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

**Physical Properties of an Aperiodic Monotile with Graphene-like Features, Chirality, and Zero Modes**

The discovery of the Hat, an aperiodic monotile, has revealed novel mathematical aspects of aperiodic tilings. Quasicrystals are also known for their peculiar electronic properties. Here we imagined how the electronic properties of a 2D material with the lattice structure of the Hat tiling would look like. We studied spectral and transport properties of a tight-binding model defined on the Hat. We found striking similarities to that of graphene (right figure) and a macroscopic number of zero energy modes (central figure). Surprisingly, a magnetic field that is exactly half of the flux quantum per plaquette localizes the zero modes only the reflected “antihats »! These antihats are highlighted in light blue in the left figure. In this work we collaborated with Prof. F. Flicker, form U. Bristol.

J. Schirmann, S. Franca, F. Flicker, A. G. Grushin Phys. Rev. Lett. 132, 086402 (2024)

**Amorphous and Polycrystalline Routes toward a Chiral Spin Liquid**

Structural disorder can help to stabilize interesting topological phases, in otherwise topologically trivial systems. In this work we show that a topological chiral spin liquid could spontaneously emerge from a gapless spin-liquid in partially amorphous and polycrystalline Kitaev materials.

Adolfo G. Grushin and Cécile Repellin Phys. Rev. Lett. **130**, 186702 (2023)

**Observation of spin-momentum locked surface states in amorphous Bi _{2}Se_{3}**

In a collaboration with the Lanzara’s and Hellman’s experimental groups at UC Berkeley, we have found signature of spin-momentum locking for the first time in an amorphous material. It is the first evidence of features attributed to topological phases in a materials that display the largest amounts of disorder medium known, amorphous solids. While topological phases are generally regarded as one of the most robust phases of matter, no amorphous material had shown evidence of topological phenomena. Using magneto-transport, spin-resolved photoemissiom spectroscopy and theoretical models, the latter developed in our group, we have shown that dispersive states in **Bi _{2}Se_{3}** are momentum locked, and likely topological. Amorphous materials are much more numerous than crystals, and are extremely well integrated in technology (DVDs, memories, solar cells). Hence, this work opens up a the search for new materials that are both amorphous and topological, which significant potential for technology.

P. Corbae et al Nature Materials (2023)

**September 2022 marks the kick-off of the ERC – CoG project TOPOMORPH!**

We are seeking talented postdocs and PhDs to join us in the quest of understanding the novel topological properties of amorphous matter, and predicting the materials where they might be realised in.

**Imaging tunable quantum Hall broken-symmetry orders in graphene**

In a collaboration with the group of Benjamin Sacépé, also at Institut Néel, we helped understand how three distinct broken-symmetry phases can emerge in graphene by tuning the screening of the Coulomb interaction by a low or high dielectric constant environment, and with a magnetic field. The three phases are a Kekulé bond order, in the image, a sublattice-unpolarized ground state that emerges at low magnetic fields, and a charge-density-wave order, which appears at higher magnetic fields. For the first time it was observed that Kekulé and charge-density-wave orders coexist with additional, secondary lattice-scale orders that enrich the phase diagram beyond current theory predictions. This screening-induced tunability of broken-symmetry orders may prove valuable to uncover correlated phases of matter in other quantum materials.

A. Coissard et al Nature** 605**, 51–56 (2022)

**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)