequencies.

Fig. 5 Impending applications and future opportunities.

(A) Subdiffractional focusing via phonon polaritons in h-BN (16, 82). Top: Au discs are deposited on the bottom surface of a h-BN slab. Middle: Image obtained on the top surface of the slab using a broadband source centered at λ0 = 12.5 μm; scale bar, 500 nm. Bottom: Image of a pattern showing subdiffractional features, acquired with λ0 = 6 μm; scale bar, 1 μm. [Reproduced from (16, 82)] (B) Schematics of a quantum-cascade laser (QCL) with emission controlled by plasmons in the top graphene layer (77, 78). [Reproduced from (78)] (C) Resonant absorption in graphene plasmonic strips for spectroscopic fingerprinting (83). [Reproduced from (83)] (D) Proposed structure for investigating cavity electrodynamics of Josephson plasmons (98). LCO, La2CuO4; LSCO, La2–xSrxCuO4; SRO, SrRuO3. [Reproduced, with permission, from (98)]

Subdiffractional focusing and imaging

Compact but mobile phonon polaritons have already been used for subwavelength focusing and imaging (Fig. 5A), taking advantage of the hyperbolic dispersion of h-BN (16, 82). These properties could find application in detector arrays and lithographic imprinting at unprecedentedly small scales.

Optical sensing

Part of the success of metal-based plasmonics lies in its application to sensing, down to single molecules. This is made possible by exploiting the large concentration of electromagnetic energy associated with these optical modes. vdW polaritons produce even higher levels of field confinement than traditional plasmonic metals and therefore hold great potential for sensing. In particular, graphene-enabled ultrasensitive detection has recently been demonstrated for biological (83) and inorganic (84) molecules (Fig. 5C).

Light emission, amplification, and lasing

Spontaneous emission from a light-emitting device can be improved by coupling the radiated energy to polaritons (2, 85). This effect is particularly pronounced at the interface with hyperbolic media, where the photon density of states is greatly enhanced (1315). The substantial field enhancement can also be used for efficient heat transfer at the nanoscale. Additionally, the low saturation threshold of graphene has been exploited in fast mode-locked lasers (86), and polaritons in WSe2 have recently been harnessed to implement an ultralow-threshold nanocavity laser (87).

Looking into the future

Polaritons in correlated van der Waals materials

Among the spectacular polaritonic effects intrinsic to vdW crystals, we highlight the Josephson plasmon originating from Cooper-pair tunneling between CuO2 planes in layered cuprate high-Tc superconductors (88). Propagating and nonequilibrium Josephson plasmons are expected to provide insights (89, 90) into the unconventional superconductivity of these materials. Furthermore, the natural hyperbolic behaviors of cuprates, topological insulators (14, 9193), and other anisotropic vdW compounds are yet to be exploited for imaging and focusing in a fashion similar to what has been done for h-BN (Fig. 5A).

Quantum and nonlinear optics with vdW polaritons

Decoherence is arguably the most serious impediment for a wide adoption of quantum technologies. The extreme concentration of electromagnetic energy associated with single polariton states in vdW materials can increase quantum interaction with neighboring optical emitters. Thus, it may be possible to reach the single-photon strong-coupling regime under ambient conditions, accompanied by nonlinearities down to the single-photon level (94). Notably, vdW materials exhibit unprecedented levels of nonlinearity, as revealed by wave-mixing experiments (95) as well as by harmonic-generation measurements (96), which are predicted to be boosted by polaritonic field enhancement (97). Further explorations of nonlinear effects in vdW high-Tc superconductors may enable manipulation of the superconducting order parameter and phase coherence under nonequilibrium conditions (98). Strongly confined plasmonic modes in vdW materials may lead to increased rates of high-order multipolar transitions, two-plasmon spontaneous emission, and spin-flip transitions (99).

The study of polaritons in vdW materials is a vibrant area of research at the vanguard of physics, materials science, and engineering. Heterostructuring of atomic vdW layers, in conjunction with the inherent sensitivity of this class of materials to external stimuli, has uncovered opportunities for on-demand photonic and polaritonic characteristics. Novel visualization techniques have revealed the rich physics of vdW layers encoded in observed images of polaritonic waves. Nanoscale near-field imaging of polaritons is emerging as an experimental method providing new insights into quantum phenomena not attainable with conventional spectroscopies. Given the omnipresence of polaritons in condensed-matter systems, we anticipate this line of inquiry to continue to unfold novel effects in other classes of quantum materials.

References and Notes

Acknowledgments: Supported by Office of Naval Research grant N00014-15-1-2671, Air Force Office of Scientific Research grant FA9550-15-1-0478, and U.S. Department of Energy grants DE-FG02-00ER45799, DOE-DE-SC0012592, and DE-SC0012375. D.N.B. is an investigator in quantum materials funded by the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF4533. F.J.G.d.A. is supported by Ministerio de Economía y Competitividad (Spain) grants MAT2014-59096-P and SEV-2015-0522 and by European Commission grants CNECT-ICT-604391 and FP7-ICT-2013-613024-GRASP.
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