Interacting spin-3/2 fermions in a Luttinger semimetal: Competing phases and their selection in the global phase diagram

Abstract

We compute the effects of electronic interactions on gapless spin-3/2 excitations that in a noninteracting system emerge at a bi-quadratic touching of Kramers degenerate valence and conduction bands, known as Luttinger semimetal. This model can describe the low-energy physics of HgTe, gray-Sn, 227 pyrochlore iridates and half-Heuslers. For the sake of concreteness we only consider the short-range components of the Coulomb interaction. By combining mean-field analysis with a renormalization group (RG) calculation, we construct multiple cuts of the global phase diagram of interacting spin-3/2 fermions at zero and finite temperature and chemical doping. Such phase diagrams display a rich confluence of competing orders, among which rotational symmetry breaking nematic insulators and time reversal symmetry breaking magnetic orders are the prominent excitonic phases. We also show that even repulsive interactions can be conducive for both s-wave and d-wave pairings. The reconstructed band structure inside the ordered phases allows us to organize them according to the energy (entropy) gain in the following (reverse) order: s-wave pairing, nematic phases, magnetic orders and d-wave pairings, at zero chemical doping. But, the paired states are always energetically superior over the excitonic ones for finite doping. The phase diagrams obtained from the RG analysis show that an ordered phase with higher energy (entropy) gain is realized at low (high) temperature. In addition, we establish a "selection rule" between the interaction channels and the resulting ordered phases, suggesting that repulsive interactions in the magnetic (nematic) channels are conducive for the nucleation of d-wave (s-wave) pairing. The proposed methodology can shed light on the global phase diagram of other strongly interacting multi-band systems, such as doped Dirac semimetal, topological insulators and the like.

arXiv commentPublished version: 36 pages, 21 figures, 4 tables (full abstract: see main text)

References in corpus (80)

• The electronic properties of graphene
• Topological Insulators
• Topological insulators and superconductors
• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi
• Tuning superconductivity in twisted bilayer graphene
• Renormalization Group Approach to Interacting Fermions
• Continuous Quantum Phase Transitions
• Correlated quantum phenomena in the strong spin-orbit regime
• Experimental Realization of a Three-Dimensional Dirac Semimetal
• Theory of Intertwined Orders in High Temperature Superconductors
• Dirac materials
• A new platform for topological quantum phenomena : Topological Insulator states in thermoelectric Heusler-related ternary compounds
• Quantum Field Theory in the Large N Limit: a review
• Topological and magnetic phases of interacting electrons in the pyrochlore iridates
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• Theory of interacting electrons on the honeycomb lattice
• Topological Kondo Insulators
• Superconductivity in the repulsive Hubbard model: an asymptotically exact weak-coupling solution
• Non-Fermi liquid and topological states with strong spin-orbit coupling
• Superconductivity in the topological semimetal YPtBi
• Topological $R$PdBi half-Heusler semimetals: a new family of non-centrosymmetric magnetic superconductors
• Intertwined vestigial order in quantum materials: nematicity and beyond
• Unconventional superconductivity in nearly flat bands in twisted bilayer graphene
• Quadratic Fermi Node in a 3D Strongly Correlated Semimetal
• Superconductivity in the noncentrosymmetric half-Heusler compound LuPtBi : A possible topological superconductor
• Beyond Triplet: Unconventional Superconductivity in a Spin-3/2 Topological Semimetal
• Observation of Unusual Topological Surface States in Half-Heusler Compounds LnPtBi (Ln=Lu, Y)
• Pairing of j=3/2 fermions in half-Heusler superconductors
• Topological Mott insulator in three-dimensional systems with quadratic band touching
• Weak Antilocalization Effect and Noncentrosymmetric Superconductivity in a Topologically Nontrivial Semimetal LuPdBi
• Interacting Weyl fermions: Phases, phase transitions and global phase diagram
• Bogoliubov Fermi surfaces: General theory, magnetic order, and topology
• Superconductivity in three-dimensional spin-orbit coupled semimetals
• The Superconducting Instabilities of the non half-filled Hubbard Model in Two Dimensions
• Magnetic field-induced insulator-semimetal transition in a pyrochlore Nd2Ir2O7
• Emergent topological phenomena in thin films of pyrochlore iridates
• A New Type of Quantum Criticality in the Pyrochlore Iridates
• Pyrochlore electrons under pressure, heat and field: shedding light on the iridates
• Superconductivity and magnetic order in the non-centrosymmetric Half Heusler compound ErPdBi
• Slater to Mott crossover in the metal to insulator transition of Nd2Ir2O7
• Topological superconductivity of spin-3/2 carriers in a three-dimensional doped Luttinger semimetal
• Pairing states of spin-3/2 fermions: Symmetry-enforced topological gap functions
• Inflated nodes and surface states in superconducting half-Heusler compounds
• Phase diagram of pyrochlore iridates: all-in-all-out magnetic ordering and non-Fermi liquid properties
• Superconductivity in non-centrosymmetric YPtBi under pressure
• Interacting line-node semimetal: Proximity effect and spontaneous symmetry breaking
• Unconventional Superconductivity in Luttinger Semimetals: Theory of Complex Tensor Order and the Emergence of the Uniaxial Nematic State
• Superconductivity in half-Heusler compound TbPdBi
• Quantum phases of interacting electrons in three-dimensional dirty Dirac semimetals
• Competing orders and topology in the global phase diagram of pyrochlore iridates
• Dielectric anomalies and interactions in the 3D quadratic band touching Luttinger semimetal Pr${}_2$Ir${}_2$O${}_7$
• Anisotropic hysteretic Hall-effect and magnetic control of chiral domains in the chiral spin states of Pr${}_2$Ir${}_2$O${}_7$
• Anisotropy induces non-Fermi-liquid behavior and nematic magnetic order in three-dimensional Luttinger semimetals
• Metallic Interface Emerging at Magnetic Domain Wall of Antiferromagnetic Insulator---Fate of Extinct Weyl Electrons
• Topological Crystalline Materials of $J=3/2$ Electrons: Antiperovskites, Dirac points, and High Winding Topological Superconductivity
• Instabilities of Weyl-loop semi-metals
• Model Hamiltonian and Time Reversal Breaking Topological Phases of Anti-ferromagnetic Half-Heusler Materials
• Excitonic instability of three-dimensional gapless semiconductors: Large-N theory
• Magnetic and superconducting phase diagram of the half-Heusler topological semimetal HoPdBi
• Topological septet pairing with spin-$\frac{3}{2}$ fermions -- high partial-wave channel counterpart of the ${}^3$He-B phase
• Singlet-Quintet Mixing in Spin-Orbit Coupled Superconductors with j=3/2 Fermions
• Doping-induced quantum spin Hall insulator to superconductor transition
• Superconductivity on the brink of spin-charge order in doped honeycomb bilayer
• Irradiated three-dimensional Luttinger semimetal: A factory for engineering Weyl 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
• Topological d+s wave superconductors in a multi-orbital quadratic band touching system
• Strain engineered higher order topological phases for spin-3/2 Luttinger fermions
• Tri-Dirac Surface Modes in Topological Superconductors
• Magnetic field induced topological semimetals near a quantum critical point of pyrochlore iridates
• Weyl Rings and enhanced susceptibilities in Pyrochlore Iridates: $k\cdot p$ Analysis of Cluster Dynamical Mean-Field Theory Results
• Kohn-Luttinger instability of the t-t' Hubbard model in two dimensions: variational approach
• Unconventional superconductivity and Surface pairing symmetry in Half-Heusler Compounds
• Superconductivity from Coulomb repulsion in three-dimensional quadratic band touching Luttinger semimetals
• Bond-ordered states and $f$-wave pairing of spinless fermions on the honeycomb lattice
• Disordered and interacting parabolic semimetals in two and three dimensions

Cited by in corpus (15)

• Metals, fractional metals, and superconductivity in rhombohedral trilayer graphene
• Competing orders and cascade of degeneracy lifting in doped Bernal bilayer graphene
• Extended Hubbard model in undoped and doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders
• Multiflavor Mott insulators in quantum materials and ultracold atoms
• Optical response of Luttinger semimetals in the normal and superconducting states
• Bogoliubov Fermi surfaces from pairing of emergent $j=3/2$ fermions on the pyrochlore lattice
• Competing magnetic orders and multipolar Weyl fermions in 227 pyrochlore iridates
• Intrinsic finite-energy Cooper pairing in $j=3/2$ superconductors
• Time reversal symmetry breaking and $d$-wave superconductivity of triple-point fermions
• Polar hairs of mixed-parity nodal superconductors in Rarita-Schwinger-Weyl metals
• Correlated interaction effects in three-dimensional semi-Dirac semimetal
• Superconductivity in doped planar Dirac insulators: A renormalization group study
• Superconductivity in three-dimensional interacting doped topological insulators
• Singular flat bands in three dimensions: Landau level spreading, quantum geometry, and Weyl reconstruction
• Critical fates induced by the interaction competition in three-dimensional tilted Dirac semimetals