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Valley-polarized nematic order in twisted moiré systems: In-plane orbital magnetism and crossover from non-Fermi liquid to Fermi liquid

Ipsita Mandal and Rafael M. Fernandes
Phys. Rev. B 107, 125142 – Published 21 March 2023
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  • INTRODUCTION
  • VALLEY-POLARIZED NEMATIC ORDER IN TBG
  • PSEUDO-GOLDSTONE MODES IN THE…
  • NON-FERMI LIQUID TO FERMI LIQUID…
  • DISCUSSION AND CONCLUSIONS
  • ACKNOWLEDGMENTS
    • References

    Abstract

    The interplay between strong correlations and nontrivial topology in twisted moiré systems can give rise to a rich landscape of ordered states that intertwine the spin, valley, and charge degrees of freedom. In this paper, we investigate the properties of a system that displays long-range valley-polarized nematic order. Besides breaking the threefold rotational symmetry of the triangular moiré superlattice, this type of order also breaks twofold rotational and time-reversal symmetries, which leads to interesting properties. First, we develop a phenomenological model to describe the onset of this ordered state in twisted moiré systems, and to explore its signatures in their thermodynamic and electronic properties. Its main manifestation is that it triggers the emergence of in-plane orbital magnetic moments oriented along high-symmetry lattice directions. We also investigate the properties of the valley-polarized nematic state at zero temperature. Due to the existence of a dangerously irrelevant coupling λ in the six-state clock model that describes the putative valley-polarized nematic quantum critical point, the ordered state displays a pseudo-Goldstone mode. Using a two-patch model, we compute the fermionic self-energy to show that down to very low energies, the Yukawa-like coupling between the pseudo-Goldstone mode and the electronic degrees of freedom promotes the emergence of non-Fermi liquid behavior. Below a crossover energy scale Ω*∼λ3/2, however, Fermi liquid behavior is recovered. Finally, we discuss the applicability of these results to other nontrivial nematic states, such as the spin-polarized nematic phase.

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    • Received 8 February 2022
    • Revised 17 January 2023
    • Accepted 8 March 2023

    DOI:https://doi.org/10.1103/PhysRevB.107.125142

    Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

    Published by the American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Electronic structureNematic orderOrder parametersQuantum phase transitions
    1. Techniques
    Fermi liquid theoryNon-Fermi-liquid theory
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Ipsita Mandal

    • Institute of Nuclear Physics, Polish Academy of Sciences, 31-342 Kraków, Poland and Department of Physics, Stockholm University, AlbaNova University Center, 106 91 Stockholm, Sweden

    Rafael M. Fernandes

    • School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA

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    Issue

    Vol. 107, Iss. 12 — 15 March 2023

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    • Figure 1
      Figure 1

      Band structure along the high-symmetry directions of the moiré Brillouin zone, for the (almost) flat bands of TBG. This is numerically computed from the six-orbital model of Ref. [53], without [(a); dashed lines] and with [(b); solid lines] valley-polarized nematic ordering. Red and blue lines refer to the two valleys. The parameters used are the same as in Ref. [53], and we have chosen Φ0=0.01tκ and α=0 for the ordered state. The energy values shown are in meV.

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    • Figure 2
      Figure 2

      Fermi surfaces in the valley-polarized nematic state arising from the flat bands of TBG: The parameters are the same as those in Fig. 1, except for α, which here assumes the values nπ/3, with n∈[0,5]. (a)–(f) correspond to n=0 to n=5, respectively, indicating the six different domains that minimize the free energy. In (a), the Fermi surfaces in the absence of valley-polarized nematic order are shown by the dashed lines. Red and blue lines refer to the two different valleys.

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    • Figure 3
      Figure 3

      Illustration of the patch model: ψa,+ denotes the fermions located at the upper light purple patch, centered at an angle θ=θ0 with respect to the global coordinate system for a circular Fermi surface of valley quantum number a (denoted by the dark purple ring). ψa,− denotes the fermions in the lower light purple patch, centred at the antipodal point θ=π+θ0, whose tangential momenta are parallel to those at θ0. Although we show here the patch construction for a circular Fermi surface for the sake of simplicity, this can be applied to any Fermi surface of a generic shape, as long as it is locally convex at each point.

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    • Figure 4
      Figure 4

      Fermionic self-energy iΣ¯(νn)/m3 as a function of the scaled Matsubara frequency ν̃n=νn/Ω*, obtained from the numerical integration of Eq. (34) by setting m=0.1 and kF=100. The dashed lines correspond to the frequency dependencies obtained from the asymptotic results in Eq. (31) [i.e., iΣ¯(νn)∼|νn|2/3] and in Eq. (33) [i.e., iΣ¯(νn)∼νn].

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