Geometric and Topological Aspects of Soft & Active Matter

Topological and geometric ideas are now a mainstay of condensed matter physics, underlying much of our understanding of conventional materials in terms of defects and geometric frustration in ordered media, and protected edge states in topological insulators. In this thesis, I will argue that such an approach successfully identifies the relevant physics in metamaterials and living matter as well, even when traditional techniques fail. I begin with the problem of kirigami mechanics, i.e., designing a pattern of holes in a thin elastic sheet to engineer a specific mechanical response. Using an electrostatic analogy, I show that holes act as sources of geometric incompatibility, a feature that can fruitfully guide design principles for kirigami metamaterials. Next I consider nonequilibrium active matter composed of self-driven interacting units that exhibit large scale collective and emergent behaviour, as commonly seen in living systems. By focusing on active liquid crystals in two dimensions, with both polar and nematic orientational order, I show how broken time-reversal symmetry due to the active drive allows polar flocks on a curved surface to support topologically protected sound modes. In an active nematic, activity instead causes topological disclinations to become spontaneously motile, driving defect unbinding to organize novel phases of defect order and chaos. In all three cases, geometric and topological ideas enable the relevant degrees of freedom to be identified, allowing complex phenomena to be treated in a tractable fashion, with novel and surprising consequences along the way

The low noise phase of a 2d active nematic

We consider a collection of self-driven apolar particles on a substrate that organize into an active nematic phase at sufficiently high density or low noise. Using the dynamical renormalization group, we systematically study the 2d fluctuating ordered phase in a coarse-grained hydrodynamic description involving both the nematic director and the conserved density field. In the presence of noise, we show that the system always displays only quasi-long ranged orientational order beyond a crossover scale. A careful analysis of the nonlinearities permitted by symmetry reveals that activity is dangerously irrelevant over the linearized description, allowing giant number fluctuations to persist though now with strong finite-size effects and a non-universal scaling exponent. Nonlinear effects from the active currents lead to power law correlations in the density field thereby preventing macroscopic phase separation in the thermodynamic limit.Comment: 17 pages, 5 figure

Topological Sound and Flocking on Curved Surfaces

Active systems on curved geometries are ubiquitous in the living world. In the presence of curvature orientationally ordered polar flocks are forced to be inhomogeneous, often requiring the presence of topological defects even in the steady state due to the constraints imposed by the topology of the underlying surface. In the presence of spontaneous flow the system additionally supports long-wavelength propagating sound modes which get gapped by the curvature of the underlying substrate. We analytically compute the steady state profile of an active polar flock on a two-sphere and a catenoid, and show that curvature and active flow together result in symmetry protected topological modes that get localized to special geodesics on the surface (the equator or the neck respectively). These modes are the analogue of edge states in electronic quantum Hall systems and provide unidirectional channels for information transport in the flock, robust against disorder and backscattering.Comment: 15 pages, 6 figure

3-D poling and drive mechanism for high-speed PZT-on-SOI Electro-Optic modulator using remote Pt buffered growth

In this work, we have demonstrated a novel method to increase the electro-optic interaction in an intensity modulator at the C-band by optimizing the growth methodology of PZT with the metal (Ti/Pt) as a base material and the PZT poling architecture. Here, we have used a patterned Pt layer for PZT deposition instead of a buffer layer. By optimizing the PZT growth process, we have been able to do poling of the fabricated PZT film in an arbitrary direction as well as have achieved an enhanced electro-optic interaction, leading to a DC spectrum shift of 304 pm/V and a V{\pi} L{\pi} value of 0.6 V-cm on a Si-based MZI. For an electro-optic modulator, we are reporting the best values of DC spectrum shift and V{\pi} L{\pi} using perovskite as an active material. The high-speed measurement has yielded a tool-limited bandwidth of > 12GHz. The extrapolated bandwidth calculated using the slope of the modulation depth is 45 GHz. We also show via simulation an optimized gap of 4.5 {\mu}m and a PZT thickness of 1 {\mu}m that gives us a less than 1 V-dB.Comment: 7 pages, 5 figures, 1 Tabl

DFT analysis and demonstration of enhanced clamped Electro-Optic tensor by strain engineering in PZT

We report $\approx$400\% enhancement in PZT Pockels coefficient on DFT simulation of lattice strain due to phonon mode softening.The simulation showed a relation between the rumpling and the Pockels coefficient divergence that happens at -8\% and 25\% strain developed in PZT film.The simulation was verified experimentally by RF sputter deposited PZT film on Pt/SiO$_2$/Si layer.The strain developed in PZT varied from -0.04\% for film annealed at 530\degree C to -0.21\% for 600\degree C annealing temperature.The strain was insensitive to RF power with a value of -0.13\% for power varying between 70-130 W. Pockels coefficient enhancement was experimentally confirmed by Si Mach Zehnder interferometer loaded with PZT and probed with the co-planar electrode.An enhancement of $\approx$300\% in Pockels coefficient was observed from 2-8 pm/V with strain increasing from -0.04\% to -0.21\%. To the best of our knowledge, this is the first time study and demonstration of strain engineering on Pockels coefficient of PZT using DFT simulation, film deposition, and photonic device fabrication.Comment: 9 Pages, 4 Figure

Highly Oriented PZT Platform for Polarization-Independent Photonic Integrated Circuit and Enhanced Efficiency Electro-Optic Modulation

We demonstrate, for the first time, sputtered PZT as a platform for the development of Si-based photonic devices such as rings, MZI, and electro-optic modulators. We report the optimization of PZT on MgO(002) substrate to obtain highly oriented PZT film oriented towards the (100) plane with a surface roughness of 2 nm. Si gratings were simulated for TE and TM mode with an efficiency of -2.2 dB/coupler -3 dB/coupler respectively with a polarization insensitive efficiency of 50% for both TE and TM mode. Si grating with an efficiency of around -10 dB/coupler and a 6 dB bandwidth of 30 nm was fabricated. DC Electro-optic characterization for MZI yielded a spectrum shift of 71 pm/V at the c-band.Comment: 11 Pages, 9 Figures, 3 Table

Defect unbinding in active nematics

We formulate the statistical dynamics of topological defects in the active nematic phase, formed in two dimensions by a collection of self-driven particles on a substrate. An important consequence of the non-equilibrium drive is the spontaneous motility of strength +1/2 disclinations. Starting from the hydrodynamic equations of active nematics, we derive an interacting particle description of defects that includes active torques. We show that activity, within perturbation theory, lowers the defect-unbinding transition temperature, determining a critical line in the temperature-activity plane that separates the quasi-long-range ordered (nematic) and disordered (isotropic) phases. Below a critical activity, defects remain bound as rotational noise decorrelates the directed dynamics of +1/2 defects, stabilizing the quasi-long-range ordered nematic state. This activity threshold vanishes at low temperature, leading to a re-entrant transition. At large enough activity, active forces always exceed thermal ones and the perturbative result fails, suggesting that in this regime activity will always disorder the system. Crucially, rotational diffusion being a two-dimensional phenomenon, defect unbinding cannot be described by a simplified one-dimensional model.Comment: 15 pages (including SI), 4 figures. Significant technical improvements without changing the result

Hydrodynamics of Active Defects: from order to chaos to defect ordering

Topological defects play a prominent role in the physics of two-dimensional materials. When driven out of equilibrium in active nematics, disclinations can acquire spontaneous self-propulsion and drive self-sustained flows upon proliferation. Here we construct a general hydrodynamic theory for a two-dimensional active nematic interrupted by a large number of such defects. Our equations describe the flows and spatio-temporal defect chaos characterizing active turbulence, even close to the defect unbinding transition. At high activity, nonequilibrium torques combined with many-body screening cause the active disclinations to spontaneously break rotational symmetry forming a collectively moving defect ordered polar liquid. By recognizing defects as the relevant quasiparticle excitations, we construct a comprehensive phase diagram for two-dimensional active nematics. Using our hydrodynamic approach, we additionally show that activity gradients can act like "electric fields", driving the sorting of topological charge. This demonstrates the versatility of our continuum model and its relevance for quantifying the use of spatially inhomogeneous activity for controlling active flows and for the fabrication of active devices with targeted transport capabilities.Comment: 18 pages, 7 figures, additional explanation provided with results unchange