different scales; generally de fi ned as singularities in a local order parameter Appear in a wide range of physical systems: liquid crystals, superconductors, super fl uids, ferro fl uids, bacterial colony, tissue development, early universe 2D melting (KTHNY transition) TD as dislocations and disclination lines in crystalline solid TD in amorphous system has been debated for a long time Displacement fi eld of deformed glass, described by Burgers vector: TD correlate very well with plasticity [1] Athermal simulation of Lennard-Jonnes glass: TD identi fi ed in eigenvector fi eld of vibrational modes [2] TD with quantized -1 charge in the displacement fi eld, generating Eshelby- like quadrupolar fi elds align to form the shear bands responsible for the yielding of amorphous solids [3] No report of direct observation of topological defects in experimental amorphous systems In this work: identify TD in the 2D colloidal system observed via optical microscopy, exploring the interplay between topology and vibrational properties Colloidal monolayer: individual particles sediment to a fl at water/air interface in a hanging-droplet con fi guration under the in fl uence of gravity [4] Binary colloidal mixture: two different masses and diameters; exhibit Brownian motion within the two- dimensional plane Particles consist of polystyrene with incorporated nanograins of iron oxide; induced magnetic dipole moment in each particle when an external magnetic fi eld is applied perpendicular to the surface Potential energy between two constituent particles separated by a distance r Dynamics can be controlled by tuning the strength of magnetic fi eld, behaves as inverse of temperature Optical microscopy to record the particle positions in the fi eld of view at a certain interval of time: N ~ 2300 Results Motivation & Goals Conclusions Experimental setup [1] M. Baggioli, I. Kriuchevskyi, T. W. Sirk, and A. Zaccone; PRL 127, 015501 (2021) [2] Z. W. Wu, Y. Chen, W.-H.Wang, W. Kob, and L. Xu; Nat. Comm. 14, 2955 (2023) [3] P. Desmarchelier, S. Fajardo, and M. L. Falk; Phys. Rev. E 109, L053002 (2024) [4] V. Vaibhav, A. Bera, A. C. Y. Liu, M. Baggioli, P. Keim, A. Zaccone; arXiv:2405.06494 (2024) References Vinay Vaibhav, Arabinda Bera, Alessio Zaccone (University of Milan, Italy) Amelia C. Y. Liu (Monash University, Australia) Matteo Baggioli (Shanghai Jiao Tong University, China) Peter Keim (Heinrich-Heine-Universität Düsseldorf, Germany) Experimental Identification of Topological Defects in 2D Colloidal Glass Well controlled colloidal monolayer with access to inter- particle interaction; allows the construction of Hessian Vibrational properties: follows Debye’s law in 2D; Boson peak Interplay between topology and vibrational properties: unveiled the presence of topological defects within the eigenspace Correlation between vDOS and the total number of defects Defects of opposite charge pair together i.e., tend to form dipole like structure; defects with same charge repel each other Strong correlation at short distance between defects with negative topological charge and soft spots i.e., correlation between anti-vortices and plasticity Vinay Vaibhav (https://vinayphys.github.io,
[email protected]) arXiv:2405.06494 Heat Current Structural correlation of defects 100 101 102 103 104 105 t (s) 100 101 102 MSD (µm2) 0 20 40 60 80 100 120 r (µm) 0 2 4 6 g(r) gAA gAB gBB Structure: pair-correlation Dynamics: mean-squared displacement Experimental realization of the colloidal monolayer a b c d a b c °250 0 250 500 750 w (Hz) 0.0 0.8 1.6 2.4 D(w) £ 10°3 0 8 16 24 w (Hz) 0.0 0.2 0.4 D(w) £ 10°3 0 20 40 60 w (Hz) 12 15 18 21 D(w)/w £ 10°6 °250 0 250 500 w (Hz) 0.00 0.05 0.10 0.15 0.20 P(w) Vibrational characteristics a b ~ H Glass Water Air x y z Repulsive Correlation between vDOS and number of topological defects Vibrational density of states Boson peak Participation ratio 0 45 90 135 180 r (µm) 0 1 2 3 gPP(r) w = 50 w = 100 w = 250 w = 330 w = 530 0 45 90 135 180 r (µm) 0 1 2 3 gPN(r) w = 50 w = 100 w = 250 w = 330 w = 530 0 45 90 135 180 r (µm) 0 1 2 3 gNN(r) w = 50 w = 100 w = 250 w = 330 w = 530 0 45 90 135 180 r (µm) 1.0 1.5 2.0 gPS (r) w = 15 w = 20 w = 30 w = 50 w = 100 0 45 90 135 180 r (µm) 1.0 1.5 2.0 gNS (r) w = 15 w = 20 w = 30 w = 50 w = 100 0 200 400 600 800 1000 x 0 200 400 600 y °0.1 0.0 0.1 0.2 Topological defects in eigenvector fi eld Correlation of defects with soft spots Pair correlation for defect pairs: defect charges with the same sign repel each other and those with opposite sign attract each other Strong correlation for small , becomes weaker with the rise in frequency Soft spots: mesoscale relaxation or rearrangements are prone to happen; identi fi ed as particles with top 10% softness Softness fi eld: ! Heterogeneous eigenvector fi eld: vortices ( ) & anti-vortices ( ) Angle fi eld is constructed using the eigenvector fi eld corresponding to using a Gaussian weight function w Topological charge q is calculated via the line integral: ! °250 0 250 500 750 w (Hz) 0.0 0.8 1.6 2.4 D(w) £ 10°3 D(w) 0 200 400 600 Nd Nd 0 8 16 24 w (Hz) 0 50 100 Nd Total number of defects Nd is the sum of +1 and -1 defects Signi fi cant anti-correlation between Nd and vDOS in the frequency range 250-340 Hz Nd ~ for small frequencies ! Pair correlation between soft spots and defects: defects with negative charge are strongly correlated with nearby soft spots Topological charge density also correlates well with soft spots Nm is such that Dynamical matrix (Hessian): constructed using long- range dipole-dipole interaction among colloids Hessian is diagonalized to obtain the normal-mode frequencies and vectors ; l = 1, 2, …, 2N Finite temperature amorphous system: a signi fi cant number of modes are unstable Compatible with Debye’s law in 2D Identi fi cation of Boson peak in 2D: 15-17 Hz Participation ratio: measure of extent of mode localisation; +1/2 (half vortex) -1/2 (half anti- vortex) +1 (vortex) +1 (vortex) -1 (anti-vortex)
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