Superconducting quantum criticality in three-dimensional Luttinger semimetals

Abstract

We study a simple model of three-dimensional fermions close to a quadratic band touching point, built from the celebrated Luttinger single-particle Hamiltonian and an attractive contact interaction between the particles. Such a system displays a novel quantum critical point between the semimetallic and an s-wave superconducting phase at which the low-energy "Luttinger fermions" are inextricably coupled to the order parameter fluctuations. The quantum critical point is perturbatively accessible near four spatial dimensions, where it features nontrivial scaling with dynamical exponent 1<z<2 and emergent rotational and particle-hole symmetries. Some features of the criticality, such as oscillatory corrections to scaling and its enhanced symmetry, are discussed.

18 pages, 4 figures, published version: added references, discussion of competing instabilities, and figure showing RG flow

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Cited by in corpus (70)

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• Pairing states of spin-3/2 fermions: Symmetry-enforced topological gap functions
• Disorder-driven destruction of a non-Fermi liquid semimetal via renormalization group
• Unconventional Superconductivity in Luttinger Semimetals: Theory of Complex Tensor Order and the Emergence of the Uniaxial Nematic State
• Phase diagram of electronic systems with quadratic Fermi nodes in $2<d<4$: $2+\epsilon$ expansion, $4-\epsilon$ expansion, and functional renormalization group
• Anisotropy induces non-Fermi-liquid behavior and nematic magnetic order in three-dimensional Luttinger semimetals
• Topological Crystalline Materials of $J=3/2$ Electrons: Antiperovskites, Dirac points, and High Winding Topological Superconductivity
• Double Weyl points and Fermi arcs of topological semimetals in non-Abelian gauge potentials
• Fate of superconductivity in three-dimensional disordered Luttinger semimetals
• d-wave superconductivity and Bogoliubov-Fermi surfaces in Rarita-Schwinger-Weyl semimetals
• Interplay of topology and electron-electron interactions in Rarita-Schwinger-Weyl semimetals
• Bogoliubov-Fermi Surfaces in Noncentrosymmetric Multicomponent Superconductors
• Bogoliubov Fermi surfaces stabilized by spin-orbit coupling
• Floquet scattering of quadratic band-touching semimetals through a time-periodic potential well
• Quantum phase transitions in Dirac fermion systems
• Superconductivity in spin-$3/2$ systems: symmetry classification, odd-frequency pairs, and Bogoliubov Fermi surfaces
• Transport in the non-Fermi liquid phase of isotropic Luttinger semimetals
• Majorana multipole response of topological superconductors
• Irradiated three-dimensional Luttinger semimetal: A factory for engineering Weyl semimetals
• Thermoelectric and thermal properties of the weakly disordered non-Fermi liquid phase of Luttinger semimetals
• Universality and stability of the edge states of chiral-symmetric topological semimetals and surface states of the Luttinger semimetal
• Pr${}_2$Ir${}_2$O${}_7$: when Luttinger semimetal meets Melko-Hertog-Gingras spin ice state
• Exotic Superconductivity with Enhanced Energy Scales in Three Band Crossing Materials
• Stability of two-dimensional asymmetric materials with a quadratic band crossing point under four-fermion interaction and impurity scattering
• Role of four-fermion interaction and impurity in the states of two-dimensional semi-Dirac materials
• Tunneling in Fermi Systems with Quadratic Band Crossing Points
• Raman response and shear viscosity in the non-Fermi liquid phase of Luttinger semimetals
• Search for plasmons in isotropic Luttinger semimetals
• Wilson-Fisher fixed points in presence of Dirac fermions
• Non-Hermitian higher-Order Weyl semimetal with surface diabolic points
• Bogoliubov-Fermi surface with inversion symmetry and electron-electron interactions: relativistic analogies and lattice theory
• Optical response of Luttinger semimetals in the normal and superconducting states
• Superconductivity from Coulomb repulsion in three-dimensional quadratic band touching Luttinger semimetals
• Ground state of the three-dimensional BCS d-wave superconductor
• Transport properties in non-Fermi liquid phases of nodal-point semimetals
• Bogoliubov Fermi surfaces from pairing of emergent $j=3/2$ fermions on the pyrochlore lattice
• Multipolar superconductivity in Luttinger semimetals
• Critical phenomena at the complex tensor ordering phase transition
• Intra-unit-cell singlet pairing mediated by altermagnetic fluctuations
• Phase transition with trivial quantum criticality in anisotropic Weyl semimetal
• Random-mass disorder in the critical Gross-Neveu-Yukawa models
• Soluble Fermionic Quantum Critical Point in Two Dimensions
• Intrinsic finite-energy Cooper pairing in $j=3/2$ superconductors
• Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry
• High orbital-moment Cooper pairs by crystalline symmetry breaking
• Quantum Criticality of Anti-ferromagnetism and Superconductivity with Relativity
• Anatomy of plasmons in generic Luttinger semimetals
• Superconductivity in Two-Dimensional Systems with Unconventional Rashba Bands
• Andreev bound states in Josephson junctions of semi-Dirac semimetals
• Time reversal symmetry breaking and $d$-wave superconductivity of triple-point fermions
• p-wave superconductivity in Luttinger semimetals
• Josephson effect of superconductors with $J=3/2$ electrons
• Quantum field theories of relativistic Luttinger fermions
• p-wave superconductivity and the axi-planar phase of triple-point fermions
• Superconducting quantum criticality and the anomalous scaling: A nonlinear relativistic equation
• Fermion-fermion interaction driven phase transitions in rhombohedral trilayer graphene
• Fate of superconductivity in disordered Dirac and semi-Dirac semimetals
• Infrared fixed points of higher-spin fermions in topological semimetals
• Quantum-critical electrodynamics of Luttinger fermions
• Critical behavior around the fixed points driven by fermion-fermion interactions and disorders in the nodal-line superconductors
• Superconductivity in Luttinger semimetals near the SU(4) limit
• Nature of Andreev bound states in Josephson junctions of triple-point semimetals
• Singular low-energy states of tilted Dirac semimetals induced by the fermion-fermion interactions
• Tunable zero-energy Dirac and Luttinger nodes in a two-dimensional topological superconductor
• Delta-function-potential junctions with quasiparticles occupying tilted bands with quadratic-in-momentum dispersion
• Intrinsic emergence of Majorana modes in Luttinger j=3/2 systems
• Transmission through rectangular potentials in semimetals featuring quadratic dispersion
• Mean-field theory for self-interacting relativistic Luttinger fermions
• Phases of three-dimensional $d$-wave superconductors with two attractive interactions