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

**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).

**Nicolas Behr (IRIF Paris-Diderot et LPTMC)**

**Stochastic Mechanics of Graph Rewriting Systems for Physicists**

Consider a statistical system evolving on a state space of graphical structures, such as e.g. a social network system. Given a set of transitions on such a system, where each transition consists of a local transformation pattern applied at random to the system's state (e.g. adding a new edge, deleting an edge,...), one may define a continuous-time Markov chain in order to study the stochastic evolution of the system. Our novel approach to this problem involves an extension of Doi's description of chemical reaction systems in terms of boson creation and annihilation operators (which later evolved into the Doi-Peliti formalism) to a general stochastic mechanics framework based on the idea of so-called rule algebras. Assuming no prior familiarity with the underlying concept of graph rewriting and related mathematics, I will give an introduction to the formalism and present a number of application examples.

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

**Lara Benfatto (CNR et Université de Rome Sapienza)**

**Berezinskii-Kosterlitz-Thouless transition in 2D superconductors**

Lecture I: The Beresinskii-Kosterlitz-Thouless transition: the two-dimensional world and its peculiarities

More than 40 years after the seminal work by Berezinskii, Kosterlitz and Thouless the

BKT transition remains one of the most spectacular phenomena in condensed matter

systems, as it has been acknowledged by the 2016 Nobel Prize. Even though it was originally formulated within the context of the two dimensional XY model for classical spins, it represents the paradigm for the superfluid transition in two dimensions. As such, it has been the subject of an intense theoretical and experimental investigation in a variety of systems, ranging from thin films of superconductors to artificial heterostructures and cold atoms.

In the first lecture I will give an introduction to the basic mathematical ingredients needed to understand the occurrence of a BKT transition within the context of the classical 2D XY model. After discussing the difference between order and rigidity for a second-order phase transition, I will discuss the peculiar role of vortices in 2D and I will derive the mapping onto the Coulomb-gas model. Finally, I will sketch the main outcomes of the renormalization-group approach for the BKT phase transition.

Lecture II: Applications to superfluids. What we should expect to see in real systems?

The Beresinskii-Kosterlitz-Thouless transition is expected to describe the metal-to-superconductor thermal transition in quasi-2D systems. However, despite many efforts along the years its signatures remain rather elusive. In this second lectures I will give an overview of the numerous attempts we made along the years to identify the mechanisms which may hinder a clear-cut observation of BKT physics in 2D films of conventional and unconventional superconductors. In particular I will discuss the role of the vortex-core energy and of the spontaneous inhomogeneity of the superconducting background which naturally emerge in disordered thin films. These effects must be seriously taken into account while addressing the famous universal jump of the superfluid density, the non-linear IV characteristics near Tc, or the paraconductivity effects while approaching it from above. Finally, I will make a comparison with some recent results within the context of cold atoms, underlying differences and analogies between the two classes of systems.

**Sophie Marbach (LPS-ENS)**

**Out-of-equilibrium Transport of Particles within Fluctuating Nanotubes**

In Nature exceptional permeability and selectivity properties are reached, for example ion channels are able to distinguish with high throughput very similar ions like Sodium and Potassium. The paradigm change as compared to nanoscale technology is that these biological filters are out-of-equilibrium, submitted to either thermal or active fluctuations – for example of the pore constriction. Here we investigate how out-of-equilibrium fluctuations of a pore may affect the translocation dynamics, in particular dispersion coefficients. Our findings demonstrate a complex interplay between transport and surface wiggling and elucidate the impact of pore agitation in a broad range of artificial and biological porins, but also, at larger scales, in vascular motion in fungi, intestinal contractions and microfluidic surface waves. These results open up the possibility that transport across membranes can be actively tuned by external stimuli, with potential applications to nanoscale pumping, osmosis and dynamical ultrafiltration.

**Vardan Kaladzhyan (KTH Royal Institute of Technology, Stockholm)**

**Topology from Triviality**

We show that bringing into proximity two topologically trivial systems can give rise to a topological phase. More specifically, we study a 1D metallic nanowire proximitised by a 2D superconducting substrate with a mixed s-wave and p-wave pairing, and we demonstrate both analytically and numerically that the phase diagram of such a setup can be richer than reported before. Thus, apart from the two "expected" well-known phases (i.e. where the substrate and the wire are both simultaneously trivial or topological), we show that there exist two peculiar phases in which the nanowire can be in a topological regime while the substrate is trivial, and vice versa.