Highly confined epsilon-near-zero and surface phonon polaritons in SrTiO3 membranes

Recent theoretical studies have suggested that transition metal perovskite oxide membranes can enable surface phonon polaritons in the infrared range with low loss and much stronger subwavelength confinement than bulk crystals. Such modes, however, have not been experimentally observed so far. Here, using a combination of far-field Fourier-transform infrared (FTIR) spectroscopy and near-field synchrotron infrared nanospectroscopy (SINS) imaging, we study the phonon polaritons in a 100 nm thick freestanding crystalline membrane of SrTiO3 transferred on metallic and dielectric substrates. We observe a symmetric-antisymmetric mode splitting giving rise to epsilon-near-zero and Berreman modes as well as highly confined (by a factor of 10) propagating phonon polaritons, both of which result from the deep-subwavelength thickness of the membranes. Theoretical modeling based on the analytical finite-dipole model and numerical finite-difference methods fully corroborate the experimental results. Our work reveals the potential of oxide membranes as a promising platform for infrared photonics and polaritonics.


Main text
Surface phonon-polaritons (SPhPs) are hybrid optical modes bound to interfaces between optically distinct media, resulting from the coupling of photons with optical phonons in polar materials.They exist within the Reststrahlen bands, the spectral regions (typically in the far-and mid-infrared range) between transverse optical (TO) and longitudinal optical (LO) phonon frequencies where the real part of the optical permittivity is negative 1 .Typically, SPhPs have a weak confinement in bulk crystals, with a wavelength close to that in free space.When the thickness of the crystal -or membrane -is decreased to the deep-subwavelength scale, SPhP modes at each interface hybridize to form two branches, with symmetric and antisymmetric distributions of the normal component of the electromagnetic field with respect to the membrane center.The antisymmetric mode is lower in energy and is propagating with a momentum significantly larger than in electromagnetic waves of the same frequency in free space; the symmetric mode is pushed up in energy and approaches the LO frequency (where the permittivity is zero) when the membrane thickness is small enough, in which case it is referred to as the epsilon-near-zero (ENZ) mode 2,3 .
To realize these applications, transferable, scalable single-crystalline thin-film materials exhibiting strong optically active low-loss phonon modes are indispensable.Some quasi-two dimensional van der Waals (vdW) compounds, such as hBN 6 , GeS 7 and -MoO3 8,9 exhibit phononpolaritons (PhPs) with low-loss and deep-subwavelength confinement, and their remarkable figures of merit have advanced various nanophotonic technologies in the infrared region [10][11][12] .These materials, however, are typically available as manually exfoliated flakes with a lateral size on the micrometer scale, limiting the scalability for device fabrication.Additionally, the omnipresent optical anisotropy of the vdW materials, although sometimes beneficial for observing some exotic optical phenomena, such as hyperbolic PhPs, may in certain cases be an unwanted complication.Furthermore, the choice of Reststrahlen bands in the vdW crystals is quite limited, which is a factor inhibiting potential applications.Thus, it is important to examine different material families offering isotropic bands in other spectral regions.Cubic and pseudocubic perovskite oxides exhibit optically intense phonon modes and also support low-loss PhPs [13][14][15][16] .In particular, strontium titanate (SrTiO3) stands out as one of the most technologically developed and broadly used materials in oxide electronics and is a host of many exciting physical phenomena, including incipient ferroelectricity 17 , dilute superconductivity 18 and interfacial 2D electron gas 19 .
In addition, SrTiO3 exhibits tunable phononic and photonic properties through electrical and optical excitations, strain control, and controlling the concentration of oxygen vacancies and chemical dopants [19][20][21][22][23][24] .Recent advances in the synthesis of freestanding, large-scale crystalline oxide membranes with the thickness close to the unit-cell limit have provided new opportunities for polaritonics and photonics [25][26][27][28][29] .For instance, theoretical studies have suggested the presence of highly confined SPhPs with a good propagation quality in ultrathin SrTiO3 and other perovskite membranes down to the monolayer limit 30 .Such phonon polaritons, however, have not been experimentally studied so far.
Here, we explore SrTiO3 membranes as a new promising platform for PhPs in the infrared regime.Combining far-field Fourier-transform infrared (FTIR) spectroscopy and near-field synchrotron infrared nanoscopy (SINS), we experimentally confirm both the antisymmetric and symmetric SPhP modes, including the radiative Berreman mode, in a 100 nm crystalline SrTiO3 membrane transferred onto a thermally oxidized silicon substrate, part of which is covered by gold (Fig. 1a).At this thickness, which is below one percent of the free-space wavelength, the symmetric mode is a truly ENZ mode, with a giant enhancement of the electromagnetic field inside the sample.Moreover, via nanoscopic broadband SINS imaging near the sample edges, we reveal propagating antisymmetric modes exhibiting a momentum 10 times larger than SPhPs of the same energy in bulk SrTiO3.The experimental results match very well with our calculated near-field scattering signals based on the extended-dipole modeling and finite-difference computations.
We prepare an epitaxial heterostructure of 100 nm SrTiO3 thin films with a 16 nm Sr2CaAl2O6 water-soluble sacrificial buffer layer synthesized on single-crystalline SrTiO3 substrates by pulsed-laser deposition (Methods and Supplementary Fig. 1).X-ray diffraction performed on the as-grown heterostructure, reveals that the films are epitaxial, single-phase, and high crystalline quality (Supplementary Fig. 2).After dissolving Sr2CaAl2O6 in deionized water, a millimeter-scale SrTiO3 film is released from the substrate of growth and transferred onto a SiO2/Si substrate.Part of the surface of the latter is coated by 50 nm thick gold (Fig. 1a,c), allowing us to directly compare the PhP properties within the same sample on top of a metal and an insulator.
The resulting membrane is free of cracks and wrinkles over an area of several hundred micrometers and of a high crystalline quality, which is retained after the lift-off, as revealed by atomicresolution scanning transmission electron microscopy (STEM) (Fig. 1b).The AFM topography (Fig. 1d) indicates that the membrane surface is atomically smooth with the RMS roughness of ~850 pm and that the edge is sharp within the resolution limited by lateral tip dimensions.
As a reference for the quantitative analysis of far-and near-field spectral data presented in this paper, we use the dielectric function  () of bulk SrTiO3 (solid lines in Fig. 2a) as a function of frequency .We obtain it by measuring the far-field FTIR reflectivity spectrum at near-normal angle of incidence on a bulk SrTiO3 crystal and fitting it using a factorized formula with three phonon oscillators , where  , and  , are the LO and TO frequencies,  , and  , are the corresponding scattering rates and  is the high-frequency dielectric constant (see Supplementary Note 1).The three modes relevant for this paper,  ,2 = 475±0.3cm -1 ,  ,3 = 546.1±0.8 cm -1 and  ,3 = 798.4±1.7 cm -1 , are shown in Fig. 2a as vertical lines (parameters of other modes are given in Supplementary Table 1).
Next, we analyze the FTIR reflectivity spectra of the SrTiO3 membrane on different substrates obtained using an infrared microscope (see Methods).Fig. 2b presents the reflectivity of the membrane laminated on Au normalized to bare gold.The reflectivity is close to one since the sample is much thinner than the optical penetration depth (Supplementary Fig. 4).
Nevertheless, one can clearly see three dips at about 475, 545 and 790 cm -1 , which are close to  ,2 ,  ,3 and  ,3 respectively (the one at  ,2 is weak but still distinguishable above the noise level, see also Supplementary Fig. 5).To understand the origin of the dips, we first calculate the reflectivity of the membrane at normal incidence ( = 0) (solid line in Fig. 2b).It reproduces the  ,3 dip, which is due to the usual optical absorption, but expectedly does not capture the LO ones because of the transverse nature of light.Second, we calculate the reflectivity at a small but finite angle of incidence ( =13º), which is consistent with the numerical aperture of the focusing objective (black dashed line in Fig. 2b).This time, the simulation mimics both LO dips remarkably well.The absence of the LO structures in the zero-angle simulation suggests that they appear due to the coupling to the z-axis (normal to the surface) component of the electric field of light.To corroborate this interpretation, we perform the same measurements using two objectives with different numerical apertures and therefore different average angles of incidence (Supplementary Fig. 5), and we clearly observe the enhancement of the LO phonon structures with the increase of .Based on this evidence, we identify both dips at  ,2 and  ,3 as the Berreman modes 3,5,31,32 , where the electric field is almost fully trapped inside the sample and oscillates perpendicular to the surface.Fig. 2c presents the reflectivity (symbols) of the same membrane laminated on SiO2/Si normalized to the bare substrate (the reflectivity normalized to gold is shown in Supplementary Fig. 6 and Supplementary Note 3).The corresponding calculations at normal incidence and for  =13º (solid and dashed lines respectively) agree well with the experiment.As the insulating substrate screens the electromagnetic field much weaker than gold, the TO mode in Fig. 2c is much more prominent than in Fig. 2b.On the other hand, the Berreman mode at  ,3 is significantly less pronounced on SiO2/Si than on gold and the one at  ,2 is hidden below the noise level.
A closer look at the experimental and model curves in Fig. 2b and 2c reveals a certain difference between the actual phonon mode frequencies in the membrane and in the bulk SrTiO3 sample.Direct least-squares fitting of the experimental curves in Fig. 2b and 2c (see Supplementary Note 4 and Supplementary Fig. 7) provides us the values of the frequency and the scattering rates for these modes (Supplementary Table 3).Notably, a red shift of 2.8, 3.4 and 8  is found respectively for the modes  ,2 ,  ,3 and  ,3 in the membrane as compared to the bulk, which is beyond the error bars.This interesting fact is possibly a strain-or surface-related effect, which deserves a separate study.
From the same fitting (Supplementary Table 3), we learn that the two Berreman modes have linewidths of 6.3 ± 1.7  and 33.1 ± 2.3  respectively, matching well the scattering rates  ,2 = 5.0 ± 0.5  and  ,3 = 27.7 ± 2.3  in bulk SrTiO3 (Supplementary Table 1).This gives rise to quality factors Q=/ of about 60 and 30 for the two longitudinal modes respectively.Such significant Q-factors result from the small values (< 0.3) of the ( ) at  =  ,2 and  3 , which are significantly lower than the values for plasmonic ENZ materials including indium tin oxide (ITO) and metals 4,33,34 .
Further insights into the nature of the phonon polaritons in the STO membrane can be inferred from scattering-type scanning near-field optical microscopy (s-SNOM), which has shown its potential for studies of ultrathin, two-dimensional, and nanostructured materials 6,8,35,36 .In our work, we perform synchrotron infrared nanospectroscopy (SINS), where broadband synchrotron IR light is focused onto the apex of a metal-coated tip of an AFM operating in tapping mode.
Scattering of light on the sharp tip provides the necessary momentum for the optical excitation of the phonon-polaritons 37 .By scanning the tip over the sample, s-SNOM amplitude () and phase (ϕ) spectra are independently measured as a function of the light frequency and the tip position x and demodulated at several harmonics of the tapping frequency (Methods).Fig. 3a (symbols) shows the second-harmonics amplitude spectrum  2 () obtained on the gold-supported SrTiO3 membrane far away from the sample edges and normalized to signal on bare gold as sketched in Fig. 3e.The data feature two outstanding asymmetric resonant peaks, just below the frequencies  ,2 and  ,3 respectively.These structures are remarkably intense, presenting a stark contrast with only a 4% percent reduction in the far-field reflectivity due to the Berreman modes (Fig. 2b).
By comparing the near-field spectrum with the momentum-and frequency-dependent Fresnel reflection coefficient  (, ) for p-polarized radiation (Fig. 3b), it is straightforward to associate them with the two symmetric ENZ modes in SrTiO3 starting at  ,2 and  ,3 at the light cone ( = /c) and showing a weak negative dispersion as the momentum increases.They are therefore direct counterparts of the radiative Berreman modes inside the light cone observed in off-normal incidence reflection spectra (Fig. 2b).
Remarkably, there are no features related to the transversal mode at  ,3 , neither in the measured spectrum nor in the calculated dispersion for the gold-supported membrane.To establish whether this absence is related to the metallicity of the substrate, we show in Fig. 3c the s-SNOM amplitude spectrum obtained on the part of the membrane that resides on SiO2/Si.One can see that the spectrum in the case of an insulating substrate is drastically different.While the signatures of the ENZ modes are still present, several new structures appear, notably peaks at 490 and 560 cm - 1 as well as an upturn below 370 cm -1 , near the limit of the experimental range.The 490 cm -1 peak (marked with '*') stems from the SiO2 optical phonons as it is present in the spectrum of the bare SiO2/Si substrate (Supplementary Note 5 and Supplementary Fig. 8).However, the 560 cm -1 peak and the 370 cm -1 upturn do not match any phonons in SiO2.To understand their provenance, we present in Fig. 3d the corresponding dispersion map for the SrTiO3/SiO2/Si structure.Now, two asymmetric strongly dispersing modes of SrTiO3 with a positive group velocity / and a nondispersing mode of SiO2 (marked with '*') are present, in addition to the ENZ modes with a weak negative dispersion already seen in Fig. 3b.By a mere frequency comparison, the 560 cm -1 peak and the 370 cm -1 upturn can now be related to the antisymmetric modes.
Yet, comparing the s-SNOM spectra and the dispersion maps is not entirely straightforward, since the AFM tip interacts with the PhPs with a broad range of momenta.
Therefore, we also simulate the spectra using the extended-dipole model (black lines in Fig. 3a and 3c) 38,39 based on the dielectric function of bulk SrTiO3 (Fig. 2a).The model curves reproduce all the experiment features remarkably well.The fact that the match is quantitatively not perfect is not surprising given the approximative character of the substitution of a real tip with an ellipsoidal extended dipole in this approach.We can conclude that the s-SNOM amplitude increases in the spectral band, where the asymmetric mode is seen in the dispersion.The attribution of the 560 cm - 1 peak and the 370 cm -1 upturn to the antisymmetric modes is thus confirmed.
Why is the antisymmetric mode only seen in the SiO2/Si-supported membrane, while the symmetric (ENZ) mode is observed on both substrates?To understand this, we present in Fig. 3f-3i a finite-difference (FD) simulation of the distribution of the electromagnetic field in the SrTiO3 membrane on both substrates at two frequencies (787 cm -1 and 560 cm -1 ) corresponding to the excitation modes with different symmetry.Here, a plane wave is incident on the sample, and a small piece of gold is placed on top of the membrane to provide the necessary in-plane momentum.
Fig. 3f and 3h show the field distribution for the case of the ENZ mode in SrTiO3 on gold and SiO2/Si, respectively.In accordance with the known properties of the ENZ modes 2,3 , the field is concentrated inside the membrane, with a very weak intensity in the substrate.Thus, the substrate has only a limited influence on the ENZ-PhPs.Fig. 3g and 3i illustrate the field distribution in the membrane on two different substrates when the antisymmetric SPhPs are excited.In contrast to symmetric ENZ-PhPs, the strongest electric field intensity is observed outside the membrane.
Obviously, the antisymmetric modes are fully suppressed in the gold-supported membrane since the high conductivity of the metal does not allow the field to spread outside SrTiO3.
Unlike ENZ modes, the antisymmetric SPhPs, having a positive group velocity, are expected to propagate and cause interference effects when the tip is near the sample edges.To verify this, we perform SINS line scans by moving the tip across the edge of the membrane on the SiO2/Si substrate and recording the near-field spectra (such as the ones on Fig. 3a and 3c) as a function of x.Fig. 4a and 4b show the position-frequency maps of the s-SNOM amplitude and phase respectively, while Fig. 4c and 4d present the corresponding spectra at selected positions.As expected, only the spectral band between about 550 and 600 cm -1 corresponding to the membrane (diamonds) and bulk crystals (circles).In the first case, C is reaching 10 and it is, as expected, close to 1 in the latter case, indicating no confinement.Fig. 4i shows the propagation length Lp =1/q2 and the quality factor  =  1 / 2 .The value of Lp ranges from 6 μm to 2 μm, decreasing with frequencies At the same time, the quality factor varies between 2 and 6, which is comparable to the value measured for the infrared plasmons in non-encapsulated graphene ( = 5) 36,42 and larger than the value measured for the terahertz plasmon in Bi2Se3 thin films ( = 3.2) 40 .However, it is significantly smaller than the quality factor for plasmons in hBN encapsulated graphene (~25) 6,8,35,36 , hyperbolic PhPs in hBN (~20) 43 and MoO3 (~20) 8 , as well as weakly confined SPhPs in bulk SrTiO3 (~25) 11 .
We note that no spatially dispersing structures are found in the similar SINS scans across the edge where the membrane is supported by gold (Supplementary Fig. 11).This is fully in agreement with the mentioned above absence of the asymmetric mode found in this case, corroborating our conclusion that propagating asymmetric SPhP modes are suppressed in metalsupported membranes.
In summary, we have experimentally observed a symmetric-antisymmetric phononpolariton mode splitting in a high-quality single crystalline membrane of SrTiO3.Due to the ultrasubwavelength sample thickness, the symmetric mode is pushed to the epsilon-near-zero regime, where the normal component of the electric field is multiple times enhanced inside the sample as compared to the external field.The propagating antisymmetric mode is found to be confined in terms of the wavelength by a factor of 10 as compared to the SPhP mode in bulk SrTiO3.The strong confinement of light and the field enhancement observed here can be exploited for various nanophotonic applications such as mid-infrared subwavelength resonators and metasurfaces.
Transferable membranes of SrTiO3 and other oxides are therefore a promising platform to realize perfect absorption and nonlinear nanophotonic applications in the infrared regime.In addition, enhanced light-matter interactions can enable the control over the paraelectric-to-ferroelectric phase transition in this material 44,45 .Notably, such membranes can be easily integrated with other photonic materials and resonators to form strongly coupled hybrid polaritons for light manipulation.Although we observed an extrinsic optical loss introduced by the SiO2/Si substrate, the SPhPs propagation in the membranes can be potentially enhanced by using less lossy substrates or even using suspended membranes 46,47 .Overall, our work demonstrates the large potential of transition-metal oxide membranes as building blocks for future long wavelength nanophotonics.

Methods
Thin-film Growth.The epitaxial heterostructure of 100 nm SrTiO3 films was synthesized with a 16 nm Sr2CaAl2O6 sacrificial layer on (001)-oriented SrTiO3 substrates via pulsed-laser deposition.The growth of the Sr2CaAl2O6 layer was carried out in dynamic argon pressure of 4 × 10 6 torr, at a growth temperature of 710 °C, a laser fluence of 1.35 J/cm 2 , and a repetition rate of 1 Hz, using a 4.8 mm 2 imaged laser spot.The growth of the SrTiO3 layer was conducted in dynamic oxygen pressure of 4 × 10 6 torr, at a growth temperature of 710 °C, a laser fluence of 0.9 J/cm 2 , and a repetition rate of 3 Hz, using a 3.0 mm 2 imaged laser spot.Dashed-dotted Vertical lines in panels a-d denote the LO and TO frequencies of bulk SrTiO3.eh, simulated distribution of the electromagnetic field, when a sample is illuminated with a plane wave and a gold nanobeam (marked with a black rectangle) is placed on top in order to excite waves with finite in-plane momenta, for the membrane on gold at 787 and 560 cm -1 , respectively (e and g), and for the membrane on SiO2/Si at the same frequencies (marked with dashed lines in panels a-d) (f and h).In gold, the electromagnetic field is negligibly small.

Figure 1 |
Figure 1 | Preparation and structural characterization of SrTiO3 membranes.a Schematics of the s-SNOM/SINS measurement on an SrTiO3 membrane.b Atomic-resolution STEM imaging of a freestanding SrTiO3 membrane suspended on a SiNx TEM grid.Inset shows the Fouriertransform of the STEM image.c The optical image of the SrTiO3 membrane transferred on a thermally oxidized Si substrate with part of the surface coated by a 50 nm thick gold film.The white arrow denotes the edge of the membrane.The inset shows the trace of SINS line scan across the edge of the membrane supported on SiO2/Si substrate.dA line scan of the height profile across the edge of the membrane.The inset indicates the trace of the line scan.

Figure 2 |
Figure 2 | Analysis of far-field reflectivity spectra of the SrTiO3 membrane.a The real and imaginary parts of the dielectric function of SrTiO3 at room temperature obtained by a factorizedformula fitting of the normal-incidence reflectivity measured on bulk SrTiO3.b Far-field reflectivity of a 100 nm SrTiO3 membrane laminated on gold (symbols) normalized to bare gold, and calculated spectra using the dielectric function of bulk SrTiO3 for normal incidence (solid line)and for  =13 o (dashed line).c Far-field reflectivity of the same SrTiO3 membrane on SiO2/Si normalized to the substrate (symbols), and calculated spectra using the dielectric function of bulk

Figure 3 |
Figure 3 | SINS spectra on a SrTiO3 membrane supported by gold-and SiO2. a and c, symbols: SINS second-harmonics amplitude spectra ("sam") of the membrane on gold-(a) and on SiO2/Si (c) normalized to the signal from bare gold ("ref").Solid lines: finite-dipole model based on the dielectric function of bulk SrTiO3.b and d, calculated imaginary part of the complex reflection coefficient  (, ) for the 100 nm SrTiO3 membrane on gold and on SiO2/Si, respectively.