Universal Fermi-surface anisotropy renormalization for interacting Dirac fermions with long-range interactions

Leaw, Jia Ning; Tang, Ho-Kin; Trushin, Maxim; Assaad, Fakher F.; Adam, Shaffique

doi:10.1073/pnas.1913096116

Cited by 11 publications

(7 citation statements)

References 25 publications

(19 reference statements)

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“…We conclude by mentioning recent work [43] that finds a universal Fermi contour anisotropy renormalization in two-dimensional, Coulomb-interacting Dirac systems. The result is seemingly consistent with the behavior of the CFL in the presence of band mass ansiotropy, α CF ≈ √ α F , as seen both in experiment and in our simulations.…”

Section: Discussionmentioning

confidence: 72%

Fermi Surfaces of Composite Fermions

Bhatt

Ippoliti

2020

J Low Temp Phys

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The fractional quantum Hall (FQH) effect was discovered in twodimensional electron systems subject to a large perpendicular magnetic field nearly four decades ago. It helped launch the field of topological phases, and in addition, because of the quenching of the kinetic energy, gave new meaning to the phrase "correlated matter". Most FQH phases are gapped like insulators and superconductors; however, a small subset with even denominator fractional fillings ν of the Landau level, typified by ν = 1/2, are found to be gapless, with a Fermi surface akin to metals. We discuss our results, obtained numerically using the infinite-Density Matrix Renormalization Group (iDMRG) scheme, on the effect of non-isotropic distortions with discrete Nfold rotational symmetry of the Fermi surface at zero magnetic field on the Fermi surface of the correlated ν = 1/2 state. We find that while the response for N = 2 (elliptical) distortions is significant (and in agreement with experimental observations with no adjustable parameters), it decreases very rapidly as N is increased. Other anomalies, like resilience to breaking the Fermi surface into disjoint pieces, are also found. This highlights the difference between Fermi surfaces formed from the kinetic energy, and those formed of purely potential energy terms in the Hamiltonian.Keywords fractional quantum Hall effect · two dimensional electron gas · Fermi surface

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Section: Discussionmentioning

confidence: 72%

Fermi Surfaces of Composite Fermions

Bhatt

Ippoliti

2020

J Low Temp Phys

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“…The discontinuity of ∂E k ∂k at Γ, K 2 in Fig. 4 can be interpreted as the anisotropy of the Fermi velocity at Γ, K 2 [67] in moiré BZ since at these k points the k path changes direction.…”

Section: Dirac Equation With Spin Connectionmentioning

confidence: 96%

An effective curved space-time geometric theory of generic twist angle graphene with application to a rotating bilayer configuration

Ma,

Datta,

Yao

2021

Preprint

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We propose a new kind of geometric effective theory based on curved space-time single valley Dirac theory with spin connection for twisted bilayer graphene under generic twist angle. This model can reproduce the nearly flat bands with particle-hole symmetry around the first magic angle. The band width is near the former results given by Bistritzer-MacDonald model or density matrix renormalization group. Even more, such geometric formalism allows one to predict the properties of rotating bilayer graphene which cannot be accessed by former theories. As an example, we investigate the Bott index of a rotating bilayer graphene. We relate this to the twodimensional Thouless pump with quantized charge pumping during one driving period which could be verified by transport measurement.

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“…The correlation effects in Dirac and Weyl fermion systems are extensively studied, and are well understood relatively [23][24][25][26][27][28][29][30][31][32][33][34]. The influence of many-body interaction on unconventional fermion systems also attracted much interest and is an important topic.…”

Section: Introductionmentioning

confidence: 99%

Correlated interaction effects in three-dimensional semi-Dirac semimetal

Wang¹,

Li²,

Zhang³

2021

Preprint

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Understanding the correlation effects in unconventional topological materials, in which the fermion excitations take unusual dispersion, is an important topic in recent condensed matter physics. We study the influence of short-range four-fermion interactions on three-dimensional semi-Dirac semimetal with an unusual fermion dispersion, that is linear along two directions but quadratic along the third one. Based on renormalization group theory, we find all of 11 unstable fixed points including 5 quantum critical points, 5 bicritical points, and one tricritical point. The physical essences of the quantum critical points are determined by analyzing the susceptibility exponents for all of the source terms in particle-hole and particle-particle channels. We also verify phase diagram of the system in the parameter space carefully through numerically studying the flows of the fourfermion coupling parameters and behaviors of the susceptibility exponents. These results are helpful for us to understand the physical properties of candidate materials for three-dimensional semi-Dirac semimetal such as ZrTe5.

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Universal Fermi-surface anisotropy renormalization for interacting Dirac fermions with long-range interactions

Cited by 11 publications

References 25 publications

Fermi Surfaces of Composite Fermions

Fermi Surfaces of Composite Fermions

An effective curved space-time geometric theory of generic twist angle graphene with application to a rotating bilayer configuration

Correlated interaction effects in three-dimensional semi-Dirac semimetal

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