The **Theory of Topological Matter** research team is a part of the Condensed Matter Theory Group of Institut Néel in Grenoble, France that is part of the CNRS, the largest governmental research agency in France.

The team is lead by Adolfo Grushin. You can find info about open positions here or by contacting us here.

## Highlights

**AKLT-States as ZX-Diagrams: Diagrammatic Reasoning for Quantum States**

In quantum physics, diagrammatic representations of mathematical operations help us interpret the physics they encode. Feynman diagrams are a popular example: the interactions between particles are represented by lines and vertices that help us understand which quantum processes are involved in a physical phenomenon, even when there are many particles involved. However, although useful and widespread, such methods cannot be used to compute directly as they are merely pictorial representations of the underlying mathematics. In this work we proposed to use the ZX-calculus, a mathematically rigorous but entirely graphical language, as a method to represent interesting quantum states and reason about them.

We found that key properties of an important family of quantum states, for example, those composed of many spins like spin chains, stem from simple equivalence relations between different ZX-diagrams. Our work establishes a new and fully diagrammatic way to reason about many-particle problems in quantum physics. We offer an innovative language with which we can formulate unsolved problems in our understanding of condensed-matter physics.

Richard D.P. East, John van de Wetering, Nicholas Chancellor, and Adolfo G. Grushin *PRX Quantum 3, 010302 January (2022)*

**Guided accumulation of active particles by topological design of a second-order skin effect**

Collective guidance of out-of-equilibrium systems without using external fields is a challenge of importance in active matter, ranging from bacterial colonies to swarms of self-propelled particles. Here we engineered a two-dimensional topographical design with where we observe spontaneous particle edge guidance and corner accumulation of self-propelled particles.

Lucas S. Palacios, Serguei Tchoumakov, Maria Guix, Ignacio Pagonabarraga, Samuel Sánchez Adolfo G. Grushin *Nature Communications*** 12**, 4691 (2021)

###### Topology and geometry under the nonlinear electromagnetic spotlight

Topological insulators respond to external fields in fundamentally different ways compared to trivial insulators. Here we reviewed what is special about topological matter, and quantum materials when they are subjected to light that has a sufficiently high intensity to reveal non-linear effects.

Qiong Ma, Adolfo G. Grushin, Kenneth S. Burch Nature Materials (2021)

###### Topological Weaire–Thorpe models of amorphous matter

Combining topologically robust responses with the long history of large-scale growth and broad applications of amorphous materials, opens a door for technological progress. Here we propose models that are realistic and topological and display useful symmetry properties despite their lack of periodicity. They allow us to predict when amorphous topological phases occur and their physical responses, opening up a path to identify, classify, and discover amorphous topological insulators.

Quentin Marsal, Dániel Varjas, and Adolfo G. Grushin PNAS 117 (48) 30260 (2020)

###### Topological circular photo-galvanic effect in the chiral multifold semimetal CoSi

The absence of mirror symmetry, or chirality, is behind striking natural phenomena found in systems as diverse as DNA and crystalline solids. A remarkable example occurs when chiral semimetals with topologically protected band degeneracies are illuminated with circularly polarized light. Under the right conditions, the part of the generated photocurrent that switches sign upon reversal of the light’s polarization, known as the circular photogalvanic effect, is predicted to depend only on fundamental constants. Here we investigate this possibility in the topological chiral semimetal CoSi, both theoretically and experimentally.

Zhuoliang Ni, K. Wang, Y. Zhang, O. Pozo, B. Xu, X. Han, K. Manna, J. Paglione, C. Felser, A. G. Grushin, F. de Juan, E. J. Mele, Liang Wu Nature Communications, 12, 154 (2021)

###### Linear and nonlinear optical responses in the chiral multifold semimetal RhSi

Another example of a chiral semimetals is RhSi. In this work, we report a comprehensive theoretical and experimental analysis of the linear and nonlinear optical responses of the chiral topological semimetal RhSi, which is known to host multifold fermions.

Zhuoliang Ni, B. Xu, M. A. Sanchez-Martinez, Y. Zhang, K. Manna, C. Bernhard, J. W. F. Venderbos, F. de Juan, C. Felser, A. G. Grushin, Liang Wu npj Quantum Materials 5, 96 (2020)