Abstract
We consider the fermionic quantum criticality of anisotropic nodal point semimetals in d=dL+dQ spatial dimensions that disperse linearly in dL dimensions, and quadratically in the remaining dQ dimensions. When subject to strong interactions, these systems are susceptible to semimetal-insulator transitions concurrent with spontaneous symmetry breaking. Such quantum critical points are described by effective field theories of anisotropic nodal fermions coupled to dynamical order parameter fields. We analyze the universal scaling in the physically relevant spatial dimensions, generalizing to a large number Nf of fermion flavors for analytic control. Landau damping by gapless fermionic excitations gives rise to nonanalytic self-energy corrections to the bosonic order-parameter propagator that dominate the long-wavelength behavior. We show that perturbative momentum shell RG leads to nonuniversal, cutof-dependent results, as it does not correctly account for this nonanalytic structure. In turn, using a completely general soft cutoff formulation, we demonstrate that the correct IR scaling of the dressed bosonic propagator can be deduced by enforcing that results are independent of the cutoff scheme. Using the soft cutoff RG with the dressed dynamical RPA boson propagator, we compute the exact critical exponents for anisotropic semi-Dirac fermions (dL=1, dQ=1) to leading order in 1/Nf and to all loop orders. Applying the same method to relativistic Dirac fermions, we reproduce the critical exponents obtained by other methods, such as conformal bootstrap. Unlike in the relativistic case, where the UV-IR connection is reestablished at the upper critical dimension, nonanalytic IR contributions persist near the upper critical line 2dL+dQ=4 of anisotropic nodal fermions. We present ε expansions in both the number of linear and quadratic dimensions. The corrections to critical exponents are nonanalytic in ε, with a functional form that depends on the starting point on the upper critical line.Received 3 August 2020Revised 22 September 2020Accepted 28 September 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.043265Published 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 SocietyPhysics Subject Headings (PhySH)Research AreasCritical phenomenaDirac fermionsFermionsQuantum phase transitionsTopological materialsCondensed Matter, Materials & Applied Physics
Highlights
The discovery of topological insulators has led to an explosion of research into topological aspects of electronic band structures in two and three dimensions [1,2]
Unlike in the relativistic case, where the UV-IR connection is reestablished at the upper critical dimension, nonanalytic IR contributions persist near the upper critical line 2dL + dQ = 4 of anisotropic nodal fermions
We prove that for interacting Dirac fermions, cutoff independent corrections are only obtained with a nonanalytic inverse order parameter propagator that scales as kd−1 in d spatial dimensions
Summary
The discovery of topological insulators has led to an explosion of research into topological aspects of electronic band structures in two and three dimensions [1,2]. The lack of Lorentz invariance and the different scaling of the density of states near the nodal points leads to distinct fermion-induced criticality in nodal fermion systems with quadratic [39,40,41,42] and semi-Dirac [43,44,45,46] band-touching points The latter are interesting because the intrinsic electronic anisotropy gives rise to highly anisotropic order-parameter correlations with different correlation-length exponents along linear and quadratic momentum directions. The bosonic propagator in anisotropic dL-dQ nodal-point semimetals remains nonanalytic, and not perturbatively renormalizable, even near the upper critical dimension line 2dL + dQ = 4 [46] This is a clear distinction from the case of relativistic fermions, with important consequences for the expansion. V we summarize the key results, compare them to the literature, and discuss possible future research
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
