Topological superconductivity in the extended Kitaev-Heisenberg model

Abstract

We study superconducting pairing in the doped Kitaev-Heisenberg model by taking into account the recently proposed symmetric off-diagonal exchange $\Gamma$. By performing a mean-field analysis, we classify all possible superconducting phases in terms of symmetry, explicitly taking into account effects of spin-orbit coupling. Solving the resulting gap equations self-consistently, we map out a phase diagram that involves several topologically nontrivial states. For $\Gamma <0$, we find a competition between a time-reversal symmetry breaking chiral phase with Chern number $\pm 1$ and a time-reversal symmetric nematic phase that breaks the rotational symmetry of the lattice. On the other hand, for $\Gamma \ge 0$ we find a time-reversal symmetric phase that preserves all the lattice symmetries, thus yielding clearly distinguishable experimental signatures for all superconducting phases. Both of the time-reversal symmetric phases display a transition to a ${\mathbb{Z}}_2$ non-trivial phase at high doping levels. Finally, we also include a symmetry-allowed spin-orbit coupling kinetic energy and show that it destroys a tentative symmetry protected topological order at lower doping levels. However, it can be used to tune the time-reversal symmetric phases into a ${\mathbb{Z}}_2$ non-trivial phase even at lower doping.

References in corpus (51)

• Anyons in an exactly solved model and beyond
• Classification of topological insulators and superconductors in three spatial dimensions
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3
• Generic spin model for the honeycomb iridates beyond the Kitaev limit
• Challenges in Design of Kitaev Materials: Magnetic Interactions from Competing Energy Scales
• Magnetic order in $\alpha$-RuCl${}_3$: a honeycomb lattice quantum magnet with strong spin-orbit coupling
• Quantum spin Hall effect in a transition metal oxide Na2IrO3
• Evidence for a Field-induced Quantum Spin Liquid in $\alpha$-RuCl${}_3$
• Spin-Rotation Symmetry Breaking in the Superconducting State of CuxBi2Se3
• Kitaev magnetism in honeycomb RuCl3 with intermediate spin-orbit coupling
• Fermionic response from fractionalization in an insulating two-dimensional magnet
• Spin-orbit excitation energies, anisotropic exchange, and magnetic phases of honeycomb RuCl3
• Density waves and Cooper pairing on the honeycomb lattice
• Topological odd-parity superconductors
• Thermodynamic evidence for nematic superconductivity in Cu${}_x$Bi${}_2$Se${}_3$
• Resonating valence bonds and mean-field d-wave superconductivity in graphite
• Crystal structure and magnetism in $\alpha$-RuCl3: an ab-initio study
• Kitaev interactions between j=1/2 moments in honeycomb Na2IrO3 are large and ferromagnetic: insights from ab initio quantum chemistry calculations
• Spin-wave excitations evidencing the Kitaev interaction in single crystalline $\alpha$-RuCl${}_3$
• First-Principles Study of the Honeycomb-Lattice Iridates Na2IrO3 in the Presence of Strong Spin-Orbit Interaction and Electron Correlations
• Anomalous thermal conductivity and magnetic torque response in the honeycomb magnet $\alpha$-RuCl${}_3$
• Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for honeycomb lattice iridates A2IrO3
• Ab initio analysis of the tight-binding parameters and magnetic interactions in Na2IrO3
• Na2IrO3 as a molecular orbital crystal
• Incommensurate Counterrotating Magnetic Order Stabilized by Kitaev Interactions in the Layered Honeycomb $\alpha$-Li${}_2$IrO${}_3$
• Kitaev-Heisenberg-J2-J3 model for the iridates A2IrO3
• Magnetization processes of zigzag states on the honeycomb lattice: Identifying spin models for $\alpha$-RuCl${}_3$ and Na${}_2$IrO${}_3$
• Doping a spin-orbit Mott Insulator: Topological Superconductivity from the Kitaev-Heisenberg Model and possible application to (Na2/Li2)IrO3
• Topological properties of spin-triplet superconductors and the Fermi surface topology in the normal state
• Superconductivity close to the Mott state: From condensed-matter systems to superfluidity in optical lattices
• Importance of anisotropic exchange interactions in honeycomb iridates. Minimal model for zigzag antiferromagnetic order in Na${}_2$IrO${}_3$
• Clues and criteria for designing Kitaev spin liquid revealed by thermal and spin excitations of honeycomb iridates Na${}_2$IrO${}_3$
• Odd-parity superconductors with two-component order parameters: nematic and chiral, full gap and Majorana node
• Kitaev Materials
• Strongly frustrated triangular spin lattice emerging from triplet dimer formation in honeycomb Li2IrO3
• Global phase diagram of a doped Kitaev-Heisenberg model
• Competition between d-wave and topological p-wave superconductivity in the doped Kitaev-Heisenberg model
• Correlated Dirac Particles and Superconductivity on the Honeycomb Lattice
• RVB Contribution to Superconductivity in $Mg{B}_2$
• Global phase diagram, possible chiral spin liquid and topological superconductivity in the triangular Kitaev-Heisenberg model
• Selection of direction of the ordered moments in Na${}_2$IrO${}_3$ and $\alpha -$RuCl${}_3$
• Unconventional pairing and electronic dimerization instabilities in the doped Kitaev-Heisenberg model
• Computational Study of the Magnetic Structure of Na${}_2$IrO${}_3$
• Defects in the (d+id)-wave superconducting state in heavily doped graphene
• Zeeman field induced topological phase transitions in triplet superconductors
• Triplet FFLO Superconductivity in the doped Kitaev-Heisenberg Honeycomb Model
• Symmetry-protected topological invariant and Majorana impurity states in time-reversal-invariant superconductors

Cited by in corpus (9)

• Hunting Majorana Fermions in Kitaev Magnets
• Electronic properties of α-RuCl3 in proximity to graphene
• Topological superconductivity in Kondo-Kitaev model
• Evidence of pair-density wave in doping Kitaev spin liquid on the honeycomb lattice
• Disorder-robust phase crystal in high-temperature superconductors stabilized by strong correlations
• Hydrated lithium intercalation into the Kitaev spin liquid candidate material $\alpha -$RuCl${}_3$
• Possible Realization of Kitaev Spin Liquids in van der Waals Heterostructures of $\alpha$-RuCl${}_3$ and Cr$X_3$ ($X$=Cl and I)
• Pairing tendencies in the doped Kitaev-Heisenberg model
• Ground State Properties of the Doped Kitaev-Heisenberg Chain: Topological Superconducting and Mott Insulating Phases Driven by Magnetic Frustration