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arXiv:2604.14146

Topological anisotropic non-Fermi liquid from a Berry-dipole semimetal

Konstantinos Ladovrechis

Published Apr 15, 2026• 0 citations
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Abstract

The interplay among topology and interactions has been a promising path towards identifying novel phases of condensed matter beyond these predicted by the established classification paradigms. In the present work, we propose such a novel phase of matter by studying the fate of a three-dimensional Berry-dipole semimetal, lying at the topological quantum critical point separating a Hopf insulator from a trivial insulator, in the presence of long-range Coulomb interactions. Utilizing large-$N_f$ analysis and an $ε$-expansion within the renormalization-group scheme, we predict the emergence of a spatially anisotropic non-Fermi liquid with enhanced Berry-dipole moment. The corresponding scaling relations of certain physical observables are derived as functions of the probed energy and temperature scale, and we conclude by providing an observational test for probing the enhanced topological features of the anisotropic non-Fermi liquid.

DOI
10.48550/arxiv.2604.14146

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The interplay among topology and interactions has been a promising path towards identifying novel phases of condensed matter beyond these predicted by the established classification paradigms. In the present work, we propose such a novel phase of matter by studying the fate of a three-dimensional Berry-dipole semimetal, lying at the topological quantum critical point separating a Hopf insulator from a trivial insulator, in the presence of long-range Coulomb interactions. Utilizing large-NfN_fNf​ analysis and an εεε-expansion within the renormalization-group scheme, we predict the emergence of a spatially anisotropic non-Fermi liquid with enhanced Berry-dipole moment. The corresponding scaling relations of certain physical observables are derived as functions of the probed energy and temperature scale, and we conclude by providing an observational test for probing the enhanced topological features of the anisotropic non-Fermi liquid.
Understanding correlation effects in topological phases and their transitions is a cutting-edge area of research in recent condensed matter physics. We study topological quantum phase transitions (TQPTs) between double-Weyl semimetals (DWSMs) and insulators, and argue that a novel class of quantum criticality appears at the TQPT characterized by emergent anisotropic non-Fermi-liquid behaviors, in which the interplay between the Coulomb interaction and electronic critical modes induces not only anisotropic renormalization of the Coulomb interaction but also strongly correlated electronic excitation in three spatial dimensions. Using the standard renormalization group methods, large N_{f} theory, and the ε=4-d method with a fermion flavor number N_{f} and spatial dimension d, we obtain the anomalous dimensions of electrons (η_{f}=0.366/N_{f}) in large N_{f} theory and the associated anisotropic scaling relations of various physical observables. Our results may be observed in candidate materials for DWSMs such as HgCr_{2}Se_{4} or SrSi_{2} when the system undergoes a TQPT.
Topological quantum phase transitions intrinsically intertwine self-similarity and topology of many-electron wave-functions, and divining them is one of the most significant ways to advance understanding in condensed matter physics. Our focus is to investigate an unconventional class of the transitions between insulators and Dirac semimetals whose description is beyond conventional pseudo relativistic Dirac Hamiltonian. At the transition without the long-range Coulomb interaction, the electronic energy dispersion along one direction behaves like a relativistic particle, linear in momentum, but along the other direction it behaves like a non-relativistic particle, quadratic in momentum. Various physical systems ranging from TiO2-VO2 heterostructure to organic material α-(BEDT-TTF)2I3 under pressure have been proposed to have such anisotropic dispersion relation. Here, we discover a novel quantum criticality at the phase transition by incorporating the long range Coulomb interaction. Unique interplay between the Coulomb interaction and electronic critical modes enforces not only the anisotropic renormalization of the Coulomb interaction but also marginally modified electronic excitation. In connection with experiments, we investigate several striking effects in physical observables of our novel criticality.
We study the effects of Coulomb interaction between 2D Weyl fermions with anisotropic dispersion which displays relativistic dynamics along one direction and nonrelativistic dynamics along the other. Such a dispersion can be realized in phosphorene under electric field or strain, in TiO_{2}/VO_{2} superlattices, and, more generally, at the quantum critical point between a nodal semimetal and an insulator in systems with a chiral symmetry. Using the one-loop renormalization group approach in combination with the large-N expansion, we find that the system displays interaction-driven non-Fermi liquid behavior in a wide range of intermediate frequencies and marginal Fermi liquid behavior at the smallest frequencies. In the non-Fermi liquid regime, the quasiparticle residue Z at energy E scales as Z∝E^{a} with a>0, and the parameters of the fermionic dispersion acquire anomalous dimensions. In the marginal Fermi-liquid regime, Z∝(|logE|)^{-b} with universal b=3/2.
Abstract A proposal to study topological models beyond the standard topological classification and that exhibit breakdown of Lorentz invariance is presented. The focus of the investigation relies on their anisotropic quantum critical behavior. We study anisotropic effects on three-dimensional (3D) topological models, computing their anisotropic correlation length critical exponent ν obtained from numerical calculations of the penetration length of the zero-energy surface states as a function of the distance to the topological quantum critical point. A generalized Weyl semimetal model with broken time-reversal symmetry is introduced and studied using a modified Dirac equation. An approach to characterize topological surface states in topological insulators when applied to Fermi arcs allows to capture the anisotropic critical exponent θ = νx/νz. We also consider the Hopf insulator model, for which the study of the topological surface states yields unusual values for ν and for the dynamic critical exponent z. From an analysis of the energy dispersions, we propose a scaling relation να¯ zα¯ = 2q and θ = νx/νz = zz/zx for ν and z that only depends on the Hopf insulator Hamiltonian parameters p and q and the axis direction α¯ . An anisotropic quantum hyperscaling relation is also obtained.
A proposal to study topological models beyond the standard topological classification and that exhibit breakdown of Lorentz invariance is presented. The focus of the investigation relies on their anisotropic quantum critical behavior. We study anisotropic effects on three-dimensional (3D) topological models, computing their anisotropic correlation length critical exponent [Formula: see text] obtained from numerical calculations of the penetration length of the zero-energy surface states as a function of the distance to the topological quantum critical point. A generalized Weyl semimetal model with broken time-reversal symmetry is introduced and studied using a modified Dirac equation. An approach to characterize topological surface states in topological insulators when applied to Fermi arcs allows to capture the anisotropic critical exponent [Formula: see text]. We also consider the Hopf insulator model, for which the study of the topological surface states yields unusual values for [Formula: see text] and for the dynamic critical exponent z. From an analysis of the energy dispersions, we propose a scaling relation [Formula: see text] and [Formula: see text] for [Formula: see text] and z that only depends on the Hopf insulator Hamiltonian parameters p and q and the axis direction [Formula: see text]. An anisotropic quantum hyperscaling relation is also obtained.
Quantum criticality, a manifestation of emergent scale invariance in electron wavefunctions arises from intricate many-body quantum entanglement. One of the natural venues for the criticality is clean undoped Dirac semimetals, known as a marginally-renormalized critical phase. The ground state is only slightly modified from the Slater-type product wavefunction because the scatterings from weak disorder and Coulomb interactions are suppressed. Here, using the renormalization group (RG) analysis, we show that a novel class of quantum criticality appears in Dirac semimetals when the disorder strength becomes sufficiently strong in the presence of Coulomb interactions so that a quantum phase transition from the marginally-renormalized critical phase to a disorder-dominated phase arises. The ground state at the critical point is a quantum critical non-Fermi liquid (NFL), characterized by the properties of strongly entangled low-energy states such as the absence of quasi-particles. Near the critical point, unusually wide temperature regions with NFL behaviors emerge.