Quantum metric induced phases in Moiré materials

Abouelkomsan, Ahmed; Yang, Kang; Bergholtz, Emil J.

doi:10.1103/physrevresearch.5.l012015

Cited by 18 publications

(3 citation statements)

References 95 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Similar methods can also be applied to address bounds on the spin stiffness for interacting ferromagnets in flat-band systems. A number of recent theoretical works have studied the interplay of berry curvature distribution and quantum geometry in interacting topological flat bands on the stability of fractional Chern insulators ( 37 – 40 ). Finding the fundamental ingredients that guarantee a robust superconducting ground state remains an interesting problem for the future.…”

Section: Discussionmentioning

confidence: 99%

Diamagnetic response and phase stiffness for interacting isolated narrow bands

Mao

Chowdhury

2023

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

Superconductivity is a macroscopic manifestation of a quantum phenomenon where pairs of electrons delocalize and develop phase coherence over a long distance. A long-standing quest has been to address the underlying microscopic mechanisms that fundamentally limit the superconducting transition temperature, T c . A platform which serves as an ideal playground for realizing “high”-temperature superconductors are materials where the electrons’ kinetic energy is quenched and interactions provide the only energy scale in the problem. However, when the noninteracting bandwidth for a set of isolated bands is small compared to the interactions, the problem is inherently nonperturbative. In two spatial dimensions, T c is controlled by superconducting phase stiffness. Here, we present a theoretical framework for computing the electromagnetic response for generic model Hamiltonians, which controls the maximum possible superconducting phase stiffness and thereby T c , without resorting to any mean-field approximation. Our explicit computations demonstrate that the contribution to the phase stiffness arises from i) “integrating out” the remote bands that couple to the microscopic current operator and ii) the density–density interactions projected on to the isolated narrow bands. Our framework can be used to obtain an upper bound on the phase stiffness and relatedly T c for a range of physically inspired models involving both topological and nontopological narrow bands with density–density interactions. We discuss a number of salient aspects of this formalism by applying it to a specific model of interacting flat bands and compare the upper bound against the known T c from independent numerically exact computations.

show abstract

Section: Discussionmentioning

confidence: 99%

Diamagnetic response and phase stiffness for interacting isolated narrow bands

Mao

Chowdhury

2023

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

show abstract

“…Our primary method of choice for the analysis of Eq. ( 1) is exact diagonalization in momentum space on finite systems with periodic boundary conditions, which has previously been applied to study other graphene moiré systems [45,46,52,[66][67][68][69]. ED provides us with an unbiased, numerically exact way of obtaining the many-body wave functions and full set of low-energy levels, which collectively constitute a spectral fingerprint for the prevalent ordered phases.…”

Section: C1 Exact Diagonalizationmentioning

confidence: 99%

Non-coplanar magnetism, topological density wave order and emergent symmetry at half-integer filling of moiré Chern bands

et al. 2023

View full text Add to dashboard Cite

Twisted double- and mono-bilayer graphene are graphene-based moiré materials hosting strongly correlated fermions in a gate-tunable conduction band with a topologically non-trivial character. Using unbiased exact diagonalization complemented by unrestricted Hartree-Fock calculations, we find that the strong electron-electron interactions lead to a non-coplanar magnetic state, which has the same symmetries as the tetrahedral antiferromagnet on the triangular lattice and can be thought of as a skyrmion lattice commensurate with the moiré scale, competing with a set of ferromagnetic, topological charge density waves featuring an approximate emergent O(3) symmetry, “rotating” the different charge density wave states into each other. Direct comparison with exact diagonalization reveals that the ordered phases are accurately described within the unrestricted Hartree-Fock approximation. Exhibiting a finite charge gap and Chern number |C|=1, the formation of charge density wave order which is intimately connected to a skyrmion lattice phase is consistent with recent experiments on these systems.

show abstract

“…6(b) and 6(c)], revealing the underlying phase is the CDW with the order momentum K t,b + . Various types of CDW phases have been identified in static TBG-hBN as competing phases against FCIs [21,[73][74][75]. The K-CDW states corresponds to a Wigner crystal, whose unit cell is tripled compared to the original moiré lattice [21].…”

Section: Many-body Physics In a Single Valleymentioning

confidence: 99%

Floquet fractional Chern insulators and competing phases in twisted bilayer graphene

Hu,

Zhou,

Liu

2023

SciPost Phys.

View full text Add to dashboard Cite

We study the many-body physics in twisted bilayer graphene coupled to periodic driving of a circularly polarized light when electron-electron interactions are taken into account. In the limit of high driving frequency \OmegaΩ, we use Floquet theory to formulate the system by an effective static Hamiltonian truncated to the order of \Omega^{-2}Ω−2, which consists of a single-electron part and the screened Coulomb interaction. We numerically simulate this effective Hamiltonian by extensive exact diagonalization in the parameter space spanned by the twist angle and the driving strength. Remarkably, in a wide region of the parameter space, we identify Floquet fractional Chern insulator states in the partially filled Floquet valence bands. We characterize these topologically ordered states by ground-state degeneracy, spectral flow, and entanglement spectrum. In regions of the parameter space where fractional Chern insulator states are absent, we find topologically trivial charge density waves and band-dispersion-induced Fermi liquids which strongly compete with fractional Chern insulator states.

show abstract

Quantum metric induced phases in Moiré materials

Cited by 18 publications

References 95 publications

Diamagnetic response and phase stiffness for interacting isolated narrow bands

Diamagnetic response and phase stiffness for interacting isolated narrow bands

Non-coplanar magnetism, topological density wave order and emergent symmetry at half-integer filling of moiré Chern bands

Floquet fractional Chern insulators and competing phases in twisted bilayer graphene

Contact Info

Product

Resources

About