Kekulé spiral order at all nonzero integer fillings in twisted bilayer graphene

Kwan, Yves H.; Wagner, Glenn; Soejima, Tomohiro; Zaletel, Michael P.; Simon, Steven H.; Parameswaran, Siddharth A.; Bultinck, Nick

doi:10.48550/arxiv.2105.05857

Cited by 9 publications

(14 citation statements)

References 121 publications

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“…KD has been observed in the related context of QHFM within the lowest LL of monolayer graphene [103][104][105] , including the imaging of an individual valley skyrmion 104 . We caution that KD in TBG has also been predicted for IKS order in the presence of a small amount of strain 20,102 .…”

Section: Detecting Skyrmionsmentioning

confidence: 79%

“…(Note that it has been argued that the effective value of w AA may be susceptible to renormalization towards the chiral limit 57 , κ = 0, due to the effects of remote bands; thus, tuning w AA may be viewed as phenomenologically modeling this downward renormalization 9 .) Sometimes, we will also incorporate heterostrain 20,58,59 with strength and a sublattice potential of strength ∆ 60 . In the absence of such single-particle perturbations, the point group is D 6 , which includes Ĉ2z , Ĉ3z and M (inplane rotation about the x-axis).…”

Section: A Interacting Bm Modelmentioning

confidence: 99%

“…For ∆ beyond a fraction of an meV, HF fails to stabilize paired skyrmions at all. In fact if the coupling is strong enough, the meanfield ground state becomes a valley Hall state with no intervalley coherence 20 . On the other hand, increasing the strength of interactions tends to favor the paired skyrmions.…”

Section: B 2e-skyrmionsmentioning

confidence: 99%

“…Indeed we believe that this is one of the few cases where such a choice impacts a physical quantity in a qualitative way. Many theoretical studies focus primarily on the type of symmetry-breaking order 5,6,8,20,64,65,[74][75][76][77][78][79][80][81][82][83] -all the schemes studied here lead to the KIVC which only requires that J, λ > 0. On the other hand, we are interested in the θ-dependence of E c which depends sensitively on the value of J itself.…”

Section: Effective Mass Of Paired Skyrmionsmentioning

confidence: 99%

“…While a purely strong-coupling treatment does not completely resolve the experimental puzzles surrounding TBG, it serves as a natural starting point for considering how various physically realistic corrections influence the competition between ordered states. In this manner, it can aid in the identification of new and distinct brokensymmetry phases that are not accessible in any obvious way from the weakly-interacting limit, but can be viewed as descending from strong-coupling ferromagnetic orders in a natural, albeit non-trivial, fashion as the system is tuned towards the physically relevant intermediatecoupling regime 20,21 .…”

Section: Introductionmentioning

confidence: 99%

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Skyrmions in twisted bilayer graphene: stability, pairing, and crystallization

Kwan¹,

Wagner²,

Bultinck³

et al. 2021

Preprint

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We study the excitations that emerge upon doping the translationally-invariant correlated insulating states in magic angle twisted bilayer graphene at various integer filling factors ν. We identify parameter regimes where these are associated with skyrmion textures in the spin or pseudospin degrees of freedom, and explore both short-distance pairing effects and the formation of long-range ordered skyrmion crystals. We perform a comprehensive analysis of the pseudospin skyrmions that emerge upon doping insulators at even ν, delineating the regime in parameter space where these are the lowest-energy charged excitations by means of self-consistent Hartree-Fock calculations on the interacting Bistritzer-MacDonald model. We explicitly demonstrate the purely electron-mediated pairing of skyrmions, a key ingredient behind a recent proposal of skyrmion superconductivity. Building upon this, we construct hopping models to extract the effective masses of paired skyrmions, and discuss our findings and their implications for skyrmion superconductivity in relation to experiments, focusing on the dome-shaped dependence of the transition temperature on the twist angle. We also investigate the properties of spin skyrmions about the quantized anomalous Hall insulator at ν = +3. In both cases, we demonstrate the formation of robust spin/pseudospin skyrmion crystals upon doping to a finite density away from integer filling.

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Section: Detecting Skyrmionsmentioning

confidence: 79%

Section: A Interacting Bm Modelmentioning

confidence: 99%

Section: B 2e-skyrmionsmentioning

confidence: 99%

Section: Effective Mass Of Paired Skyrmionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Skyrmions in twisted bilayer graphene: stability, pairing, and crystallization

Kwan¹,

Wagner²,

Bultinck³

et al. 2021

Preprint

Self Cite

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Exact Landau Level Description of Geometry and Interaction in a Flatband

et al. 2021

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Flatbands appear in many condensed matter systems, including the two-dimensional electron gas in a high magnetic field, correlated materials, and moiré heterostructures. They are characterized by intrinsic geometric properties such as the Berry curvature and Fubini-Study metric. The influence of the band geometry on electron-electron interaction is difficult to understand analytically because the geometry is in general nonuniform in momentum space. In this work, we study the topological flatband of Chern number C = 1 with a momentum-dependent but positive definite Berry curvature that fluctuates in sync with Fubini-Study metric. We derive an exact correspondence between such ideal flatbands and Landau levels and show that the band geometry fluctuation gives rise to a new type of interaction in the corresponding Landau levels that depends on the center of mass of two particles. We characterize such interactions by generalizing the usual Haldane pseudopotentials. This mapping gives exact zero-energy ground states for short-ranged repulsive generalized pseudopotentials in flatbands, in analogy to fractional quantum Hall systems. Driving the center-of-mass interactions beyond the repulsive regime leads to a dramatic reconstruction of the ground states towards gapless phases. The generalized pseudopotential could be a useful basis for future numerical studies.

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Correlated insulators, semimetals, and superconductivity in twisted trilayer graphene

Christos,

Sachdev,

Scheurer

2021

Preprint

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Motivated by recent experiments indicating strong superconductivity and intricate correlated insulating and flavor-polarized physics in mirror-symmetric twisted trilayer graphene, we study the effects of interactions in this system close to the magic angle, using a combination of analytical and numerical methods. We identify asymptotically exact correlated many-body ground states at all integer filling fractions ν of the flat bands. To determine their fate when moving away from these fine-tuned points, we apply self-consistent Hartree-Fock numerics and analytic perturbation theory, with good agreement between the two approaches. This allows us to construct a phase diagram for the system as a function of ν and the displacement field, the crucial experimental tuning parameter of the system, and study the spectra of the different phases. The phase diagram is dominated by a correlated semimetallic intervalley coherent state and an insulating sublattice-polarized phase around charge neutrality, ν = 0, with additional spin-polarization being present at quarter (ν = −2) or three quarter (ν = +2) fillings of the quasi-flat bands. We further study the superconducting instabilities emerging from these correlated states, both in the absence and in the additional presence of electron-phonon coupling, also taking into account possible Wess-Zumino-Witten terms. In the experimentally relevant regime, we find triplet pairing to dominate, possibly explaining the observed violation of the Pauli limit. Our results have several consequences for experiments as well as future theoretical work and illustrate the rich physics resulting from the interplay of almost flat bands and dispersive Dirac cones in twisted trilayer graphene. CONTENTS 1. Continuum model and low-energy degrees of freedom 2. Single-particle symmetries 3. Interaction and form factors B. Exact statements about the interacting groundstates 1. Turning on the coupling between the subsystems 2. Behavior of Goldstone modes C. Hartree-Fock functional 1. General form

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Kekulé spiral order at all nonzero integer fillings in twisted bilayer graphene

Cited by 9 publications

References 121 publications

Skyrmions in twisted bilayer graphene: stability, pairing, and crystallization

Skyrmions in twisted bilayer graphene: stability, pairing, and crystallization

Exact Landau Level Description of Geometry and Interaction in a Flatband

Correlated insulators, semimetals, and superconductivity in twisted trilayer graphene

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