Quadratic Fermi node in a 3D strongly correlated semimetal

We explore the ferromagnetic quantum critical point in a three-dimensional semimetallic system with upward-and downward-dispersing bands touching at the Fermi level. Evaluating the static spin susceptibility to leading order in the coupling between the fermions and the fluctuating ferromagnetic order parameter, we find that the ferromagnetic quantum critical point is masked by an incommensurate, longitudinal spin density wave phase. We first analyze an idealized model which, despite having strong spin-orbit coupling, still possesses O(3) rotational symmetry generated by the total angular momentum operator. In this case, the direction of the incommensurate spin density wave propagation can point anywhere, while the magnetic moment is aligned along the direction of propagation. Including symmetry-allowed anisotropies in the fermion dispersion and the coupling to the order parameter field, however, the ordering wavevector instead breaks a discrete symmetry and aligns along either the [111] or [100] direction, depending on the signs and magnitudes of these two types of anisotropy. PACS numbers:For decades it has been understood that electron interactions may lead to interesting consequences at low energy scales in three-dimensional (3D) semimetallic systems, in which spin-orbit coupling combines with cubic crystalline symmetries, leading to a band degeneracy at the Fermi energy. 1-8 Such a band structure has long been known to occur in HgTe and α-Sn (gray tin), and has possibly been discovered more recently in the pyrochlore Pr 2 Ir 2 O 7 . 9-14 Since the low-energy effective theory for these systems was first developed by Luttinger 1 , it has been argued using various approaches that interactions could lead to an excitonic instability at low temperatures 2,6 , or that the system may be described by an exotic non-Fermi liquid phase, characterized by nontrivial power-law scaling of various physical quantities with temperature. [3][4][5] In more recent work, the properties of such a system near an Ising antiferromagnetic quantum critical point were explored, and the critical theory was found to be governed by unusual critical exponents and emergent spatial anisotropy of the fermion dispersion. 7 The theory describing the quantum phase transition into an insulating nematic phase has also been developed recently. 8In this work we explore the fate of a 3D semimetal in the vicinity of a ferromagnetic (FM) quantum critical point. Working at zero temperature and approaching the quantum critical point from the paramagnetic side, we find that it is unstable toward an incommensurate spin density wave (SDW) phase. In the most symmetric version of the theory, there is a combined O(3) rotational symmetry for spin and spatial degrees of freedom, which is spontaneously broken by the SDW wavevector. The O(3) symmetry is reduced to a discrete symmetry by either of two sources of anisotropy: the Yukawa coupling of the fermions to the fluctuating FM field, or the dispersion of the fermions themselves.(Throughout this work, by anisotro...

Section: Case Of Isotropic Fermion Dispersionmentioning

confidence: 99%

Incommensurate spin density wave at a ferromagnetic quantum critical point in a three-dimensional parabolic semimetal

Murray

Vafek

2015

“…As a genuine many-body phenomenon, dynamical mass generation is inaccessible to perturbation theory. Similarly to QED 3 [10][11][12] and graphene [26][27][28], a possible excitonic instability can, however, be revealed by a nonperturbative solution of the gap equation for the fermion Green's function G(ω, p), (6) involving the full vertex function Γ(ω, p; ν, q) and Coulomb Green's function V (ω, p). The latter in turn is screened by the fermion polarization,…”

Section: Field Theory For 3d Qbt Systemmentioning

confidence: 99%

“…Note that in real space then V (r) ∝ 1/r 2 , as anticipated above. If we furthermore assume ∆( p) ≡ ∆(| p|), the integral over frequency and spherical angles in the gap equation (6) gives…”

Section: Static Approximationmentioning

confidence: 99%

“…HgTe, for instance, shows the quantum spin Hall effect in quantum well structures [3] and becomes a 3D strong topological insulator under uniaxial strain [4]. The pyrochlore iridates R 2 Ir 2 O 7 (where R is a rare-earth element) that display a metallic paramagnetic state presumably also host a 3D QBT point at the Fermi level [5,6]. This scenario has been employed to explain the anomalous low-temperature behavior measured in Pr 2 Ir 2 O 7 [7].…”

Section: Introductionmentioning

confidence: 99%

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Excitonic instability of three-dimensional gapless semiconductors: Large-Ntheory

Janssen

Herbut

2016

Three-dimensional gapless semiconductors with quadratic band touching, such as HgTe, α-Sn, or Pr2Ir2O7 are believed to display a non-Fermi-liquid ground state due to long-range electronelectron interaction. We argue that this state is inherently unstable towards spontaneous formation of a (topological) excitonic insulator. The instability can be parameterized by a critical fermion number Nc. For N < Nc the rotational symmetry is spontaneously broken, the system develops a gap in the spectrum, and features a finite nematic order parameter. To leading order in the 1/N expansion and in the static approximation, the analogy with the problem of dynamical mass generation in (2+1)-dimensional quantum electrodynamics yields Nc = 16/[3π(π − 2)]. Taking the important dynamical screening effects into account, we find that Nc ≥ 2.6(2) and therefore safely above the physical value of N = 1. Some experimental consequences of the nematic ground state are discussed.

“…In a 3D semimetal with quadratic dispersion, the Coulomb interaction is found to be relevant and cause non-Fermi liquid (NFL) behaviors [42]. It is interesting to notice that recent ARPES experiments have discovered NFL behavior in a 3D quadratic semimetal material Pr 2 Ir 2 O 7 [64]. Moreover, in a 3D anisotropic Weyl semimetal [48] and a 3D nodal-line semimetal [51], the FL description is robust because the Coulomb interaction is irrelevant.…”

Section: Introductionmentioning

confidence: 99%

Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals

Wang¹,

Liu²,

Zhang³

2017

A sufficiently strong long-range Coulomb interaction can induce excitonic pairing in gapless Dirac semimetals, which generates a finite gap and drives semimetal-insulator quantum phase transition. This phenomenon is in close analogy to dynamical chiral symmetry breaking in high energy physics. In most realistic Dirac semimetals, including suspended graphene, Coulomb interaction is too weak to open an excitonic gap. The Coulomb interaction plays a more important role at low energies in a two-dimensional semi-Dirac semimetal, in which the fermion spectrum is linear in one component of momenta and quadratic in the other, than a Dirac semimetal, and indeed leads to breakdown of Fermi liquid theory. We study dynamical excitonic gap generation in a two-dimensional semi-Dirac semimetal by solving the Dyson-Schwinger equation, and show that a moderately strong Coulomb interaction suffices to induce excitonic pairing. Additional short-range four-fermion coupling tends to promote excitonic pairing. Among the available semi-Dirac semimetals, we find that TiO2/VO2 nanostructure provides a promising candidate for the realization of excitonic insulator. We also apply the renormalziation group method to analyze the strong coupling between the massless semi-Dirac fermions and the quantum critical fluctuation of excitonic order parameter at the semimetal-insulator quantum critical point, and reveal non-Fermi liquid behaviors of semi-Dirac fermions.