## Topological mechanisms in physics:

from stars to electrons

DIEP focus session on topology | 25th January 2022| 14:50 - 16:30 | hybrid | Physics@Veldhoven

## Randall Kamien

## Cristiane de Morais Smith

## Elisabetta Pallante

## Organizers and chairs: Luca Giomi and Jácome Armas

## Jay Armas

## An invitation to topological mechanisms

###### Topology plays a crucial role in physics. Historically, the discovery of high-temperature superconductivity led to the realisation that Landau symmetry-breaking theory was insufficient to characterise all known phases of matter, in turn leading to the notion of topological order. Topological order and its characterisation has been key for understanding quantum matter, in particular the fractional quantum Hall effect, topological insulators and applications to quantum computing. However, topological phases of matter and topological characterisation schemes are not just a quantum matter affair. During the past few years it has become clear that topological phases of matter are present at all length scales, from particle physics to soft matter and astrophysics. This session covers multiple contexts in the physics in which topology is key in understanding physical systems. In particular, in the understanding of dislocations in crystals and other soft matter systems, in unravelling the topological mechanisms underlying hydrodynamic edge modes in geophysics and astrophysics, in characterising non-Hermitian systems, and in the understanding of Yang-Mills theory, confinement and the early universe. This session features R. Kamian, world expert in topological aspects of condensed matter physics, and talks by C. de Morais Smith, E. Pallante, and J. Armas on aspects of topology that range from geophysics to high-energy physics.

## Programme:

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###### Crystals and other condensed matter systems described by density waves often exhibit dislocations. Here we show, by considering the topology of the ground state manifolds (GSMs) of such systems, that dislocations in the density phase field always split into disclinations, and that the disclinations themselves are constrained to sit at particular points in the GSM. Consequently, the topology of the GSM forbids zero-energy dislocation glide, giving rise to a Peierls-Nabarro barrier.

###### The topological origin of the Peierls-Nabarro barrier

Randall Kamien, University of Pennsylvania| 14:50-15:15

In this talk, I discuss a few recent experiments, in which 2D electron lattices were engineered on the nanoscale using STM manipulation of adatoms on the surface of copper. First, I show that it is possible to control the geometry of the lattice and the orbital degrees of freedom. Then, we control the effective dimension of the electronic structure by creating a fractal. Finally, we investigate topological states, namely the robustness of the zero modes in a breathing Kagome lattice, which is the first experimental realization of a designed electronic higher-order topological insulator, and the fate of the edge modes in a Kekule structure, upon varying the type of boundary of the sample.

###### Atom-by-atom engineering of topological states of matter

Cristiane de Morais Smith, Utrecht U. | 15:15-15:40

###### â€‹

Since their formulation halfway through the twentieth century, Yang-Mills theories and their topological aspects set the foundations of the Standard Model of particle physics and have continued to inspire a wide range of theoretical attempts at further understanding elementary particles’ interactions and their role in the early universe. Combining historical milestones to recent developments, we discuss how topology relates to physics in this context, from the phenomenon of confinement to the phase diagram of Yang-Mills theories coupled to matter, the role of spacetime dimensions and the possible role of axions in the history of the universe.

###### Topology in contemporary particle physics

Elisabetta Pallante, U. Groningen | 15:40-16:05

###### Topological waves in hydrodynamics

Jay Armas, UvA | 16:05-16:30

Topological methods are useful in describing the appearance of chiral edge modes in quantum matter. In this talk, I will instead focus on classical hydrodynamic systems confined to two dimensional surfaces in the context of geophysics and soft matter. I will show that using a combination of topological band theory and real space analysis, there exists a system-independent mechanism behind topological protection in two-dimensional passive and active fluids. This allows us to formulate an index theorem linking the number of modes, determined by the topology of Fourier space, to the real space topology of the surface on which they are hosted. With this framework in hand, I will review two examples of topological waves in two-dimensional fluids, namely oceanic shallow-water waves propagating on the Earth's rotating surface and momentum waves in active polar fluids spontaneously "flocking" on surfaces of revolution. I will also show how this work generalizes to the context of astrophysics.