Periodic Reporting for period 1 - TOPOMORPH (Amorphous topological matter: Predicting new phases with enhanced properties in a vast pool of amorphous materials)
Période du rapport: 2022-09-01 au 2025-02-28
In everyday life we experience that certain materials are do not conduct electricity, insulators like wood or diamond, while others are electrical conductors, like copper or gold.
In the last decades, researchers have found out that there is an intermediate possibility.
Certain materials can be insulating in their interior, while still conduct in their exterior, at their surfaces or edges. More surprisingly, the conduction in this materials, called topological insulators, is organized efficiently.
Electrons separate to move inside electronic highways, allowing a very efficient conduction. Researchers have shown that this behaviour is very robust, and possibly useful to design new electronic devices, including quantum computers.
However, most of the topological insulators we know are very well organized, clean crystals. This means that not only they are expensive to grow for technology, but also that our theories to describe them are limited to very ordered solids, or more generally, states of matter. In this project we want to go beyond this understanding by formulating theories of topological phases of matter in solids where the atomic arrangements are not nicely ordered, like in crystals. Amorphous materials, like glass in your windows, are cheap to grow, but we currently lack the theoretical mathematical modelling to understand whether topological phases can exist there. Understanding whether this is the case can help experimental scientists to design devices that are scalable for technology, while retaining the nice topological properties we are after.
The three goals of this ERC project are
1. Establishing a novel methodology to predict and classify novel topological insulators and metals in a large pool of amorphous materials.
2. Defining unaccounted for topological phases that require amorphous lattices to exist resulting in superior capabilities, with and without strong interactions.
3. Predicting the first amorphous topological superconductors.
In the last decades, researchers have found out that there is an intermediate possibility.
Certain materials can be insulating in their interior, while still conduct in their exterior, at their surfaces or edges. More surprisingly, the conduction in this materials, called topological insulators, is organized efficiently.
Electrons separate to move inside electronic highways, allowing a very efficient conduction. Researchers have shown that this behaviour is very robust, and possibly useful to design new electronic devices, including quantum computers.
However, most of the topological insulators we know are very well organized, clean crystals. This means that not only they are expensive to grow for technology, but also that our theories to describe them are limited to very ordered solids, or more generally, states of matter. In this project we want to go beyond this understanding by formulating theories of topological phases of matter in solids where the atomic arrangements are not nicely ordered, like in crystals. Amorphous materials, like glass in your windows, are cheap to grow, but we currently lack the theoretical mathematical modelling to understand whether topological phases can exist there. Understanding whether this is the case can help experimental scientists to design devices that are scalable for technology, while retaining the nice topological properties we are after.
The three goals of this ERC project are
1. Establishing a novel methodology to predict and classify novel topological insulators and metals in a large pool of amorphous materials.
2. Defining unaccounted for topological phases that require amorphous lattices to exist resulting in superior capabilities, with and without strong interactions.
3. Predicting the first amorphous topological superconductors.
Work performed:
For Goal 1, we developed novel methodology and models for amorphous topological matter. We have successfully applied those to real materials, understanding some of their experimental signatures and solidifying our descriptors of topological insulators and metals under extreme disorder.
Notably, a key step to achieve Goal 3 is to generalize topology to topological amorphous metals. Since we would like to model topological amorphous superconductors we need to understand their normal state first. Hence a good part of the work done in Task 1.1 focused on metals. In this realm we have:
The main aim of Goal 2, was to find topological amorphous phases with no crystalline counterparts, and establish amorphous topological phases with strong correlations. In this realm we hit a milestone early in the project where we found a phase that falls within both categories: a strongly interacting phase that is caused by the non-crystallinity of the lattice.
During this reporting period, we also followed an unexpected and very promising emergent research direction, overlapping strongly with Goal 2 and WP2. In March 2023 a new quasicrystalline lattice, the Hat tiling, was discovered by mathematicians. The methods we developed in order to progress towards Goal 1 were applicable to this new tiling. Hence, our expertise and research directions naturally aligned with this discovery, placing us at an advantageous position to provide understanding of the possible physical properties of this new set of lattices. This as one of our main and most impactful achievements.
The aim of Goal 3 is to predict the first amorphous topological superconductor, and is currently under development.
The most significant developments of the project so far are
1. The local order of amorphous systems directly revealed by Angle Photoemission Spectroscopy.
2. A relatively minimal number of defects is needed to create a topological chiral spin-liquid in amorphous and polycrystalline materials.
3. The spectral localizer can be used to characterize topological metals.
4. The Hat quasicrystaline tiling and the related family of tilings are as a door to new phenomena between quasicrystals and crystals.
For Goal 1, we developed novel methodology and models for amorphous topological matter. We have successfully applied those to real materials, understanding some of their experimental signatures and solidifying our descriptors of topological insulators and metals under extreme disorder.
Notably, a key step to achieve Goal 3 is to generalize topology to topological amorphous metals. Since we would like to model topological amorphous superconductors we need to understand their normal state first. Hence a good part of the work done in Task 1.1 focused on metals. In this realm we have:
The main aim of Goal 2, was to find topological amorphous phases with no crystalline counterparts, and establish amorphous topological phases with strong correlations. In this realm we hit a milestone early in the project where we found a phase that falls within both categories: a strongly interacting phase that is caused by the non-crystallinity of the lattice.
During this reporting period, we also followed an unexpected and very promising emergent research direction, overlapping strongly with Goal 2 and WP2. In March 2023 a new quasicrystalline lattice, the Hat tiling, was discovered by mathematicians. The methods we developed in order to progress towards Goal 1 were applicable to this new tiling. Hence, our expertise and research directions naturally aligned with this discovery, placing us at an advantageous position to provide understanding of the possible physical properties of this new set of lattices. This as one of our main and most impactful achievements.
The aim of Goal 3 is to predict the first amorphous topological superconductor, and is currently under development.
The most significant developments of the project so far are
1. The local order of amorphous systems directly revealed by Angle Photoemission Spectroscopy.
2. A relatively minimal number of defects is needed to create a topological chiral spin-liquid in amorphous and polycrystalline materials.
3. The spectral localizer can be used to characterize topological metals.
4. The Hat quasicrystaline tiling and the related family of tilings are as a door to new phenomena between quasicrystals and crystals.
The main results beyond the state of the art so far are the following:
Amorphous materials display order in momentum space: We discovered and characterized the first signals of local order in amorphous topological insulators. Photoemission spectra clearly display rotationally symmetric features that repeat in radial momenta. The extent to which these could be observed in experiment was unknown.
The agreement between experimental and theory is surprisingly good. We gave an explanation to the strong renormalization of the Fermi velocity of the surface states, which had remained unexplained.
It opened novel questions such as the different intensities of the peaks. As the first example of direct visualization in photoemission of amorphous local order it opens a new door to characterize amorphous solids, topological or not. In this sense we believe it was a breakthrough in solid-state physics.
Spectral localizer characterizes topological metals: Before our work it was unclear how to characterize topology in all strongly disordered metals. Together with postdoc Dr. Franca, we showed that trivial and topological metals differ in their spectral localizer eigenvalues, a quantum mechanical operator that measures wannierizability of a given Hamiltonian. When applied to amorphous CoSi it described a new topological semimetallic phase: the topological diffusive metal. This phase differs from the crystalline phase in that it has no exact degeneracies of localizer eigenstates, indicating a topological diffusive metallic phase. This was a relatively unexpected development in the sense that defining topological markers for metals in disordered systems was not expected to be possible.
Amorphous and polycrystalline spin-liquids can be topological: We predicted that, as amorphicity is increased, a gapless chiral spin liquid defined in the Honeycomb lattice, will turn into a topological chiral spin-liquid in an amorphous lattice. The latter is a long-sought phase and realistic proposals required an external magnetic field. Our proposal disposes of external magnetic fields and reframes disorder as a beneficial perturbation to realize a topological chiral spin-liquid.
Physical properties of the new quasicrystalline Hat tiling: We published the first theoretical analysis of the physical properties that this quasicrystal would have if it would be realized as a solid. We found that it shares properties with both crystals, notably graphene, and other properties found in quasicrystal, such as exact zero modes.
We have since then established a connection between the scattering of electronic waves in this quasicrystal with the scattering of seismic waves. This resulted in an unexpected, but we believe potentially quite impactful, collaboration with seismologists which are interested in signal processing.
We were able to show that detector arrays based on the Hat quasicrystal geometry seem to be efficient at beating certain limits of signal processing found for periodic arrays.
Amorphous materials display order in momentum space: We discovered and characterized the first signals of local order in amorphous topological insulators. Photoemission spectra clearly display rotationally symmetric features that repeat in radial momenta. The extent to which these could be observed in experiment was unknown.
The agreement between experimental and theory is surprisingly good. We gave an explanation to the strong renormalization of the Fermi velocity of the surface states, which had remained unexplained.
It opened novel questions such as the different intensities of the peaks. As the first example of direct visualization in photoemission of amorphous local order it opens a new door to characterize amorphous solids, topological or not. In this sense we believe it was a breakthrough in solid-state physics.
Spectral localizer characterizes topological metals: Before our work it was unclear how to characterize topology in all strongly disordered metals. Together with postdoc Dr. Franca, we showed that trivial and topological metals differ in their spectral localizer eigenvalues, a quantum mechanical operator that measures wannierizability of a given Hamiltonian. When applied to amorphous CoSi it described a new topological semimetallic phase: the topological diffusive metal. This phase differs from the crystalline phase in that it has no exact degeneracies of localizer eigenstates, indicating a topological diffusive metallic phase. This was a relatively unexpected development in the sense that defining topological markers for metals in disordered systems was not expected to be possible.
Amorphous and polycrystalline spin-liquids can be topological: We predicted that, as amorphicity is increased, a gapless chiral spin liquid defined in the Honeycomb lattice, will turn into a topological chiral spin-liquid in an amorphous lattice. The latter is a long-sought phase and realistic proposals required an external magnetic field. Our proposal disposes of external magnetic fields and reframes disorder as a beneficial perturbation to realize a topological chiral spin-liquid.
Physical properties of the new quasicrystalline Hat tiling: We published the first theoretical analysis of the physical properties that this quasicrystal would have if it would be realized as a solid. We found that it shares properties with both crystals, notably graphene, and other properties found in quasicrystal, such as exact zero modes.
We have since then established a connection between the scattering of electronic waves in this quasicrystal with the scattering of seismic waves. This resulted in an unexpected, but we believe potentially quite impactful, collaboration with seismologists which are interested in signal processing.
We were able to show that detector arrays based on the Hat quasicrystal geometry seem to be efficient at beating certain limits of signal processing found for periodic arrays.