- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Correlated fractional Dirac materials

Bitan Roy1,* and Vladimir Juričić2,3,†

  • 1Department of Physics, Lehigh University, Bethlehem, Pennsylvania 18015, USA
  • 2Departamento de Física, Universidad Técnica Federico Santa María, Casilla 110, Valparaíso, Chile
  • 3Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, 106 91 Stockholm, Sweden

  • *bitan.roy@lehigh.edu
  • †vladimir.juricic@su.se
PDF

Phys. Rev. Research 5, L032002 – Published 10 July, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L032002

Abstract

Fractional Dirac materials (FDMs) feature a fractional energy-momentum relation E(k)∼|k|α, where α(<1) is a real noninteger number, in contrast to that in conventional Dirac materials with α=1. Here we analyze the effects of short- and long-range Coulomb repulsions in two- and three-dimensional FDMs. Only a strong short-range interaction causes nucleation of a correlated insulator that takes place through a quantum critical point. The universality class of the associated quantum phase transition is determined by the correlation length exponent ν−1=d−α and dynamic scaling exponent z=α, set by the band curvature. On the other hand, the fractional dispersion is protected against long-range interaction due to its nonanalytic structure. Rather, a linear Dirac dispersion gets generated under coarse graining, and the associated Fermi velocity increases logarithmically in the infrared regime, thereby yielding a two-fluid system. Altogether, correlated FDMs unfold a rich landscape accommodating unconventional emergent many-body phenomena.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (29)

  1. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81, 109 (2009).
  2. N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90, 015001 (2018).
  3. G. Xu, H. Weng, Z. Wang, X. Dai, and Z. Fang, Chern Semimetal and the Quantized Anomalous Hall Effect in HgCr2Se4, Phys. Rev. Lett. 107, 186806 (2011).
  4. C. Fang, M. J. Gilbert, X. Dai, and B. A. Bernevig, Multi-Weyl Topological Semimetals Stabilized by Point Group Symmetry, Phys. Rev. Lett. 108, 266802 (2012).
  5. B.-J. Yang and N. Nagaosa, Classification of stable three-dimensional Dirac semimetals with nontrivial topology, Nat. Commun. 5, 4898 (2014).
  6. B. Bradlyn, J. Cano, Z. Wang, M. G. Vergniory, C. Felser, R. J. Cava, and B. A. Bernevig, Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals, Science 353, aaf5037 (2016).
  7. G. Montambaux, F. Piéchon, J.-N. Fuchs, and M. O. Goerbig, Merging of Dirac points in a two-dimensional crystal, Phys. Rev. B 80, 153412 (2009).
  8. B. Roy, P. Goswami, and V. Juričić, Interacting Weyl fermions: Phases, phase transitions, and global phase diagram, Phys. Rev. B 95, 201102(R) (2017).
  9. B. Roy and M. P. Foster, Quantum Multicriticality near the Dirac-Semimetal to Band-Insulator Critical Point in Two Dimensions: A Controlled Ascent from One Dimension, Phys. Rev. X 8, 011049 (2018).
  10. D. J. Gross and A. Neveu, Dynamical symmetry breaking in asymptotically free field theories, Phys. Rev. D 10, 3235 (1974).
  11. M. Gärttner, S. V. Syzranov, A. M. Rey, V. Gurarie, and L. Radzihovsky, and M. Garttner, Disorder-driven transition in a chain with power-law hopping, Phys. Rev. B 92, 041406(R) (2015).
  12. S. N. Kempkes, M. R. Slot, S. E. Freeney, S. J. M. Zevenhuizen, D. Vanmaekelbergh, I. Swart, and C. M. Smith, Design and characterization of electrons in a fractal geometry, Nat. Phys. 15, 127 (2019).
  13. J. Shang, Y. Wang, M. Chen, J. Dai, X. Zhou, J. Kuttner, G. Hilt, X. Shao, J. M. Gottfried, and K. Wu, Assembling molecular Sierpiński triangle fractals, Nat. Chem. 7, 389 (2015).
  14. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L032002 for the derivation of DOS and OC, details of RG analysis in FDMs with short- and long-range Coulomb repulsion, and details of the lattice model for FDMs.
  15. Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. I, Phys. Rev. 122, 345 (1961).
  16. B. Roy and V. Juričić, Strain-induced time-reversal odd superconductivity in graphene, Phys. Rev. B 90, 041413(R) (2014).
  17. J. A. Gracey, Computation of critical exponent η at O(1/N3) in the four Fermi model in arbitrary dimensions, Int. J. Mod. Phys. A 09, 727 (1994).
  18. L. Rosa, P. Vitale, and C. Wetterich, Critical Exponents of the Gross-Neveu Model from the Effective Average Action, Phys. Rev. Lett. 86, 958 (2001).
  19. B. Roy and S. Das Sarma, Quantum phases of interacting electrons in three-dimensional dirty Dirac semimetals, Phys. Rev. B 94, 115137 (2016).
  20. J. Gonzalez, F. Guinea, and M. A. H. Vozmediano, Non-Fermi liquid behavior of electrons in the half-filled honeycomb lattice (A renormalization group approach), Nucl. Phys. B 424, 595 (1994).
  21. P. Goswami and S. Chakravarty, Quantum Criticality between Topological and Band Insulators in 3+1 Dimensions, Phys. Rev. Lett. 107, 196803 (2011).
  22. P. Hosur, S. A. Parameswaran, and A. Vishwanath, Charge Transport in Weyl Semimetals, Phys. Rev. Lett. 108, 046602 (2012).
  23. B. Roy and V. Juričić, Optical conductivity of an interacting Weyl liquid in the collisionless regime, Phys. Rev. B 96, 155117 (2017).
  24. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Oxford University Press, Oxford, 2002).
  25. B. Roy, V. Juričić, and I. F. Herbut, Emergent Lorentz symmetry near fermionic quantum critical points in two and three dimensions, J. High Energy Phys. 04 (2016) 018.
  26. T. C. Lang and A. M. Läuchli, Quantum Monte Carlo Simulation of the Chiral Heisenberg Gross-Neveu-Yukawa Phase Transition with a Single Dirac Cone, Phys. Rev. Lett. 123, 137602 (2019).
  27. H-K. Tang, J. N. Leaw, J. N. B. Rodrigues, I. F. Herbut, P. Sengupta, F. F. Assaad, and S. Adam, The role of electron-electron interactions in two-dimensional Dirac fermions, Science 361, 570 (2018).
  28. D. Jafferis, A. Zlokapa, J. D. Lykken, D. K. Kolchmeyer, S. I. Davis, N. Lauk, H. Neven, and M. Spiropulu, Traversable wormhole dynamics on a quantum processor, Nature (London) 612, 51 (2022).
  29. A. J. Kollár, M. Fitzpatrick, and A. A. Houck, Hyperbolic lattices in circuit quantum electrodynamics, Nature (London) 571, 45 (2019).

Outline

Information

Phys. Rev. Research 5, L032002– Published 10 July, 2023
  • Received 29 January 2023
  • Accepted 16 May 2023
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation