Valerio Peri

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Peri

First Name

Valerio

ORCID

0000-0002-0727-3808

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Publications 1 - 10 of 10

Superfluid Weight Bounds from Symmetry and Quantum Geometry in Flat Bands
Herzog-Arbeitman, Jonah; Peri, Valerio; Schindler, Frank; et al. (2022)
Physical Review Letters
Flat-band superconductivity has theoretically demonstrated the importance of band topology to correlated phases. In two dimensions, the superfluid weight, which determines the critical temperature through the Berezinksii-Kosterlitz-Thouless criteria, is bounded by the Fubini-Study metric at zero temperature. We show this bound is nonzero within flat bands whose Wannier centers are obstructed from the atoms—even when they have identically zero Berry curvature. Next, we derive general lower bounds for the superfluid weight in terms of momentum space irreps in all 2D space groups, extending the reach of topological quantum chemistry to superconducting states. We find that the bounds can be naturally expressed using the formalism of real space invariants (RSIs) that highlight the separation between electronic and atomic degrees of freedom. Finally, using exact Monte Carlo simulations on a model with perfectly flat bands and strictly local obstructed Wannier functions, we find that an attractive Hubbard interaction results in superconductivity as predicted by the RSI bound beyond mean field. Hence, obstructed bands are distinguished from trivial bands in the presence of interactions by the nonzero lower bound imposed on their superfluid weight.
Crystalline Topology: from Metamaterials to Flat-Band Superconductors
Peri, Valerio (2022)
Symmetries crucially underlie the classification of topological phenomena in condensed matter physics. The first endeavors in the study of topological effects in non-interacting systems focused predominantly on the role of symmetries that act locally in space. Nevertheless, most materials, both natural as well as engineered, also possess crystalline symmetries. Recent theoretical works unveiled that these crystalline symmetries can stabilize flavors of topology that have been previously overlooked. The contribution of this dissertation to the field of crystalline topological insulators is twofold. First, with the help of mechanical metamaterials, we provide the experimental validation of two variants of topology that necessitate crystalline symmetries: higher-order and fragile topology. Second, we theoretically establish the relevance of these topological effects to stabilize superconductivity once interactions are included in bands with quenched kinetic energy. The idea of higher-order topology is rooted in the extension of the modern theory of charge polarization to higher multipole moments. A two-dimensional topological insulator with a quantized quadrupole moment is predicted to have gapped yet topological one-dimensional edge modes, which stabilize zero-dimensional in-gap corner states. While based on the concept of charge moments, we can use the same theory as an elegant tool to characterize the bands of neutral bosonic systems such as photonic or phononic crystals. Here, we present the first observation of higher-order topological bands in an elastic metamaterial. We characterize experimentally the bulk, edge, and corner physics and find the predicted gapped edge and in-gap corner states. We further corroborate our findings by comparing the mechanical properties of a topologically non-trivial system to samples in other phases. Fragile topological bands, instead, challenge our very notion of topology: while answering to the most basic definition of topology, one can trivialize these bands through the addition of trivial ones. Moreover, they lack a rigorous bulk-boundary correspondence that ensures conducting gapless edge modes in the bulk's gap of the system. Here, we fully characterize the symmetry properties of the response of an acoustic metamaterial to establish the topologically fragile nature of its bands. Additionally, we identify a protected spectral signature associated with this flavor of topology in the form of spectral flow under twisted boundary conditions. Narrow fragile topological bands also emerge when one stacks two layers of graphene on top of each other with a small relative twist angle. Superconductivity was recently observed at partial fillings of these bands. It is an intriguing question whether the topological properties of the bands play any role in the superconducting transition. In two-dimensional systems such as twisted bilayer graphene, the superfluid weight determines the critical temperature through the Berezinksii-Kosterlitz-Thouless mechanism. At the mean-field level, the superfluid weight is bounded by the quantum metric of the bands. A non-zero Chern number or fragile topology, in turn, set a lower bound for the quantum metric. Here, we show that there exist bounds also within bands where space group symmetries force the electrons to be displaced from the atomic sites, even when their Berry curvature is identically zero. Furthermore, using exact Monte Carlo simulations, we find that an attractive Hubbard interaction in flat bands results in superconductivity as predicted by our bounds, thereby extending their validity beyond the mean-field regime. These results establish the importance of crystalline topology for flat-band superconductivity.
Fragile Topology and Flat-Band Superconductivity in the Strong-Coupling Regime
Peri, Valerio; Song, Zhi-Da; Bernevig, B. Andrei; et al. (2021)
Physical Review Letters
In flat bands, superconductivity can lead to surprising transport effects. The superfluid “mobility”, in the form of the superfluid weight Ds, does not draw from the curvature of the band but has a purely band-geometric origin. In a mean-field description, a nonzero Chern number or fragile topology sets a lower bound for Ds, which, via the Berezinskii-Kosterlitz-Thouless mechanism, might explain the relatively high superconducting transition temperature measured in magic-angle twisted bilayer graphene (MATBG). For fragile topology, relevant for the bilayer system, the fate of this bound for finite temperature and beyond the mean-field approximation remained, however, unclear. Here, we numerically use exact Monte Carlo simulations to study an attractive Hubbard model in flat bands with topological properties akin to those of MATBG. We find a superconducting phase transition with a critical temperature that scales linearly with the interaction strength. Then, we investigate the robustness of the superconducting state to the addition of trivial bands that may or may not trivialize the fragile topology. Our results substantiate the validity of the topological bound beyond the mean-field regime and further stress the importance of fragile topology for flat-band superconductivity
Structural oddities
Peri, Valerio; Huber, Sebastian (2020)
Nature Physics
Acoustic spin-Chern insulator induced by synthetic spin–orbit coupling with spin conservation breaking
Deng, Weiyin; Huang, Xueqin; Lu, Jiuyang; et al. (2020)
Nature Communications
Topologically protected surface modes of classical waves hold the promise to enable a variety of applications ranging from robust transport of energy to reliable information processing networks. However, both the route of implementing an analogue of the quantum Hall effect as well as the quantum spin Hall effect are obstructed for acoustics by the requirement of a magnetic field, or the presence of fermionic quantum statistics, respectively. Here, we construct a two-dimensional topological acoustic crystal induced by the synthetic spin-orbit coupling, a crucial ingredient of topological insulators, with spin non-conservation. Our setup allows us to free ourselves of symmetry constraints as we rely on the concept of a non-vanishing “spin” Chern number. We experimentally characterize the emerging boundary states which we show to be gapless and helical. More importantly, we observe the spin flipping transport in an H-shaped device, demonstrating evidently the spin non-conservation of the boundary states.
Non-Abelian chiral spin liquid on a simple non-Archimedean lattice
Peri, Valerio; Ok, S.; Tsirkin, S.S.; et al. (2020)
Physical Review B
Experimental characterization of fragile topology in an acoustic metamaterial
Peri, Valerio; Song, Zhi-Da; Serra-Garcia, Marc; et al. (2020)
Science
Axial-field-induced chiral channels in an acoustic Weyl system
Peri, Valerio; Serra-Garcia, Marc; Ilan, Roni; et al. (2019)
Nature Physics
Condensed-matter and other engineered systems, such as cold atoms, photonic or phononic metamaterials, have proved to be versatile platforms for the observation of low-energy counterparts of elementary particles from relativistic field theories. These include the celebrated Majorana modes, as well as Dirac and Weyl fermions. An intriguing feature of the Weyl equation is the chiral symmetry, where the two chiral sectors have an independent gauge freedom. Although this freedom leads to a quantum anomaly, there is no corresponding axial background field coupling differently to opposite chiralities in quantum electrodynamics. Here, we provide the experimental characterization of the effect of such an axial field in an acoustic metamaterial. We implement the axial field through an inhomogeneous potential and observe the induced chiral Landau levels. From the metamaterials perspective these chiral channels open the possibility for the observation of non-local Weyl orbits and might enable unidirectional bulk transport in a time-reversal-invariant system.
Weyl orbits without an external magnetic field
Peri, Valerio; Dubcek, Tena; Valenti, Agnes; et al. (2020)
Physical Review B
Weyl semimetals in a magnetic field give rise to interesting nonlocal electronic orbits: the ballistic transport through the bulk enabled by the chiral Landau levels is combined with a momentum-space sliding along the surface Fermi-arc driven by the Lorentz force. Bulk chiral Landau levels can also be induced by axial fields whose sign depends on the chirality of the Weyl point. However, the microscopic perturbations that give rise to them can be described in terms of gauge fields only in the low-energy sectors around the Weyl points. In addition, since pseudofields are intrinsic, there is no apparent reason for a Lorentz force that causes sliding along the Fermi arcs. Therefore, the existence of nonlocal orbits driven exclusively by pseudofields is not obvious. Here we show that for systems with at least four Weyl points in the bulk spectrum, nonlocal orbits can be induced by axial fields alone. We discuss the underlying mechanisms by a combination of analytical semiclassical theory, the microscopic numerical study of wave-packet dynamics, and a surface Green's function analysis.
Design and characterization of all 2D fragile topological bands
Bird, Samuel; Devescovi, Chiara; Engeler, Pascal; et al. (2025)
PNAS Nexus
Designing topological materials with specific topological indices is a complex inverse problem, traditionally tackled through manual, intuition-driven methods that are neither scalable nor efficient for exploring the vast space of possible material configurations. In this work, we develop an algorithm that leverages the covariance matrix adaptation evolution strategy to optimize the Fourier representation of the periodic functions shaping the designer material’s characteristics. This includes mass profiles or dielectric tensors for phononic and photonic crystals, respectively, as much as synthetic potentials applicable to ultra-cold atomic systems. We demonstrate our methodology with a detailed characterization of a class of topological bands known as “fragile topological,” showcasing the algorithm’s capability to address both topological characteristics and spectral quality, and demonstrating the experimental feasibility of realizing all of the classified fragile topological phases. This automation not only streamlines the design process but also significantly expands the potential for identifying and constructing high quality designer materials across the wide range of platforms, and is readily extendable to other setups, including higher-dimensional and nonlinear systems.

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Valerio Peri

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