Fig. 1: Characterisations of TBG drum and butterfly-shaped hysteresis loop.<\/b> a<\/b> Optical image of Device A with three TBG drums (1, 2, 3) contacted by a Ti\/Au lead. The right panel shows the schematics of the moir\u00e9 pattern formed by a twist angle of \u03b8\u00a0~\u00a012\u00b0, where alternating AA, AB and, BA stacked regions appear (scale bar: 1\u2009nm). b<\/b> Sketch of our experiment combining electrostatic actuation, optical displacement readout, and micro-Raman spectroscopy. The TBG (with its static displacement \u03be) is represented by the dark blue dashed line; its flexural motion is sketched in light blue. M, LEF, and APD represent a mirror, a long-pass edge filter, and an avalanche photodiode, respectively. c<\/b> Raman spectrum of TBG measured at the centre of drum 2 (D\u00a0=\u00a08\u2009\u03bcm) by excitation at 532 nm plus the extended spectral region for the \\({{{{\\rm{R}}}}}^{{\\prime} }\\) mode. Inset: a mini-Brillouin zone with a twist angle dependent lattice vector q(\u03b8). d<\/b> The frequencies of the G and the \\({{{{\\rm{R}}}}}^{{\\prime} }\\) modes extracted from Raman spectra measured with Vdc varying from \u00a0\u2212\u00a09 V to 0 V. The straight dashed line is a guide for the eye. Error bars are extracted from the fits to the Raman spectra. e<\/b> The resonant mechanical response measured in drum 3 (D\u00a0=\u00a012\u2009\u03bcm) at Vdc\u00a0=\u00a0\u2212\u00a010 V shows a large Q of \u00a0~\u00a01900 at room temperature. f<\/b> Mechanical frequency responses measured with Vdc undergoing the forward-then-backward sweep sequence (indicated by arrows), forming a butterfly-shaped hysteresis loop.<\/p>\n We first estimate \u03b8 from the moir\u00e9 superlattice-activated Raman mode. Figure\u00a01<\/a>c shows the Raman spectrum of the suspended TBG measured at the centre of drum 2 with a 532 nm excitation (see Methods), which shows two main features: the strong G mode and the weak \\({{{{\\rm{R}}}}}^{{\\prime} }\\) mode, arising from the zone-centred (i.e., zero momentum) phonons and the moir\u00e9 superlattice-activated phonons with momentum \\(q(\\theta )=\\frac{8\\pi }{\\sqrt{3}a}\\sin (\\frac{\\theta }{2})\\) (as shown in the inset to Fig.\u00a01<\/a>c), respectively. The value of \u03b8 is extracted from the frequency of the \\({{{{\\rm{R}}}}}^{{\\prime} }\\) mode, which is close to the target value specified in the fabrications. Figure\u00a01<\/a>d shows the positions of the \\({{{{\\rm{R}}}}}^{{\\prime} }\\) mode and of the G mode as the gate voltage Vdc decreases from 0 V to \u00a0\u2212\u00a09 V. Surprisingly, both modes are less sensitive to Vdc, within our experimental accuracy, than the G mode in monolayer graphene (MLG)35<\/a>. Meanwhile, the intensity of the G mode remains almost unchanged for Vdc down to \u00a0\u2212\u00a05 V before decreasing by \u00a0~\u00a010% at Vdc\u00a0=\u00a0\u2212\u00a09 V (see Fig.\u00a0S1<\/a>c and Methods). These observations indicate that the Vdc-induced tensile strain is negligible compared to the initial built-in strain (\u03f50), which means that our TBG drums are under high tensile stress.<\/p>\n Large Q at room temperature<\/p>\n Figure\u00a01<\/a>e shows the mechanical response of drum 3 (D\u00a0=\u00a012\u2009\u03bcm) at Vdc\u00a0=\u00a0\u2212\u00a010 V. The resonant frequency fr and corresponding Q are extracted by fitting a linear harmonic resonator model to the measured response (see Methods). The largest Q we measure reaches \u00a0~\u00a01900 at room temperature, more than one order of magnitude higher than Q in graphene resonators at room temperature9<\/a>. Note that such large Q appears at the gate voltage far from the near-zero DC bias, in contrast to graphene resonators35<\/a>. We observe that resonances with unusually large Q exhibit a butterfly-shaped hysteresis loop as the gate voltage is cycled.<\/p>\n Butterfly-shaped hysteresis loop<\/p>\n To measure the hysteretic nanomechanical responses, we increase and decrease the gate voltage in cycles. Figure\u00a01<\/a>f shows the amplitude response as a function of drive frequency and Vdc under a forward-then-backward sweep between Vdc\u2009=\u2009\u00b1\u00a09.5\u2009V, forming a butterfly-shaped hysteresis loop that crosses at Vdc\u00a0=\u00a00 V (white-dashed arrows in Fig.\u00a01<\/a>f). Within the butterfly-shaped hysteresis loop, fr increases by only \u00a0~\u00a05%, which is far less than the typical value of \u00a0~\u00a050% in the low-tensioned MLG drum35<\/a>. Note that all of the mechanical data in this study are from drum 2 in Device A unless otherwise stated. The butterfly-shaped hysteresis loop also shrinks as the sweep range decreases (Fig.\u00a0S5<\/a>a). We find that such viscoelastic responses can be controllably obtained by specifying \u03b8 close to 15\u00b0 in our TBG drums, whereas the TBG with \u03b8\u2009=\u20090\u00b0 does not show a butterfly-shaped hysteresis loop. Supplementary Section\u00a0S3<\/a> provides the statistics on the hysteresis loops of our TBG drums with increasing \u03b8. It suggests that the viscoelasticity in TBG drums is angle-dependent, as we discuss below.<\/p>\n Viscoelastic behaviours<\/p>\n To study the dependence of the shape of the frequency loop on the step rate dVdc\/dt, in Fig.\u00a02<\/a>a we show the hysteresis loops measured at three different values of dVdc\/dt. They have been recorded in a backward-then-forward sequence with a step size of 0.25 V. Remarkably, the maximal fr reached by the loop is revealed with the slow step rate. Furthermore, the width of the hysteresis loop, \u0394Vdc, defined by the largest Vdc shift between the forward and backward traces, shows a non-linear monotonic increase with increasing dVdc\/dt, as shown by the experimental data in Fig.\u00a02<\/a>d.<\/p>\n Fig. 2: Rate and time dependent hysteresis loops and gate tuning of the quality factors Q.<\/b> a<\/b> Resonant frequency loops at different step rates, dVdc\/dt. \u25cb, \u25a1, \u2662 correspond to a slow, medium, and fast step rate, respectively. The arrows indicate the direction of the sweep. b<\/b> Schematic of the flexural drum vibration (top panel) and the reduced viscoelastic model (bottom panel). The membrane flexural motion is modelled by a mass (M) connected to a spring (k) and a dashpot (\u03b7s) in parallel (Kelvin-Voigt model) to include the effects of viscoelasticity. D is the diameter of the drum. c<\/b> Experimental and fitted (\u03f50\u2009=\u20092.67\u2009\u00d7\u200910\u22124 and \u03b7s\u2009=\u200910.5\u2009\u00d7\u20091015\u2009Pa\u2009s) resonant frequency loop under the slow stepping rate (\u25cb). d<\/b> Experimental and calculated \u0394Vdc as a function of dVdc\/dt. e<\/b> Evolution of fr and Q upon repeating the forward-then-backward step sweep of Vdc in three consecutive rounds (1st, 2nd, 3rd) for two traces (trace 1 and trace 2) corresponding to different initialisations. ts is the time interval (only denoted between two different rounds) when the step direction is reversed.<\/p>\n Below we consider various mechanisms that may explain our observations. We rule out contamination as the origin of the viscoelastic behaviour by reproducing the hysteresis loop on optimally clean TBG drums fabricated by the all-dry transfer method (see Supplementary section\u00a0S1.4<\/a> for surface characterization by atomic force microscopy). Euler instabilities36<\/a> and mechanically conservative nonlinearities36<\/a>, which would also give rise to hysteresis frequency loops, can be safely ruled out. Nonlinearities can be disregarded because the shape of our frequency loops does not depend on the strength of the driving force (Fig.\u00a0S9<\/a>). Sliding motion at the clamping points can also be excluded because such a sliding produces a plateau for fr near the switching points37<\/a>.<\/p>\n Alternatively, a process that may account for our observations is a viscoelastic one. We model the TBG drums as a spring and a dashpot connected in parallel (Fig.\u00a02<\/a>b), known as the Kelvin-Voigt model (KVM), to include the effects of viscoelasticity1<\/a>. The constitutive relation is expressed as a first-order linear differential equation, \\(\\sigma=E(\\epsilon+{\\tau }_{\\sigma }\\frac{{{{\\rm{d}}}}\\epsilon }{{{{\\rm{d}}}}t}\\, )\\), where \u03c3 is stress, \u03f5 is strain, E is Young\u2019s modulus, \u03c4\u03c3\u00a0=\u00a0\u03b7\/E is the relaxation time, with \u03b7 the viscosity of the material. Based on this constitutive equation, the resonant frequency of TBG drums is expressed as (see Methods):<\/p>\n $${f}_{{{{\\rm{r}}}}}=\\frac{1}{2\\pi }\\sqrt{\\frac{E}{4{m}_{{{{\\rm{eff}}}}}{D}^{2}}({k}_{0}+{k}_{{{{\\rm{s}}}}})}$$<\/p>\n \n (1)\n <\/p>\n with the normal term \\({k}_{0}=2{\\epsilon }_{0}+\\frac{3}{2}{z}^{2}\\), the viscoelastic term \\({k}_{{{{\\rm{s}}}}}=\\frac{3}{2}{\\tau }_{\\sigma {{{\\rm{s}}}}}z\\frac{{{{\\rm{d}}}}z}{{{{\\rm{d}}}}t}\\), where z\u2009=\u2009\u03be\/D is the dimensionless deflection at the centre of the drum, \u03f50 is the built-in strain, \u03c4\u03c3s\u2009=\u2009\u03b7s\/E with \u03b7s the viscosity of the dashpot, and meff is the effective mass of the vibrational mode. The dynamical equation of motion for z can be constructed from the force equilibrium relation (see Methods). The parameters obtained by numerically solving the dynamical equation are plugged into Eq. (1<\/a>) to calculate fr. Using these experimental parameters, the KVM reproduces the shape of the frequency loops well, as shown in Fig.\u00a02<\/a>c for a slow step rate (see Supplementary section\u00a0S2.2<\/a> for the fits to butterfly-shaped loops and the stepping-dependent butterfly-shaped loops). The model also reproduces the relationship between \u0394Vdc and dVdc\/dt (Fig.\u00a02<\/a>d). The implications of the non-linear relationship revealed in Fig.\u00a02<\/a>d are twofold: first, \u0394Vdc will decrease to zero for an extremely slow rate, namely without any hysteresis loop; second, \u0394Vdc will saturate for a fast rate, corresponding to the case where the dynamic system can not follow the external stimuli. Therefore, the time dependence of fr is slow on the scale of the ring-down time and on the scale of the vibrational period.<\/p>\n To gain an intuitive understanding of the behaviour of TBG drums as the gate voltage is cycled, we estimate the damping force, \\({F}_{{{{\\rm{d}}}}}=S\\cdot {\\eta }_{{{{\\rm{s}}}}}\\frac{{{{\\rm{d}}}}\\epsilon }{{{{\\rm{d}}}}t}\\approx 1.859\\times 1{0}^{-4}\\) N, with S the surface area of the drum and viscous energy losses \\({E}_{{{{\\rm{v}}}}}=S\\cdot \\oint {\\eta }_{{{{\\rm{s}}}}}\\frac{{{{\\rm{d}}}}\\epsilon }{{{{\\rm{d}}}}t}\\,{{{\\rm{d}}}}\\epsilon \\approx 1.41\\times 1{0}^{-13}\\) J, based on the frequency loop in Fig.\u00a02<\/a>c which we fit with two parameters, namely \u03f50\u00a0=\u00a02.67\u00a0\u00d7\u00a010\u22124 and \u03b7s\u00a0=\u00a010.5\u00a0\u00d7\u00a01015 Pa\u00a0s, yielding \u03c4\u03c3s\u00a0\u2248\u00a0104 s. Our damping force corresponds to a shear stress \u03b3\u00a0=\u00a0Fd\/S\u00a0\u2248\u00a03.7 MPa, which is larger than in bilayer graphene38<\/a>, but comparable to that in twisted MoS239<\/a>. The proportions of k0 and ks corresponding to Fig.\u00a01<\/a>e and Fig.\u00a02<\/a>c are provided in Fig.\u00a0S6<\/a>b and Fig.\u00a0S7<\/a>c, respectively. We find that the increase in fr within the frequency loop can be fully accounted for by the viscoelastic spring constant ks. For drum 4 in Device B where Vdc is cycled between \u00a0\u2212\u00a05 V and \u00a0\u2212\u00a01 V, we obtain \u03f50\u00a0=\u00a03.82\u00a0\u00d7\u00a010\u22124, \u03b7s\u00a0=\u00a08.9\u00a0\u00d7\u00a01015 Pa\u00a0s, \u03c4\u03c3s\u00a0\u2248\u00a0104 s, Fd\u00a0\u2248\u00a02.867\u00a0\u00d7\u00a010\u22124 N, Ev\u00a0=\u00a06.1\u00a0\u00d7\u00a010\u221214 J, and \u03b3\u00a0\u2248\u00a02.5 MPa.<\/p>\n We further test the dynamic nature of the system by repeating the backward-then-forward sweeps in three consecutive rounds, as shown in Fig.\u00a02<\/a>e. Two traces are recorded, corresponding to different initial fr. A slow convergence to a steady state, where a perfect loop, i.e., with no gaps or crossings at the switching points, is observed in the third round. Trace 2 shows a much smoother path as its initial fr closed to the steady state.<\/p>\n Furthermore, within a resonant frequency loop, we find that Q follows fr, both increasing and decreasing concomitantly. The tunability of Q shows an approximately linear increase as decreasing gate voltage (Fig.\u00a02<\/a>e). Such enhancements of Q are expected to depend on the gate voltage stepping rate (see Fig.\u00a0S11<\/a>a) via ks as discussed above. These observations are in stark contrast to the conventional phenomena for 2-D nanoelectromechanical resonators, where the Q decreases rapidly with increasing electrostatic pressure, which is still a subject of debate35<\/a>.<\/p>\n Viscoelastic dissipation dilution<\/p>\n To explore the mechanism of energy dissipation related to high-frequency mechanical vibrations (tens of MHz), in Fig.\u00a03<\/a>a we show Q extracted from the frequency loop corresponding to Fig.\u00a02<\/a>c, where the linear increments with slightly different slopes are revealed for forward and backward sweeps with a step size of 0.25 V. The different increments in Q under other step rates are given in Fig.\u00a0S11<\/a>a. Figure\u00a03<\/a>b summarises Q as a function of Vdc for three drums in Device A. The large drum tends to have a large Q, which is consistent with many reports in the literature40<\/a>. There are also a few jumps in Q, as shown in Fig.\u00a03<\/a>b for drum 3 under a large gate voltage sweep. Such an observation may suggest the existence of further stick-slip actions beyond the atomic scale41<\/a>.<\/p>\n Fig. 3: Viscoelastic dissipation dilution.<\/b> a<\/b> Quality factors Q corresponding to Fig.\u00a02<\/a>c for both forward and backward sweeps. b<\/b> Q extracted from the mechanical response spectra and as a function of Vdc for drum 1 (D\u00a0=\u00a06\u2009\u03bcm), drum 2 (D\u00a0=\u00a08\u2009\u03bcm) and drum 3 (D\u00a0=\u00a012\u2009\u03bcm), respectively. The dashed arrows denote the Q jumps revealed in drum 3. The solid lines in (a, b<\/b>) are linear fits to the experimental data (see Supplementary section\u00a0S2.2<\/a>). c<\/b> Top panel: the extended Kelvin-Voigt model, i.e., the intrinsic friction dashpot \u03b7i is added in parallel to the model that has been introduced in Fig.\u00a02<\/a>b, but here \u03b7s is explicitly replaced by a \u201clossless” viscoelastic spring ks. Bottom panel: a cartoon of the Prandtl-Tomlison model, where the tip slides on top of a one-dimensional chain of springs, which moves on top of a fixed potential. d<\/b> The Vdc-dependent Q extracted from the ring-down measurements (Ring.) and fitting of the mechanical responses (M.R.) in drum 11 (D\u00a0=\u00a012\u2009\u03bcm) of Device E. Error bars in the traces of Ring. and M.R. are extracted from the fits of energy decay and mechanical responses, respectively. Note that the ringdown trace has been shifted up by 50 for direct comparison (see Methods). e<\/b> Energy decay traces (in log scale) at different Vdc in drum 11 (D\u2009=\u200912\u2009\u03bcm) of Device E (see Methods).<\/p>\n Firstly, we use our estimates of \u03b7s and \u03f50 to estimate the contribution of dissipation dilution in our measurements. The phenomenon of dissipation dilution refers to the reduction in energy dissipation from the contribution of a lossless potential that stores part of the elastic energy of mechanical resonators. The lossless potential may originate from e.g., a geometrical nonlinear deformation12<\/a>. Such dissipation dilution could not explain our observations, since the small elastic energy increments are fully accounted for by the viscoelastic term ks in Eq. (1<\/a>). However, due to a long viscoelastic relaxation time (\u03c4\u03c3s\u2009\u2248\u2009104\u2009s for drum 2) compared to the vibrational period \u00a0\u2248\u00a010\u22125 s, such a term can play a similar role as that of a nonlinear deformation to store elastic energy and contribute a \u201clossless” spring constant ks within the period of the oscillator. In order to provide an intuitive picture, we propose an extended KVM (Fig.\u00a03<\/a>c, top panel), where the intrinsic dissipation is modelled by a new dashpot (\u03b7i) in parallel to the spring (k0) and viscoelastic dashpot (\u03b7s) that have been introduced in Fig.\u00a02<\/a>b, but here \u03b7s has been replaced by ks. The intrinsic Q can be defined by the material loss tangent, Qint\u2009=\u20091\/tan(\u03d5), where \u03d5 is the phase lag between stress and strain. Q is characterised by Q\u2009=\u2009DQ\u2009\u00d7\u2009Qint, where DQ\u00a0=\u00a0(1\u2009+\u2009ks\/k0) is called the dilution coefficient. Based on the outputs from KVM (see Fig.\u00a0S7<\/a>), DQ\u2009\u2248\u20091.06 is found for Vdc\u2009=\u2009\u22129.5\u2009V as compared to Vdc\u2009=\u2009\u22126\u2009V, which is less than the experimental DQ\u00a0\u2248\u00a01.20 (forward) and DQ\u00a0\u2248\u00a01.22 (backward), as shown in Fig.\u00a03<\/a>a.<\/p>\n We further estimate the impacts of ks on intrinsic damping rate \u0393\u00a0=\u00a0f\/Qint, which is not included in the conventional model of dissipation dilution12<\/a>. The extracted \u0393 corresponding to Fig.\u00a03<\/a>b is shown in Fig.\u00a0S10<\/a>a. Notably, three drums in Device A follow a similar slope of \u00a0~\u00a03 kHz V\u22121. Intrinsic damping arises from the atomic-scale stick-slip behaviour that gives rise to friction. It is commonly interpreted by the Prandtl-Tomlinson model, where a particle is pulled by a linear spring of stiffness kd to slide on a periodic energy landscape (Fig.\u00a03<\/a>c, bottom panel). The stick-slip action only occurs if the corrugation registration energy is large enough, i.e., 2E0\u03c02\/kdb2\u00a0>\u00a01, where E0 and b are the amplitude and period of the energy corrugation42<\/a>. Otherwise, the stick-slip behaviour would undergo the transition to continuous motion without dissipation, thus reducing \u0393. The viscoelastic stiffness ks creates a lateral, time-dependent heterostrain that makes the atom slide on a lattice (Fig.\u00a03<\/a>c, bottom panel), and as such can be considered as a driving kd. The sliding resistance can be reduced or even eliminated by increasing ks by Vdc, reinforcing the effect of dissipation dilution.<\/p>\n Our mechanism of reinforced viscoelastic dissipation dilution is markedly different from the electrical tuning of Q in nanotubes43<\/a>,44<\/a>. It is also different from the electrical tuning of Q in graphene due to Ohmic dissipation, where Q decreases as \u2223Vdc\u2223 increases45<\/a>. Because our measurements do not involve charge transport through the resonator, we believe that the phenomena we observe have a purely mechanical origin. Remarkably, a transition from the purely mechanical region with enhanced Q to the usual electrostatic region with decreased Q as increasing \u2223Vdc\u2223 is revealed for with \u03b8\u00a0~\u00a04\u00b0 (Fig.\u00a03<\/a>d), with \u03b8\u00a0~\u00a010.\u00a05\u00b0 (Fig.\u00a0S16<\/a>d) and another drum of \u03b8\u00a0~\u00a012\u00b0 (Device G) with a small built-in strain introduced by annealing (Fig.\u00a0S8<\/a>i). In fact, we can separate the dissipation as 1\/Q\u00a0=\u00a01\/Qnormal\u2009+\u20091\/Qviscoelastic. Thus, if the normal term competes with the viscoelastic one, either by reducing \u03f50 as in Device G or by reducing viscosity in the case of a small twist angle (Device E), the electrostatic region with decreased Q returns.<\/p>\n To obtain the direct information on the dissipation dynamics, we further perform the ring-down measurements (see Methods) in drum 11 of Device E. The vibrational amplitude at resonant frequency decays exponentially in time as \u221d e\u2212t\/(2\u03c4) upon stopping the drive, with \u03c4 the decay time constant, which gives Q\u00a0=\u00a02\u03c0fr\u03c4. The energy decay traces (in log scale) corresponding to different Vdc are shown in Fig.\u00a03<\/a>e. Q obtained from the ring-down measurements is identical to the trajectory extracted by fitting of the mechanical responses (Fig.\u00a03<\/a>d). Further controlled ring-down measurements using gate voltage pulses or tiny ramps to capture the discrete Q jumps (as shown in Fig.\u00a03<\/a>b) are needed to elucidate the underlying mechanism.<\/p>\n","protected":false},"excerpt":{"rendered":"Large TBG drumhead resonators The TBG drumhead nanomechanical resonators are prepared by a \u2018tear-and-stack\u2019 method using both wet…\n","protected":false},"author":2,"featured_media":43295,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3845],"tags":[3965,17354,24114,3966,24115,24116,74,24117,70,17353,16,15],"class_list":{"0":"post-43294","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-humanities-and-social-sciences","9":"tag-interfaces-and-thin-films","10":"tag-mechanical-and-structural-properties-and-devices","11":"tag-multidisciplinary","12":"tag-nems","13":"tag-optomechanics","14":"tag-physics","15":"tag-raman-spectroscopy","16":"tag-science","17":"tag-surfaces","18":"tag-uk","19":"tag-united-kingdom"},"share_on_mastodon":{"url":"https:\/\/pubeurope.com\/@uk\/114386204424481158","error":""},"_links":{"self":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/43294","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=43294"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/43294\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media\/43295"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media?parent=43294"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/categories?post=43294"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/tags?post=43294"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"figure](\"https:\/\/www.europesays.com\/uk\/wp-content\/uploads\/2025\/04\/41467_2025_58981_Fig1_HTML.png\")
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