Device fabrication<\/p>\n
The flakes used for device fabrication were mechanically exfoliated from bulk crystals (HQ Graphene, WSe2, NIMS hexagonal boron nitride (hBN), NGS natural graphite) onto silicon substrates. They were stacked together inside a N2-filled glovebox using a standard dry-transfer method56<\/a>. In this technique, the flakes are aligned with submicrometre precision and subsequently picked up with a transparent polymer stamp consisting of a dome-shaped polydimethylsiloxane (PDMS) covered with a thin polycarbonate (PC) film. The finished vdW heterostructure was then released onto a silicon substrate with a 285-nm-thick SiO2 layer and prepatterned electrodes (approximately 15-nm gold with about 5-nm titanium adhesion layer). Before the release step, the device was aligned with respect to the electrode pattern such that each few-layer graphene flake (top gate, contact and back gate) was connected to a separate electrode. Finally, the PC residue was removed by dissolving it in either chloroform or dichloromethane.<\/p>\n For both devices, the thicknesses of the encapsulating hBN layers were selected to ensure either constructive (device A) or destructive (device B) interference between resonant light reflected from various interfaces away from the WSe2 monolayer region. This choice guarantees almost Lorentzian lineshapes of excitonic optical transitions in the WSe2 monolayer reflectance contrast spectra, which greatly facilitates resolving weak spectral signatures of the WC. In particular, device A, along with two approximately 30-nm-thick hBN layers separating WSe2 from the top and bottom few-layer graphene gates, consisted of a third ~40-nm-thick hBN capping layer (Fig. 1a<\/a>). By contrast, no hBN capping layer was used for device B. For both samples, the doping density in the WSe2 monolayer was tuned by applying top-gate voltage VTG, keeping the bottom gate at the ground potential. Device A showed no signatures of electrical hysteresis when VTG was ramped in a loop. To avoid residual gate hysteresis for device B (Supplementary Figs. 3<\/a> and 4<\/a>), its charge configuration was reset before each measurement by sweeping the gate voltage to \u20134\u2009V with the imaging light on.<\/p>\n Experimental setup<\/p>\n Our experiments were carried out in a closed-cycle cryostat equipped with a superconducting magnet (up to 9\u2009T). The sample was mounted on x\u2013y\u2013z piezoelectric stages inside a variable-temperature insert (VTI) filled with He exchange gas to ensure efficient thermal contact, allowing the sample temperature to be tuned from 1.6\u2009K to room temperature. Reflectance measurements were performed in a confocal geometry (Extended Data Fig. 1<\/a>) using a supercontinuum laser (30-MHz repetition rate) coupled to a motorized filter and a single-mode fibre, enabling the automatic selection of excitation spectral range. The excitation light was collimated before entering the VTI through a wedged window, and then focused onto the sample surface onto a diffraction-limited spot by a microscope objective with a large numerical aperture (0.8). The excitation power in front of the VTI window was monitored with a fast photodiode and actively stabilized using a proportional\u2013integral\u2013derivative (PID) controller coupled to a voltage-controlled variable optical attenuator. Except for the optical spin orientation experiments, the power value was kept in the range of a few tens of nanowatts to ensure that the excitons did not perturb the probed electronic system. The light reflected from the sample was collected by the same objective, directed into the detection path by a beamsplitter, coupled into a single-mode fibre, and finally dispersed by a spectrometer equipped with a Peltier-cooled charge-coupled device (CCD) camera, enabling recording of the spectra. The polarizations of both excitation and detection beams were controlled with a set of linear polarizers and achromatic waveplates.<\/p>\n Analysis of reflectance spectra<\/p>\n To determine \u0394R\/R0, the measured reflectance spectrum R is normalized using the reference spectrum R0 acquired in a region of the device featuring all layers except for the WSe2 monolayer. The reflectance contrast is then determined at each photon energy as Rc \u2261 \u0394R\/R0 = ((R \u2212 Cdark) \u2212 (R0 \u2212 Cdark))\/(R0 \u2212 Cdark), where Cdark denotes the dark counts of the CCD camera.<\/p>\n The derivative of the reflectance contrast with respect to the energy and gate voltage was obtained using a standard symmetric difference quotient method. To reduce the noise, the numerical derivative is approximated as \\(R{\\prime} ({V}_{{\\rm{G}},n})=\\left[\\left({R}_{{\\rm{c}}}\\right.({V}_{{\\rm{G}},n+\\delta })-{R}_{{\\rm{c}}}({V}_{{\\rm{G}},n-\\delta })\\right]\/\\left[{V}_{{\\rm{G}},n+\\delta }-{V}_{{\\rm{G}},n-\\delta }\\right]\\) and \\(R{\\prime} ({E}_{n})=\\left[\\left({R}_{{\\rm{c}}}\\right.({E}_{n+\\delta {\\prime} })-{R}_{{\\rm{c}}}({E}_{n-\\delta {\\prime} })\\right]\/\\left[{E}_{n+\\delta {\\prime} }-{E}_{n-\\delta {\\prime} }\\right]\\), where the index n denotes subsequent points8<\/a>. The step \u03b4 in gate voltage and \\(\\delta {\\prime}\\) in energy are chosen such that noise from abrupt changes in Rc occurring within \u0394ne of a few 1010\u2009cm\u22122 or \u0394E \u2272 1\u2009meV is suppressed.<\/p>\n Fitting the spectral energies of optical resonances<\/p>\n To determine the energies of the main excitonic transitions (X, APS and APT) in the reflectance contrast spectra, we fit their spectral profiles with the following dispersive Lorentzian formula8<\/a>,27<\/a>,57<\/a><\/p>\n $$\\begin{array}{l}{\\mathcal{L}}({E}_{0},A,\\gamma ,\\varphi ;E\\,)=A\\cos \\varphi \\frac{\\gamma \/2}{{(E-{E}_{0})}^{2}+{\\gamma }^{2}\/4}+A\\sin \\varphi \\frac{{E}_{0}-E}{{(E-{E}_{0})}^{2}+{\\gamma }^{2}\/4}+B(E\\,),\\end{array}$$<\/p>\n \n (2)\n <\/p>\n where E denotes the photon energy, whereas A, E0 and \u03b3 represent the amplitude, peak energy and linewidth of the analysed optical resonance, respectively. The parameter \u03c6 represents the phase shift induced by the interference of light reflected off different interfaces within the heterostructure, which depends on both resonance energy and amplitude. Finally, B(E) accounts for a background term stemming from spectral proximity of other resonances, which is assumed to be either constant B(E) = C or polynomially dependent on the photon energy. For the APs, we assume that both transitions have a common phase. Moreover, at densities below ~1011\u2009cm\u22122\u2014where the APs become very weak\u2014their phase and linewidths are fixed at values obtained for a higher ne. Coherent with previous works8<\/a>,27<\/a>,57<\/a>, this method allows us to precisely reproduce the lineshapes of all three main resonances (Extended Data Fig. 4a<\/a>).<\/p>\n Owing to their markedly smaller intensities, the umklapp-scattered exciton and WP resonances cannot be fitted using the above procedure. Instead, to extract their spectral positions, we directly fit the differentiated d2(\u0394R\/R0)\/dVTGdE spectra, where the umklapp transitions are greatly amplified due to their much larger blueshifts compared with the main excitonic resonances. To quantitatively describe the resulting spectral profiles, we assume that the evolution of the UX or WP lineshape \\({{\\mathcal{L}}}_{{\\rm{U}}}({E}_{{\\rm{U}}},{A}_{{\\rm{U}}},{\\gamma }_{{\\rm{U}}},{\\varphi }_{{\\rm{U}}};E)\\) is dominated by the linear-in-density energy blueshift. This allows us to approximate its differentiated spectral profile \\({{\\mathcal{D}}}_{{\\rm{U}}}({E}_{{\\rm{U}}},{A}_{{\\rm{U}}},{\\gamma }_{{\\rm{U}}},{\\varphi }_{{\\rm{U}}};E)\\) in the following way:<\/p>\n $$\\begin{array}{l}{{\\mathcal{D}}}_{{\\rm{U}}}({E}_{{\\rm{U}}},{A}_{{\\rm{U}}},{\\gamma }_{{\\rm{U}}},{\\varphi }_{{\\rm{U}}};E\\,)\\\\=\\displaystyle\\frac{{d}^{\\,2}}{d{V}_{{\\rm{TG}}}dE}{{\\mathcal{L}}}_{{\\rm{U}}}({E}_{{\\rm{U}}},{A}_{{\\rm{U}}},{\\gamma }_{{\\rm{U}}},{\\varphi }_{{\\rm{U}}};E\\,)\\\\\\,\\approx \\left(\\displaystyle\\frac{d{E}_{{\\rm{U}}}}{d{{\\rm{V}}}_{{\\rm{TG}}}}\\right)\\times \\displaystyle\\frac{\\partial }{\\partial {E}_{{\\rm{U}}}}\\displaystyle\\frac{d}{dE}{{\\mathcal{L}}}_{{\\rm{U}}}({E}_{{\\rm{U}}},{A}_{{\\rm{U}}},{\\gamma }_{{\\rm{U}}},{\\varphi }_{{\\rm{U}}};E\\,)\\\\ \\,={\\tilde{A}}_{{\\rm{U}}}\\displaystyle\\frac{\\cos {\\varphi }_{{\\rm{U}}}\\left[{\\gamma }_{{\\rm{U}}}^{2}\/4-3{(E-{E}_{{\\rm{U}}})}^{2}\\right]{\\gamma }_{{\\rm{U}}}\/2+\\sin {\\varphi }_{{\\rm{U}}}(E-{E}_{{\\rm{U}}})\\left[-3{\\gamma }_{{\\rm{U}}}^{2}\/4+{(E-{E}_{{\\rm{U}}})}^{2}\\right]}{{\\left[{\\gamma }_{{\\rm{U}}}^{2}\/4+{(E-{E}_{{\\rm{U}}})}^{2}\\right]}^{3}},\\end{array}$$<\/p>\n \n (3)\n <\/p>\n where \\({\\tilde{A}}_{{\\rm{U}}}=2{A}_{{\\rm{U}}}\\times d{E}_{{\\rm{U}}}\/d{V}_{{\\rm{TG}}}\\) is the effective amplitude of the analysed umklapp transition in the differentiated spectrum, whereas \u03b3U, \u03c6U and EU denote its linewidth, phase and energy, respectively. In view of their negligible amplitudes, the phases of all three umklapp resonances can be fixed at the same value corresponding to the low-oscillator-strength limit of the phase of an optical resonance in the analysed device8<\/a>. It is determined based on the transfer-matrix (TM) simulations of the device reflectivity spectrum58<\/a>,59<\/a> (described in the next section) and further confirmed by the phase of two AP resonances in the low-density limit, yielding \u03c6U \u2248 3.0 for device A and \u03c6U \u2248 0.3 for device B. To facilitate the fitting procedure, the linewidths of the umklapp resonances are always constrained within reasonable ranges, and assumed to increase with ne for UX. The fitting itself is carried out within a narrow spectral window around a given resonance. In the case of WPs, each transition is first individually fitted. The obtained parameters are then partially constrained and used as a starting point for a final fit of the two WP branches with the sum of two \\({{\\mathcal{D}}}_{{\\rm{U}}}\\) profiles that is further corrected by a background term accounting for the tails of the main X and AP resonances in the spectrum. This is justified by their relatively large energy distance from both WP resonances. This assumption does not hold for the UX resonance, which spectrally overlaps with the main exciton resonance. To account for this, the UX is fitted using a sum of its expected profile \\({{\\mathcal{D}}}_{{\\rm{U}}}\\) and numerically computed second derivative of the dispersive Lorentzian profile fitted beforehand to the X resonance. As shown in Extended Data Fig. 4b<\/a>, these procedures enable us to accurately reproduce the spectra of both WP and UX transitions and quantitatively extract their energies.<\/p>\n Determination of spectral weights of optical resonances<\/p>\n Although dispersive Lorentzian fitting described in the earlier section allows for a precise determination of the spectral positions of optical resonances, the amplitudes obtained in such a way do not directly correspond to the oscillator strengths. Whenever we are interested in the latter (for normalizing the WC phase diagrams (Fig. 2c<\/a> and Supplementary Fig. 4c<\/a>) and for analysing the density-dependent AP intensities (Extended Data Figs. 2<\/a> and 3<\/a>)), we use a more complex TM model58<\/a>,59<\/a>,60<\/a>,61<\/a>. In this case, each resonance is described with the following complex susceptibility: \u03c7(E) = \u2212(\u210fc\/E0)\u03b3rad\/(E \u2212 E0 + i\u03b3nrad\/2), where E is the photon energy; E0 is the resonance energy; and \u03b3nrad\/\u210f and \u03b3rad\/\u210f denote its non-radiative and free-space radiative decay rates, respectively, with the latter being directly proportional to the oscillator strength. Assuming the hBN thicknesses from the \u2018Device fabrication\u2019 section and standard values of hBN\/graphene\/SiO2 refractive indices8<\/a>,61<\/a>, we can aptly reproduce the interference pattern within the vdW heterostructure, thereby correctly capturing the lineshapes of optical resonances, as shown for the example spectra in Extended Data Fig. 6a,b<\/a>. In these fits, analogously to the case of dispersive Lorentzian profile fitting, the TM-calculated spectra are overlaid on a background term. Moreover, non-radiative broadening \u03b3nrad controlling the linewidths of APs is assumed to be the same for both singlet and triplet branches, and fixed in the low-density regime below a few 1010\u2009cm\u22122. By performing such fitting at various electron densities, we can directly determine ne-dependent oscillator strengths of the main AP\/X resonances as fAP\/X(ne) = \u03b3rad,AP\/X(ne)\/\u03b3rad,X relative to that of the X at charge neutrality (set by \u03b3rad,X).<\/p>\n Given their inherently weak nature, WP transitions cannot be easily fitted with a similar TM model, particularly near the WC melting point. In this regime, tracing WP intensities requires alternative approaches (see the \u2018Analysis of WC melting\u2019 section) that do not allow for quantitative extraction of fWP. This is, however, possible at low temperatures in a selected density range in which the WC is stable and WP transitions are spectrally well separated from the X\/AP resonances. To facilitate the TM fitting in this regime, we first subtract the fitted AP and X spectral profiles, as well as similarly corrected reflectance spectrum measured at charge neutrality (to suppress the influence of residual etaloning in our setup). These data are then further corrected by subtracting a linearly dependent background fitted in the spectral range between X and APT. Finally, the WP resonances in the resulting background-corrected spectrum are fitted using the above-described TM model with fixed energies obtained based on the dispersive Lorentzian model. As shown in Extended Data Fig. 6c,d<\/a>, this procedure reproduces the WP lineshapes reasonably well, allowing us to extract their density-dependent spectral weights fWP\/fAP relative to the corresponding AP branches (Extended Data Fig. 6e<\/a>). Despite the fact that their peak-to-peak amplitudes are more than a few tens of times smaller than that of APs, the WPs exhibit sizably larger linewidth, presumably due to additional broadening channels stemming from the WC disorder (Supplementary Section 1<\/a>). For this reason, fWP\/fAP can be as high as 10%\u201320% in the low-density regime, supporting our conclusion of the substantial hybridization of AP and WP transitions. Still, we stress that in view of complex background subtraction procedures, the extracted fWP\/fAP values are fraught with large uncertainties, which are probably larger than the statistical error bars shown in Extended Data Fig. 6e<\/a>.<\/p>\n Calibration of doping density<\/p>\n Since the energy splitting between the UX\/WP transitions and the corresponding main X\/AP resonances is determined by the WC lattice constant, which, in turn, depends on ne, it is crucial for our analysis to accurately determine ne. To this end, we describe our device as a parallel-plate capacitor, which allows us to express ne as ne = (CTG\/e) \u00d7 (VTG \u2212 V0), where e is an elementary charge, V0 is the voltage corresponding to the onset of electron filling into the conduction band and CTG is the geometrical capacitance between the top gate and WSe2 monolayer per unit area of the device.<\/p>\n To determine V0, we analyse the VTG-dependent AP oscillator strengths and X energies that are extracted based on TM or dispersive Lorentzian fitting of their spectral profiles (see the \u2018Fitting the spectral energies of optical resonances\u2019 and \u2018Determination of spectral weights of optical resonances\u2019 sections). Consistent with the Fermi polaron model17<\/a>,62<\/a>, the spectral weights of singlet and triplet AP resonances exhibit a linear increase with VTG in the low-density regime (Extended Data Fig. 2a<\/a> shows example results obtained at T = 1.6\u2009K). Importantly, linear fits to both increasing trends extrapolate to the zero oscillator strength at exactly the same voltage, which precisely corresponds to V0. This value is consistent with that corresponding to the onset of doping-induced X blueshift (Extended Data Fig. 2b<\/a>).<\/p>\n The capacitance CTG is, in turn, extracted based on Shubnikov\u2013de Haas oscillations of the optical transitions at a high magnetic field (8\u2009T). These oscillations arise from the successive filling of LLs (Extended Data Fig. 3a<\/a>), giving rise to characteristic cusps in energies and intensities of exciton\u2013polaron transitions at integer LL filling factors27<\/a>,61<\/a>,63<\/a>. In our analysis, we focus on the low-density regime in which the electrons primarily fill the states in a single valley, and trace the local maxima (minima) of APT oscillator strength in \u03c3+ (\u03c3\u2212) polarization (Extended Data Fig. 3b,c<\/a>). Together with VTG corresponding to the onset of electron doping, this allows us to determine gate voltages corresponding to subsequent \u03bd = 0, 1, 2, 3. As shown in Extended Data Fig. 3d<\/a>, they are very well reproduced by a linear relation \u03bd = (CTG\/e) \u00d7 (h\/eB) \u00d7 (VTG \u2212 V0), enabling us to extract CTG\/e = (5.9 \u00b1 0.3) \u00d7 1011\u2009cm\u22122\u2009V\u22121. Importantly, this result agrees well with the geometrical capacitance calculated based on the hBN thickness of 30\u2009nm and the hBN dielectric constant of \u03f5hBN = 3.1 (refs. 64<\/a>,65<\/a>).<\/p>\n Calibration of the sample temperature<\/p>\n For all measurements, the sample temperature was determined using the temperature sensor of the VTI. To verify this calibration, we analyse the temperature-induced redshift in the exciton resonance, which arises from the shrinkage of the semiconducting bandgap Eg(T) and is well described by the Varshni formula66<\/a>:<\/p>\n $${E}_{{\\rm{g}}}(T\\,)={E}_{0}-\\frac{\\alpha {T}^{2}}{T+\\beta },$$<\/p>\n \n (4)\n <\/p>\n where E0 denotes the low-temperature limit, and \u03b1 and \u03b2 are material-specific parameters previously reported as \u03b1 = 0.424\u2009meV\u2009K\u22121 and \u03b2 = 170\u2009K for monolayer WSe2 (ref. 67<\/a>). As shown in Extended Data Fig. 5<\/a>, this dependence accurately reproduces the temperature evolution of the exciton energy at charge neutrality in our device, with E0 serving as the only fitting parameter. The excellent agreement confirms the reliability of our temperature calibration.<\/p>\n Analysis of WC melting<\/p>\n To determine the temperature- and doping-dependent intensities of umklapp and WP resonances, we pursue a similar approach to that introduced in our previous study8<\/a>. In the first step, UX\/WP spectral weights at a given T and ne are estimated by integrating out the absolute value of background-corrected differentiated reflectance signal \u2223d2(\u0394R\/R0)\/dVTGdE \u2212 B(E, ne)\u2223 over a narrow window \\({E}_{\\min } < E < {E}_{\\max }\\) around each resonance. The background B(E, ne) is obtained separately for UX\/WP at each ne by averaging polynomial profiles fitted to the data at high temperatures (above 35\u2009K), where the umklapp features become indiscernible. To facilitate a quantitative comparison between different UX\/WP branches, the integration windows are taken to be equally wide for each of them. Moreover, their spectral positions are adjusted to compensate for doping- and temperature-induced shifts of umklapp transitions. In particular, at a given ne, the windows are displaced according to the temperature-induced energy shift of the neutral exciton EX(T) at charge neutrality (Fig. 2b<\/a> and Supplementary Fig. 4b<\/a>).<\/p>\n In the second step, the above-determined spectral weights of umklapp resonances are normalized with the fitted oscillator strengths f(ne, T) of the corresponding main X\/AP resonances. This finally allows us to calculate the relative intensities of exciton umklapp or WP transitions as<\/p>\n $${I}_{{\\rm{U}}}({n}_{{\\rm{e}}},T\\,)=\\frac{\\int_{{E}_{\\min }}^{{E}_{\\max }}\\left\\vert\\frac{{d}^{\\,2}(\\Delta R\/{R}_{0})}{d{V}_{{\\rm{TG}}}\\,dE}-B(E,{n}_{{\\rm{e}}})\\right\\vert{dE}}{f({n}_{{\\rm{e}}},T\\,)}.$$<\/p>\n \n (5)\n <\/p>\n The extracted values of IU(ne, T) for UX and both WPS,T are plotted as a function of ne and T in Fig. 2c<\/a> and Supplementary Fig. 4c<\/a> for devices A and B, respectively, revealing the WC phase diagrams.<\/p>\n Comparison between optical signatures of electron and hole WCs<\/p>\n To gain further insights into the mechanisms of the Wigner polaron formation, we perform measurements under hole doping in device A. Extended Data Fig. 7a,b<\/a> shows a representative comparison of the low-temperature reflectance spectra measured as a function of electron (ne) and hole (nh) densities (both calibrated using the procedure described in the \u2018Calibration of doping density\u2019 section). In both cases, the spectra are plotted using the same colour scale and differentiated with respect to the energy and respective carrier density (rather than the gate voltage), ensuring a consistent correspondence between colour and differentiated signal.<\/p>\n The key difference between the electron and hole optical responses is the presence of only one APS resonance in the hole spectra. This stems from the opposite ordering of spin-orbit-split bands in the valence band (Fig. 1d<\/a>), which allows only a singlet hole trion to be bound. By contrast, the low-density evolution of the X resonance is similar for both carrier species, in each case displaying the familiar Bragg umklapp signature UX of WC formation. In general, the hole UX exhibits similar detuning from the main exciton determined by the same mX \u2248 0.68m0 (see also the linecut in Extended Data Fig. 7c<\/a>), yet showing a non-trivial fine structure at nh \u2273 3 \u00d7 1011\u2009cm\u22122 before completely disappearing around a critical density comparable with that of the electron WC. Although understanding the origin of this fine structure requires further studies, the fact the hole WC persists to much larger densities than ~1 \u00d7 1011\u2009cm\u22122 reported in ref. 12<\/a> for ultraclean flux-grown WSe2 monolayers further supports our conjecture on the role of disorder in stabilizing both electron and hole crystalline phases in our devices.<\/p>\n Alongside the UX transition, also for hole doping, the spectra exhibit a faint blueshifting resonance (WPS) in the energy range between APS and X, whose properties align with the Wigner polaron picture. In particular, it appears only at low densities. Moreover, its energy splitting from the APS exhibits a linear increase \\({\\varDelta }_{{\\rm{h}}}+{h}^{2}{n}_{{\\rm{h}}}\/\\sqrt{3}{m}_{{\\rm{X}}}\\) (Extended Data Fig. 7b<\/a>, dashed line) with the slope determined by the exciton mass mX and a similar zero-density energy offset \u0394h \u2248 7\u2009meV as for the WPs on the electron side. These observations are consistent with our interpretation that WPs are not limited to a specific spin structure of optical excitations in electron-doped WSe2, but rather are general excitations of sufficiently robust WCs. We stress, however, that the unequivocal identification of hole WPS as a WP is hindered by the relatively small binding energy of the hole APS, which causes the WPS transition to appear in the tail of X already at very low hole densities. The spectral overlap between these two resonances increases for nh \u2273 3 \u00d7 1011\u2009cm\u22122, rendering WPS no longer discernible in this regime. Consequently, direct evidence for the WP formation for a setting in which only one trion is bound merits further studies of other transition metal dichalcogenide monolayers.<\/p>\n","protected":false},"excerpt":{"rendered":"Device fabrication The flakes used for device fabrication were mechanically exfoliated from bulk crystals (HQ Graphene, WSe2, NIMS…\n","protected":false},"author":2,"featured_media":1144244,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_share_on_mastodon":"0"},"categories":[3845],"tags":[11701,11700,11705,11704,20546,3968,11699,11702,11703,85239,12374,74,22503,70,11698,13811,16,15],"class_list":["post-1144243","post","type-post","status-publish","format-standard","has-post-thumbnail","category-physics","tag-atomic","tag-classical-and-continuum-physics","tag-complex-systems","tag-condensed-matter-physics","tag-electronic-properties-and-materials","tag-general","tag-mathematical-and-computational-physics","tag-molecular","tag-optical-and-plasma-physics","tag-optical-spectroscopy","tag-phase-transitions-and-critical-phenomena","tag-physics","tag-quantum-fluids-and-solids","tag-science","tag-theoretical","tag-two-dimensional-materials","tag-uk","tag-united-kingdom"],"share_on_mastodon":{"url":"https:\/\/pubeurope.com\/@uk\/117082183861549936","error":""},"_links":{"self":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/1144243","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/comments?post=1144243"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/1144243\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media\/1144244"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media?parent=1144243"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/categories?post=1144243"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/tags?post=1144243"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}