Electron-phonon interactions and instabilities in Weyl semimetals under magnetic fields and torsional strain
Pontificia Universidad Católica de Chile（智利天主教 Pontificia 大学）；Universidad Nacional Autónoma de México（墨西哥国立自治大学）；Center for Nanotechnology and Advanced Materials CIEN-UC（纳米技术与先进材料中心 CIEN-UC）
Fabian Jofre Parra, Daniel A. Bonilla, Enrique Muñoz
We study the presence of an external magnetic field, in combination with torsional strain, over the electron-phonon interactions in a type I Weyl semimetal. This particular superposition of field and strain, modeled in the continuum approximation by an effective gauge field, leads to an asymmetric pseudo-magnetic field at each Weyl node of opposite chirality. Therefore, we also studied the role of nodal asymmetry in the properties of the system by means of the Kadanoff-Wilson renormalization group and the corresponding flow equations. By solving those, we discuss the evolution of the coupling parameters of the theory, and analyze possible fixed points and lattice (Peierls) instabilities emerging from interactions between phonons with the chiral Landau level in the very strong pseudo-magnetic field regime.
In this article, we consider a theoretical model for a type I Weyl semimetal, under the presence of a diluted uniform concentration of torsional dislocations. By a mathematical analysis for partial wave scattering (phase-shift) for the T-matrix, we obtain the corresponding retarded and advanced Green's functions that include the effects of multiple scattering events with the ensemble of randomly distributed dislocations. Combining this analysis with the Kubo formalism, and including vertex corrections, we calculate the electronic conductivity as a function of temperature and concentration of d…
Type II Weyl semimetal, a three dimensional gapless topological phase, has drawn enormous interest recently. These topological semimetals enjoy overtilted dispersion and Weyl nodes that separate the particle and hole pocket. Using perturbation renormalization group, we identify possible renormalization of the interaction vertices, which show a tendency toward instability. We further adopt a self-consistent mean-field approach to study possible instability of the type II Weyl semimetals under short-range electron-electron interaction. It is found that the instabilities are much easier to form i…
The behavior of three-dimensional (3D) semimetals under strong magnetic fields is a topic of recurring interest in condensed matter physics. Recently, the advent of Weyl and Dirac semimetals has brought about an interesting platform for potentially uncovering phases of matter that combine nontrivial band topology and interactions. While electronic instabilities of such semimetals at strong magnetic fields have been explored theoretically and experimentally, the role of electron-phonon interactions therein has been largely neglected. In this paper, we study the interplay of electron-electron an…
We investigate the interplay of many-body and band structure effects of interacting Weyl semimetals (WSM). Attractive and repulsive Hubbard interactions are studied within a model for a time-reversal-breaking WSM with tetragonal symmetry, where we can approach the limit of weakly coupled planes and coupled chains by varying the hopping amplitudes. Using a slab geometry, we employ the variational cluster approach to describe the evolution of WSM Fermi arc surface states as a function of interaction strength. We find spin and charge density wave instabilities which can gap out Weyl nodes. We ide…
We consider the role of coordinate dependent tetrads ("Fermi velocities"), momentum space geometry, and torsional Landau levels (LLs) in condensed matter systems with low-energy Weyl quasiparticles. In contrast to their relativistic counterparts, they arise at finite momenta and an explicit cutoff to the linear spectrum. Via the universal coupling of tetrads to momentum, they experience geometric chiral and axial anomalies with gravitational character. More precisely, at low-energy, the fermions experience background fields corresponding to emergent anisotropic Riemann-Cartan and Newton-Cartan…
We introduce (3+1) dimensional models of short-range-interacting electrons that form a strongly correlated many-body state whose low-energy excitations are relativistic neutral fermions coupled to an emergent gauge field, $\text{QED}_{4}$. We discuss the properties of this critical state and its instabilities towards exotic phases such as a gapless `composite' Weyl semimetal and fully gapped topologically ordered phases that feature anyonic point-like as well as line-like excitations. These fractionalized phases describe electronic insulators. They may be further enriched by symmetries which r…
We study the quantum critical phenomena emerging at the transition from triple-Weyl semimetal to band insulator, which is a topological phase transition described by the change of topological invariant. The critical point realizes a new type of semimetal state in which the fermion dispersion is cubic along two directions and quadratic along the third. Our renormalization group analysis reveals that, the Coulomb interaction is marginal at low energies and even arbitrarily weak Coulomb interaction suffices to induce an infrared fixed point. We compute a number of observable quantities, and show …
We perform mean-field study of possible magnetic instabilities in Dirac semimetals. We find that Dirac electrons naturally host antiferromagnetic or spin density wave ground states, though their specific configurations may vary depending on specific model, as well as chemical potential and temperature. We also discuss paramagnetic susceptibility of Dirac semimetals. In the cases, when Dirac electrons do not have orbital momentum, the magnetic properties may be $μ$ and $T$ independent.
We attentively investigate the effects of short-range fermion-fermion interactions on the low-energy properties of both two-dimensional type-I and type-II tilted Dirac semimetals by means of the renormalization group framework. Practicing the standard renormalization group procedures via taking into account all one-loop corrections gives rise to the coupled energy-dependent evolutions of all interaction parameters, which are adopted to carefully examine whether and how the fermion-fermion interactions influence the low-energy physical behaviors of tilted Dirac fermions. After carrying out the …
We study the effect of short range interactions in three dimensional nodal-line semimetals with linear band crossings. We analyze the Yukawa theories for gapped instabilities in the charge, spin and superconducting channels using the Wilsonian renormalization group framework, employing a large number of fermion flavors $N_{f}$ for analytical control. We obtain stable non-trivial fixed points and provide a unified description of the critical exponents for the ordering transitions in terms of the number of order parameter components $N_{b}$ systematically to order $1/N_{f}$. We show that in all …
Motivated by the experimental detection of superconductivity in the low-carrier density half-Heusler compound YPtBi, we study the pairing instabilities of three-dimensional strongly spin-orbit coupled semimetals with a quadratic band touching point. In these semimetals the electronic structure at the Fermi energy is described by spin j=3/2 quasiparticles, which are fundamentally different from those in ordinary metals with spin j=1/2. We develop a general approach to analyzing pairing instabilities in j=3/2 materials by decomposing the pair scattering interaction into irreducible channels, pro…
In this paper, we investigate the theory of dynamical axion string emerging from chiral symmetry breaking in three-dimensional Weyl semimetals. The chiral symmetry is spontaneously broken by a charge density wave (CDW) order which opens an energy gap and converts the Weyl semimetal into an axion insulator. Indeed, the phase fluctuations of the CDW order parameter act as a dynamical axion field $θ({\vec{x}},t)$ and couples to electromagnetic field via $\mathcal{L}_θ=\frac{θ(\vec{x},t)}{32π^2} ε^{στνμ} F_{στ} F_{νμ}.$ Additionally, when the axion insulator is coupled to the background geometry/s…
We compute the effects of generic short-range interactions on gapless electrons residing at the quantum critical point separating a two-dimensional Dirac semimetal (DSM) and a symmetry-preserving band insulator (BI). The electronic dispersion at this critical point is anisotropic ($E_{\mathbf k}=\pm \sqrt{v^2 k^2_x + b^2 k^{2n}_y}$ with $n=2$), which results in unconventional scaling of physical observables. Due to the vanishing density of states ($\varrho(E) \sim |E|^{1/n}$), this anisotropic semimetal (ASM) is stable against weak short-range interactions. However, for stronger interactions t…
We show that topological states are often developed in two dimensional semimetals with quadratic band crossing points (BCPs) by electron-electron interactions. To illustrate this, we construct a concrete model with the BCP on an extended Lieb lattice and investigate the interaction-driven topological instabilities. We find that the BCP is marginally unstable against infinitesimal repulsions. Depending on the interaction strengths, topological quantum anomalous/spin Hall, charge nematic, and nematic-spin-nematic phases, develop separately. Possible physical realizations of quadratic BCPs are pr…
We investigate interacting spin susceptibilities in lattice models for $\mathcal{T}$-reversal symmetry-broken Weyl semimetals. We employ a random phase approximation (RPA) method for the spin-SU(2)-symmetry-broken case that includes mixtures of ladder and bubble diagrams, beyond a SU(2)-symmetric case. Within this approach, the relations between the tendency towards magnetic order and the band structure tilt parameter $γ$ under different temperatures are explored. The critical interaction strength $U_c$ for magnetic ordering decreases as the tilt term changes from type-I Weyl semimetals to typ…
Influence of short-range four-fermion interactions on quadratic and cubic nodal line fermion systems is studied by renormalization group theory. It is found that arbitrarily weak four-fermion interaction could drive quadratic or cubic nodal line fermion system to a new phase. According to the initial conditions and value of fermion flavor, the system may appear three kinds of instabilities. First, quadratic or cubic nodal line is split into conventional nodal lines, thus the system becomes nodal line semimetal. Second, finite excitonic gap is generated, and the system becomes an excitonic insu…
We perform a mean-field study of the phase diagram of interacting Weyl semimetals with broken parity, that is, with different densities of right- and left-handed quasiparticles. As a simple model system, we consider the Wilson-Dirac Hamiltonian with the chiral chemical potential and on-site repulsive interactions. We find that the chiral chemical potential somewhat shrinks the region of the pion condensation (Aoki phase) in the parameter space of the bare mass and the interaction strength, so that the condensation thresholds are at smaller interaction strengths. The renormalized chiral chemica…
We study the quantum many-body ground states of electrons on the half-filled honeycomb lattice with short- and long-ranged density-density interactions as a model for graphene. To this end, we employ the recently developed truncated-unity functional renormalization group (TU-fRG) approach which allows for a high resolution of the interaction vertex' wavevector dependence. We connect to previous lattice quantum Monte Carlo (QMC) results which predict a stabilization of the semimetallic phase for realistic \emph{ab initio} interaction parameters and confirm that the application of a finite biaxi…
Based on the SO(2)-invariant slave-boson scheme, the static charge, orbital, and excitonic susceptibilities in the extended Falicov-Kimball model are calculated. Analyzing the phase without long-range order we find instabilities towards charge order, orbital order, and the excitonic insulator (EI) phase. The instability towards the EI is in agreement with the saddle-point phase diagram. We also evaluate the dynamic excitonic susceptibility, which allows the investigation of uncondensed excitons. We find qualitatively different features of the exciton dispersion at the semimetal-EI and at the s…
3+1-dimensional Weyl fermions in interacting systems are described by effective quasi-relativistic Green's functions parametrized by a 16 element matrix $e^μ_α$ in an expansion around the Weyl point. The matrix $e^μ_α$ can be naturally identified as an effective tetrad field for the fermions. The correspondence between the tetrad field and an effective quasi-relativistic metric $g_{μν}$ governing the Weyl fermions allows for the possibility to simulate different classes of metric fields emerging in general relativity in interacting Weyl semimetals. According to this correspondence, there can b…
Strong long-wavelength electron-phonon coupling in Ta$_2$Ni(Se,S)$_5$
Yale University（耶鲁大学）；Max Planck Institute for the Structure and Dynamics of Matter（马克斯·普朗克物质结构动力学研究所）；University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Lab（劳伦斯伯克利国家实验室）；Cornell High Energy Synchrotron Source, Cornell University（康奈尔大学康奈尔高能同步辐射光源）；Argonne National Laboratory（阿贡国家实验室）
