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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Quantum geometry in quantum materials

Quantum geometry, characterized by the quantum geometric tensor, plays a central role in diverse physical phenomena in quantum materials. This pedagogical review introduces the concept and highlights its implications across multiple domains, including optical responses, Landau levels, fractional Chern insulators, superfluid weight, spin stiffness, exciton condensates, and electronphonon coupling. By integrating these topics, we emphasize the broad significance of quantum geometry in understanding emergent behaviors in quantum systems and conclude with an outlook on open questions and future directions.

Condensed-matter physics↗
DOE OSTI2020

Quantum simulation of hyperbolic space with circuit quantum electrodynamics: From graphs to geometry

We show how quantum many-body systems on hyperbolic lattices with nearest-neighbor hopping and local interactions can be mapped onto quantum field theories in continuous negatively curved space. Here, the underlying lattices have recently been realized experimentally with superconducting resonators and therefore allow for a table-top quantum simulation of quantum physics in curved background. Our mapping provides a computational tool to determine observables of the discrete system even for large lattices, where exact diagonalization fails. As an application and proof of principle we quantitatively reproduce the ground state energy, spectral gap, and correlation functions of the noninteracting lattice system by means of analytic formulas on the Poincaré disk, and show how conformal symmetry emerges for large lattices. This sets the stage for studying interactions and disorder on hyperbolic graphs in the future. Importantly, our analysis reveals that even relatively small discrete hyperbolic lattices emulate the continuous geometry of negatively curved space, and thus can be used to experimentally resolve fundamental open problems at the interface of interacting many-body systems, quantum field theory in curved space, and quantum gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Universal suppression of superfluid weight by non-magnetic disorder in $s$-wave superconductors independent of quantum geometry and band dispersion

Motivated by the experimental progress in controlling the properties of the energy bands in superconductors, significant theoretical efforts have been devoted to study the effect of the quantum geometry and the flatness of the dispersion on the superfluid weight. In conventional superconductors, where the energy bands are wide and the Fermi energy is large, the contribution due to the quantum geometry is negligible, but in the opposite limit of flat-band superconductors the superfluid weight originates purely from the quantum geometry of Bloch wave functions. Here, we study how the energy band dispersion and the quantum geometry affect the disorder-induced suppression of the superfluid weight. In particular, we consider non-magnetic disorder and s-wave superconductivity. Surprisingly, we find that the disorder-dependence of the superfluid weight is universal across a variety of models, and independent of the quantum geometry and the flatness of the dispersion. Our results suggest that a flat-band superconductor is as resilient to disorder as a conventional superconductor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Quantum geometry embedded in unitarity of evolution: Revealing its impacts as geometric oscillation and dephasing in spin resonance and crystal bands

Quantum Hall effects provide intuitive ways of revealing the topology in crystals, i.e., each quantized “step” represents a distinct topological state. Here, we seek a counterpart for “visualizing” quantum geometry, which is a broader concept. Here we show how geometry emerges in quantum as an intrinsic consequence of unitary evolution, composing a framework compatible with quantum metric and independent of specific details or approximations, suggesting quantum geometry may have widespread applicability. Indeed, we exemplify geometric observables, such as oscillation, dephasing, in magnetic resonance or band driving scenarios. Anomalies, supported by both analytic and numerical solutions, underscore the advantages of adopting a geometric perspective, potentially yielding distinguishable experimental signatures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Discrete quantum geometry and intrinsic spin Hall effect

We show that the quantum geometry of the Fermi surface can be numerically described by a three-dimensional discrete quantum manifold. This approach not only avoids singularities in the Fermi sea, but it also enables the precise computation of the intrinsic Hall conductivity resolved in spin, as well as any other local properties of the Fermi surface. The method assures numerical accuracy when the Fermi level is arbitrarily close to singularities, and it remains robust when Kramers degeneracy is protected by symmetry. Furthermore, the approach is demonstrated by calculating the anomalous Hall and spin Hall conductivities of a two-band lattice model of a Weyl semimetal and a full-band ab initio model of zinc-blende GaAs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Superconductivity-induced spectral weight transfer due to quantum geometry

Optical spectral weight transfer associated with the onset of superconductivity at high-energy scales compared with the superconducting gap has been observed in several systems such as high-T c cuprates. While there are still debates on the origin of this phenomenon, a consensus is that it is due to strong correlation effects beyond the BCS theory. Here, we show that there is another route to a nonzero spectral weight transfer based on the quantum geometry of the conduction band in multiband systems. Further, we discuss applying this idea to the cuprates and twisted multilayer graphene.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Superfluid Weight Bounds from Symmetry and Quantum Geometry in Flat Bands

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.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Probing electromagnetic nonreciprocity with quantum geometry of photonic states

Reciprocal and nonreciprocal effects in dielectric and magnetic materials provide crucial information about the microscopic properties of electrons. However, experimentally distinguishing the two has proven to be challenging, especially when the associated effects are extremely small. To this end, we propose a contactless detection using a cross-cavity device where a material of interest is placed at its center. We show that the optical properties of the material, such as Kerr and Faraday rotation, or birefringence, manifest in the coupling between the cavity's electromagnetic modes and in the shift of their resonant frequencies. By calculating the dynamics of a geometrical photonic state, we formulate a measurement protocol based on the quantum metric and quantum process tomography that isolates the individual components of the material's complex refractive index and minimizes the quantum mechanical Cramér-Rao bound on the variance of the associated parameter estimation. Our approach is expected to be applicable across a broad spectrum of experimental platforms including Fock states in optical cavities, or coherent states in microwave and THz resonators. Published by the American Physical Society 2025

Petrides, Ioannis (ORCID:0000000174842444)↗
DOE OSTI2021

Anomalous electrodynamics and quantum geometry in the Dirac-Harper model for a graphene bilayer

In this work, graphene bilayers with layer antisymmetric strains are studied using the Dirac-Harper model for a pair of single layer Dirac Hamiltonians coupled by a one-dimensional moiré-periodic interlayer tunneling amplitude. This model hosts low energy, nearly dispersionless bands near charge neutrality that support anomalous polarizations of its charge multipole distributions. These are analyzed introducing a generalized Berry curvature that encodes the field-induced dynamics of multipole fields allowed in a chiral medium with time reversal symmetry. The formulation identifies a reciprocity relation between responses to layer-symmetric and layer-antisymmetric in-plane electric fields and reveals momentum-space quantum oscillations produced by a spatial pattern of band inversions on the moiré scale.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Evidence for Dirac flat band superconductivity enabled by quantum geometry

In a flat band superconductor, the charge carriers’ group velocity v F is extremely slow. Superconductivity therein is particularly intriguing, being related to the long-standing mysteries of high-temperature superconductors and heavy-fermion systems. Yet the emergence of superconductivity in flat bands would appear paradoxical, as a small v F in the conventional Bardeen–Cooper–Schrieffer theory implies vanishing coherence length, superfluid stiffness and critical current. Here, using twisted bilayer graphene, we explore the profound effect of vanishingly small velocity in a superconducting Dirac flat band system. Using Schwinger-limited non-linear transport studies we demonstrate an extremely slow normal state drift velocity v n ≈ 1,000 m s –1 for filling fraction ν between -1/2 and -3/4 of the moiré superlattice. In the superconducting state, the same velocity limit constitutes a new limiting mechanism for the critical current, analogous to a relativistic superfluid. Importantly, our measurement of superfluid stiffness, which controls the superconductor’s electrodynamic response, shows that it is not dominated by the kinetic energy but instead by the interaction-driven superconducting gap, consistent with recent theories on a quantum geometric contribution. Here we find evidence for small Cooper pairs, characteristic of the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation crossover, with an unprecedented ratio of the superconducting transition temperature to the Fermi temperature exceeding unity and discuss how this arises for ultra-strong coupling superconductivity in ultra-flat Dirac bands.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Nonlinear photoconductivities and quantum geometry of chiral multifold fermions

Here, chiral multifold fermions are quasiparticles that appear only in chiral crystals such as transition metal silicides in the cubic B20 structure (i.e., the CoSi family), and they may show exotic physical properties. Here we study the injection and shift photoconductivities and also the related geometrical quantities for several types of chiral multifold fermions, including spin-1/2 as well as pseudospin-1 and -3/2 fermions, dubbed as Kramers Weyl, triple-point, and Rarita-Schwinger-Weyl (RSW) fermions, respectively. We utilize the minimal symmorphic model to describe the triple-point fermions (TPF). We also consider the more realistic model Hamiltonian for the CoSi family including both linear and quadratic terms. We find that injection currents due to circularly polarized light are quantized as a result of the Chern numbers carried by the multifold fermions within the linear models. Surprisingly, we discover that in the TPF model, the linear shift conductivities, responsible for the shift current generation by linearly polarized light, are proportional to the pseudo spin-orbit coupling and independent of photon frequency. In contrast, for the RSW and Kramer Weyl fermions, the linear shift conductivity is linearly proportional to photon frequency. The numerical results agree with the power-counting analysis for quadratic Hamiltonians. The frequency independence of the linear shift conductivity could be attributed to the strong resonant symplectic Christoffel symbols of the flat bands. Moreover, the calculated symplectic Christoffel symbols show significant peaks at the nodes, suggesting that the shift currents are due to the strong geometrical response near the topological nodes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Higher Vortexability: Zero-Field Realization of Higher Landau Levels

The rise of moiré materials has led to experimental realizations of integer and FCIs in small or vanishing magnetic fields. At the same time, a set of minimal conditions sufficient to guarantee an Abelian fractional state in a flat band were identified, namely “ideal" or “vortexable" quantum geometry. Such vortexable bands share essential features with the LLL, while excluding the need for more fine-tuned aspects such as flat Berry curvature. A natural and important generalization is to ask if such conditions can be extended to capture the quantum geometry of higher Landau levels, particularly the first (1LL), where non-Abelian states at ν = 1/2, 2/5 are known to be competitive. The possibility of realizing these states at zero magnetic field, and perhaps even more exotic ones, could become a reality if we could identify the essential structure of the 1LL in Chern bands. In this work, we introduce a precise definition of 1LL quantum geometry, along with a figure of merit that measures how closely a given band approaches the 1LL. Furthermore, periodically strained Bernal graphene is shown to realize such a 1LL structure even in zero magnetic field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗