Topological superconductivity of spin-3/2 carriers in a three-dimensional doped Luttinger semimetal

Abstract

We investigate topological Cooper pairing, including gapless Weyl and fully gapped class DIII superconductivity, in a three-dimensional doped Luttinger semimetal. The latter describes effective spin-3/2 carriers near a quadratic band touching and captures the normal-state properties of the 227 pyrochlore iridates and half-Heusler alloys. Electron-electron interactions may favor non-$s$-wave pairing in such systems, including even-parity $d$-wave pairing. We argue that the lowest energy $d$-wave pairings are always of complex (e.g., $d+id$) type, with nodal Weyl quasiparticles. This implies $\varrho (E)\sim |E{|}^2$ scaling of the density of states (DoS) at low energies in the clean limit, or $\varrho (E)\sim |E|$ over a wide critical region in the presence of disorder. The latter is consistent with the $T$-dependence of the penetration depth in the half-Heusler compound YPtBi. We enumerate routes for experimental verification, including specific heat, thermal conductivity, NMR relaxation time, and topological Fermi arcs. Nucleation of any $d$-wave pairing also causes a small lattice distortion and induces an $s$-wave component; this gives a route to strain-engineer exotic $s+d$ pairings. We also consider odd-parity, fully gapped $p$-wave superconductivity. For hole doping, a gapless Majorana fluid with cubic dispersion appears at the surface. We invent a generalized surface model with $\nu$-fold dispersion to simulate a bulk with winding number $\nu$. Using exact diagonalization, we show that disorder drives the surface into a critically delocalized phase, with universal DoS and multifractal scaling consistent with the conformal field theory (CFT) SO($n$)${}_{\nu }$, where $n\to 0$ counts replicas. This is contrary to the naive expectation of a surface thermal metal, and implies that the topology tunes the surface renormalization group to the CFT in the presence of disorder.

Published Version in PRB (Editors' Suggestion): 49 Pages, 17 Figures, 3 Tables

References in corpus (32)

• Weyl and Dirac Semimetals in Three Dimensional Solids
• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Anderson Transitions
• The space group classification of topological band insulators
• Discovery of Weyl fermion semimetals and topological Fermi arc states
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• Two Energy Scales and two Quasiparticle Dynamics in the Superconducting State of Underdoped Cuprates
• Bogoliubov Fermi surfaces in superconductors with broken time-reversal symmetry
• Topological $R$PdBi half-Heusler semimetals: a new family of non-centrosymmetric magnetic superconductors
• Topological surface states in nodal superconductors
• Rare region effects dominate weakly disordered 3D Dirac points
• Topological Mott insulator in three-dimensional systems with quadratic band touching
• Weak Antilocalization Effect and Noncentrosymmetric Superconductivity in a Topologically Nontrivial Semimetal LuPdBi
• Topological field theory and thermal responses of interacting topological superconductors
• Competing Nematic, Anti-ferromagnetic and Spin-flux orders in the Ground State of Bilayer Graphene
• Superconductivity in three-dimensional spin-orbit coupled semimetals
• A New Type of Quantum Criticality in the Pyrochlore Iridates
• Pairing states of spin-3/2 fermions: Symmetry-enforced topological gap functions
• Inflated nodes and surface states in superconducting half-Heusler compounds
• Diffusive Quantum Criticality in Three Dimensional Disordered Dirac Semimetals
• Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors
• Unconventional Superconductivity in Luttinger Semimetals: Theory of Complex Tensor Order and the Emergence of the Uniaxial Nematic State
• Weyl fermions with arbitrary monopole in magnetic fields: Landau levels, longitudinal magnetotransport, and density-wave ordering
• Model Hamiltonian and Time Reversal Breaking Topological Phases of Anti-ferromagnetic Half-Heusler Materials
• Majorana surface modes of nodal topological pairings in spin-$\frac{3}{2}$ semi-metals
• Irradiated three-dimensional Luttinger semimetal: A factory for engineering Weyl semimetals
• New Quantum Transition in Weyl Semimetals with Correlated Disorder
• Surface transport coefficients for three-dimensional topological superconductors
• Weyl Rings and enhanced susceptibilities in Pyrochlore Iridates: $k\cdot p$ Analysis of Cluster Dynamical Mean-Field Theory Results
• Critical Percolation Without Fine Tuning on the Surface of a Topological Superconductor
• Disordered and interacting parabolic semimetals in two and three dimensions

Cited by in corpus (68)

• Second-order Dirac superconductors and magnetic field induced Majorana hinge modes
• Higher-order topological superconductors in $\mathcal{P}$-, $\mathcal{T}$-odd quadrupolar Dirac materials
• Antiunitary symmetry protected higher order topological phases
• Vortex and Surface Phase Transitions in Superconducting Higher-order Topological Insulators
• d-wave superconductivity and Bogoliubov-Fermi surfaces in Rarita-Schwinger-Weyl semimetals
• Experimental consequences of Bogoliubov Fermi surfaces
• Interplay of topology and electron-electron interactions in Rarita-Schwinger-Weyl semimetals
• Bogoliubov Fermi surfaces stabilized by spin-orbit coupling
• Tunneling of multi-Weyl semimetals through a potential barrier under the influence of magnetic fields
• Superconductivity in spin-$3/2$ systems: symmetry classification, odd-frequency pairs, and Bogoliubov Fermi surfaces
• Magnus Hall effect in three-dimensional topological semimetals
• Multiflavor Mott insulators in quantum materials and ultracold atoms
• Dynamical construction of Quadrupolar and Octupolar topological superconductors
• Transmission and conductance across junctions of isotropic and anisotropic three-dimensional semimetals
• Majorana multipole response of topological superconductors
• Thermoelectric and thermal properties of the weakly disordered non-Fermi liquid phase of Luttinger semimetals
• Tuning the Parity Mixing of Singlet-Septet Pairing in a Half-Heusler Superconductor
• Topological d+s wave superconductors in a multi-orbital quadratic band touching system
• Instability of $j=3/2$ Bogoliubov Fermi-surfaces
• Strain engineered higher order topological phases for spin-3/2 Luttinger fermions
• Symmetry, nodal structure, and Bogoliubov Fermi surfaces for nonlocal pairing
• Stability of two-dimensional asymmetric materials with a quadratic band crossing point under four-fermion interaction and impurity scattering
• Interacting spin-3/2 fermions in a Luttinger semimetal: Competing phases and their selection in the global phase diagram
• Raman response and shear viscosity in the non-Fermi liquid phase of Luttinger semimetals
• Dielectric and electronic properties of three-dimensional Luttinger semimetals with a quadratic band touching
• Criticality Across the Energy Spectrum from Random, Artificial Gravitational Lensing in Two-Dimensional Dirac Superconductors
• Power-law Temperature Dependence of the Penetration Depth in a Topological Superconductor due to Surface States
• Chiral flat band superconductivity from symmetry-protected three-band crossings
• Dielectric function and plasmons of doped three-dimensional Luttinger semimetals
• Campbell penetration depth in low carrier density superconductor YPtBi
• 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
• Using Disorder to Identify Bogoliubov Fermi-Surface States
• Multipolar superconductivity in Luttinger semimetals
• Transport properties in non-Fermi liquid phases of nodal-point semimetals
• Topological Anomalous Skin Effect in Weyl Superconductors
• Bogoliubov Fermi surfaces from pairing of emergent $j=3/2$ fermions on the pyrochlore lattice
• Antiferromagnetic spin fluctuations and unconventional superconductivity in topological superconductor candidate YPtBi revealed by ${}^{195}$Pt-NMR
• Intrinsic finite-energy Cooper pairing in $j=3/2$ superconductors
• From local spin nematicity to altermagnets: Footprints of band topology
• High orbital-moment Cooper pairs by crystalline symmetry breaking
• Nodal pair density waves from a quarter-metal in crystalline graphene multilayers
• Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry
• Superconductivity in PtSbS with a Noncentrosymmetric Cubic Crystal Structure
• Stability of Bogoliubov Fermi Surfaces within BCS Theory
• Hybrid Dispersion Dirac semimetal and Hybrid Weyl phases in Luttinger Semimetals: A dynamical approach
• Time reversal symmetry breaking and $d$-wave superconductivity of triple-point fermions
• Anisotropic RKKY interactions mediated by $j=3/2$ quasiparticles in half-Heusler topological semimetal
• Spin-orbit-coupled superconductivity with spin-singlet non-unitary pairing
• Discontinuous Transition to Superconducting Phase
• p-wave superconductivity in Luttinger semimetals
• Polar hairs of mixed-parity nodal superconductors in Rarita-Schwinger-Weyl metals
• Quantized thermal and spin transports of dirty planar topological superconductors
• How spectrum-wide quantum criticality protects surface states of topological superconductors from Anderson localization: Quantum Hall plateau transitions (almost) all the way down
• Mixed-parity octupolar pairing and corner Majorana modes in three dimensions
• Infrared fixed points of higher-spin fermions in topological 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
• Superconductivity in Luttinger semimetals near the SU(4) limit
• Superconductivity in doped planar Dirac insulators: A renormalization group study
• Electronic Properties of BaPtP with a Noncentrosymmetric Cubic Crystal Structure
• Intrinsic emergence of Majorana modes in Luttinger j=3/2 systems
• Critical fates induced by the interaction competition in three-dimensional tilted Dirac semimetals
• Electronic structure and hinge states of strained half-Heusler compounds LiSbZn and LiBiZn
• Singular flat bands in three dimensions: Landau level spreading, quantum geometry, and Weyl reconstruction
• Beyond spin-1/2: Multipolar spin-orbit coupling in noncentrosymmetric crystals with time-reversal symmetry
• Phases of three-dimensional $d$-wave superconductors with two attractive interactions