### Attention : désormais les séminaires ont lieu tous les lundis à 10h45 en salle 523 du LPTMC - Tour 12-13

**Alexei Kornyshev (Imperial College London)**

**Electrochemical plasmonics: A path to electrotunable self-assembling optical metamaterials (scenarios navigated by theory)**

This talk will overview a new direction of research based on voltage-controlled self-assembly of plasmonic nanoparticles at electrochemical interfaces, the optical properties of which can dramatically vary with assembly structure and density.

Progress in photonic metamaterials was made possible by advances in nanotechnology. Many such materials, however, can only perform a single function. Not surprisingly, a premier conference in the field opened with a provocative statement: “The time of meta-materials is over… It is the time of tuneable metamaterials” (N. Zheludev). Realization of such platforms would allow properties of such functional metamaterials to be tuned in real-time, with major implications for absorbers in solar cells, antennae, super-lenses, cloaking, sensors – amongst others.

Tunability can be reached by utilization of fine physical effects, but also changing the structure of materials in real time. Our team at Imperial (led by J.B. Edel – nanofluidics, optics, analytical science; A.R. Kucernak – experimental electrochemistry; and myself – theory development, theory-based navigation of experiments and analysis of the data) in collaboration with M. Urbakh at Tel Aviv University (theory) have responded to this challenge first with developing the ‘nanotechnology-free’ concept of chemically tuneable self-assembly of plasmonic nanoparticles, such as quasi-2D arrays NPs at a liquid|liquid (LLI) and solid|liquid (SLI) interfaces [1,2]. We have demonstrated that such arrays could be used for ultrasensitive SERS detection of trace analytes –e.g. proxies for pollutants, illegal substances, terror agents – that get into ‘hot spots’ between NP’s [3]. The array structure was controlled by tuning the composition of the solutions (electrolyte concentration or pH). We further performed a complex study of the structure and optical properties of such arrays within the same setup, via a combination of grazing incidence, small angle X-ray scattering and in situ optical reflectivity. From the X-ray and optical data, we could determine (from a combination of experimental [4] and original theoretical [5] results) the average distance between NPs, the long-range order, and reflectivity –all as a function of electrolyte concentration. Incorporating the obtained values of array’s ‘lattice constants’ into the theory of optical reflectance from such arrays [5], we could calculate the reflectance spectra for each electrolyte concentration and compare them with those measured in the same system [4]. Excellent match between the theory and experiments has demonstrated that the underlying physics works exactly as expected! These studies gave us confidence that we could chemically control these nanoplasmonic platforms, i.e. generate tuneable self-assembled metamaterials. However, this did not incorporate real-time reversible control.

It was clear, that electrochemistry will be the game changer here. At electrochemical interfaces, with tiny voltage variation, one can create localised electric fields that may dramatically change the structures of adsorbed charged NP arrays and their optical properties. We demonstrated this by creating the first electrically switchable mirror based on voltage controlled self-assembly of gold NPs at the interface of two immiscible electrolytic solutions [6]. We have shown that it is possible to transition between a mirror and window and back using just 0.5 V - voltage variation through its effect on the density of the NP arrays and their resulting optical response. Furthermore, a different kind of switch based on voltage-controlled adsorption-desorption of NPs on a metal substrate, the principle of which has been described theoretically in [7], was reported in [8]. A set of other scenarios were also considered (see e.g.[9]).

[1] J.B. Edel, A.A. Kornyshev, M. Urbakh, “Self-Assembly of Nanoparticle Arrays for Use as Mirrors, Sensors, and Antennas”, ACS Nano 7, 9526-9632 (2013).

[2] J. Edel, A.A. Kornyshev, A. Kucernak, M. Urbakh, “Fundamentals and applications of self-assembled plasmonic nanoparticles at interfaces”, Chemical Society Reviews 45, 1581-1596 (2016).

[3] M.P. Cecchini, V.A. Turek, J. Paget, A.A. Kornyshev, J.B. Edel, “Self-assembled nanoparticle arrays for multi-phase trace analyte detection”, Nature Materials 12, 165-171 (2013).

[4] L.Velleman, D. Sikdar, V.A. Turek, S.J. Roser, A.R., Kucernak, A.A. Kornyshev, J.B. Edel, “Tuneable 2D self-assembly of plasmonic nanoparticles at liquid | liquid interfaces”, Nanoscale , 8 19229 (2016).

[5] D. Sikdar, A.A. Kornyshev, “Theory of tailorable optical response of two dimensional arrays of plasmonic nanoparticles at dielectric interfaces”, Sci. Rep. 6, #33712 (2016).

[6] Y. Montelongo, D. Sikdar, Y. Ma, A.J.S. McIntosh, L. Velleman, A.R. Kucernak, J.B. Edel, A.A. Kornyshev, “Electrotuneable nanoplasmonic liquid mirror”, Nature Materials 16, 1127-1135 (2017). https://youtu.be/68J0yLvrvJE

[7] D. Sikdar, S. Bin Hasan, M. Urbakh, J. Edel, A.A.Kornyshev, “Unravelling the optical responses of nanoplasmonic mirror-on-mirror metamaterials”, Phys.Chem.Chem.Phys. 18, 20486-20498 (2016).

[8] Y. Ma, C. Zagar, D. Klemme, D. Sikdar, L. Velleman, Y. Montelongo, S.-H. Oh, A.R. Kucernak; J.B. Edel, A.A. Kornyshev,

"A tunable nanoplasmonic mirror at an electrochemical interface", ACS Photonics 5, 4604-4616 (2018).

[9] H. Weir, J.B. Edel, A.A. Kornyshev, D. Sikdar, “Towards electrotuneable Fabry-Perot Interferometer”, Sci.Rep. 8, 2045-2322 (2018); D. Sikdar, A.Bucher, C.Zagar, A.A. Kornyshev, “Electrochemical plasmonic metamaterials: towards, fast electrotuneable reflecting nanoshutters, Faraday Disc. 199, 585-602 (2017).

**ATTENTION JOUR INHABITUEL**

**Cécile Repellin (MIT)**

**Detecting fractional Chern insulators through circular dichroism**

Great efforts are currently devoted to the engineering of topological Bloch bands in ultracold atomic gases. Recent achievements in this direction, together with the possibility of tuning inter-particle interactions, suggest that strongly-correlated states reminiscent of fractional quantum Hall (FQH) liquids could soon be generated in these systems. In this experimental framework, where transport measurements are limited, identifying unambiguous signatures of FQH-like states constitutes a challenge on its own. Here, we demonstrate that the fractional nature of the quantized Hall conductance, a fundamental characteristic of FQH states, could be detected in ultracold gases through a circular-dichroic measurement, namely, by monitoring the energy absorbed by the atomic cloud upon a circular drive. We validate this approach by comparing the circular-dichroic signal to the many-body Chern number, and discuss how such measurements could be performed to distinguish FQH-type states from competing states. Our scheme offers a practical tool for the detection of topologically-ordered states in quantum-engineered systems, with potential applications in solid state.

**Christophe Texier (LPTMS Orsay)**

**Counting the equilibria of a directed polymer in a random medium and Anderson localisation**

I will discuss a new connection between two different problems: the counting of equilibria of a directed polymer in a random medium (DPRM) and the problem of Anderson localisation for the 1D Schrödinger equation. Using the Kac-Rice formula, it is possible to express the mean number of equilibria of a DPRM in terms of functional determinants. In the one dimensional situation, these functional determinants can be calculated thanks to the Gelfand-Yaglom method, showing that the mean number of equilibria of the DPRM growth exponentially with the length of the polymer, with a rate controlled by the generalized Lyapunov exponent (GLE) of the localisation problem (cumulant generating function of the log of the wave function). The GLE is solution of a spectral problem studied by combining numerical approaches and WKB-like approximation. Furthermore, the formalism can be extended in order to obtain the number of equilibria at fixed energy, providing the (annealed) distribution of the energy density of the line over the equilibria.

**ATTENTION HORAIRE INHABITUEL**

**Stefanos Kourtis (Boston University) **

**Solving constrained counting problems with tensor networks**

In this talk, I will present newly developed physics-inspired methods for the solution of counting constraint satisfaction problems (#CSPs). #CSP instances can be reformulated as interacting models whose zero-temperature partition function represents the volume of the solution manifold. I will introduce practical methods to compute such partition functions based on tensor network contraction. In this formulation, computational complexity can be viewed as a manifestation of quantum entanglement, and controlling the growth of entanglement throughout tensor network contraction can yield a significant computation speedup. Using some hard counting problems as benchmarks, I will demonstrate that tensor network methods can be a useful tool for solving some hard classes of #CSPs. I will conclude with an outline of ongoing work on extensions of this framework, such as the simulation of existing and near-term quantum circuits.

**ATTENTION SALLE INHABITUELLE: salle de séminaire de l'INSP tour 22-23 salle 317 (3ème étage)**

**Jérôme Cayssol (LOMA Bordeaux)**

**Dirac/Weyl fermions in condensed matter: from 1D to 3D**

Dirac systems and topological materials are two rapidly growing and evolving fields in modern condensed matter physics, with a very long history from soliton and quantum Hall physics in the early eighties; and also a more recent history dating from the isolation of graphene in 2004 and the prediction of topological insulators in 2005. In these lectures, i will discuss the topogical aspects of non-interacting fermions on lattices and their relation to Dirac fermions. The goal will be to introduce the basic concepts (topological invariants, quantized electromagnetic response, bulk-boundary correspondance, Dirac fermions, symmetries,…) on simple, yet very rich, models with a progression from one-dimensional (1D) chains to three-dimensional (3D) crystals.

In the first lecture (Thursday 4/10/18), i will use the Su-Schrieffer-Heeger and Rice-Mele models to introduce the concepts of Berry-Zak phase, winding numbers and zero energy end states in 1D. Then we will discuss how those ideas can be transposed and extended to 2D lattices, using the Bernevig-Hughes-Zhang model as a typical example of a Chern insulator. The relations between Berry curvature, Chern number, quantized Hall effect will be detailled.

The second lecture (Friday 5/10) will treat further aspects of 2D topological insulators with an emphasis on graphene (Haldane and Kane-Mele models) and a discussion of topological invariants in presence of time-reversal symmetry. I will conclude by a short list of experimental realisations of 1D and 2D topological systems. If time allows, i will discuss briefly 3D topological insulators and semimetals (Dirac and Weyl semimetals).