Spin Hall conductivity in the Kane-Mele-Hubbard model at finite temperature

Abstract

The Kane-Mele model is known to show a quantized spin Hall conductivity at zero temperature. Including Hubbard interactions at each site leads to a quantum phase transition to an XY antiferromagnet at sufficiently high interaction strength. Here, we use the two-particle self-consistent approach (TPSC), which we extend to include spin-orbit coupling, to investigate the Kane-Mele-Hubbard model at finite temperature and half-filling. TPSC is a weak to intermediate coupling approach capable of calculating a frequency- and momentum-dependent self-energy from spin and charge fluctuations. We present results for the spin Hall conductivity and correlation lengths for antiferromagnetic spin fluctuations for different values of temperature, spin-orbit coupling and Hubbard interaction. The vertex corrections, which here are analogues of Maki-Thompson contributions, show a strong momentum dependence and give a large contribution in the vicinity of the phase transition at all temperatures. Their inclusion is necessary to observe the quantization of the spin Hall conductivity for the interacting system in the zero temperature limit. At finite temperature, increasing the Hubbard interaction leads to a decrease of the spin Hall conductivity. This decrease can be explained by band-gap renormalization from scattering of electrons on antiferromagnetic spin fluctuations.

arXiv comment11 pages, 8 figures

References in corpus (71)

• Spintronics: Fundamentals and applications
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Spin torque switching with the giant spin Hall effect of tantalum
• Magnetic switching by spin torque from the spin Hall effect
• Experimental observation of the spin-Hall effect in a two dimensional spin-orbit coupled semiconductor system
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps
• Spin-orbit gap of graphene: First-principles calculations
• Evidence for Helical Edge Modes in Inverted InAs/GaSb Quantum Wells
• Nonlocal edge state transport in the quantum spin Hall state
• Realization of Quantum Spin Hall State in Monolayer 1T'-WTe2
• Observation of the Quantum Spin Hall Effect up to 100 Kelvin in a Monolayer Crystal
• Edge conduction in monolayer WTe2
• Interacting topological insulators: a review
• Non-perturbative many-body approach to the Hubbard model and single-particle pseudogap
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Topological Insulators and Mott Physics from the Hubbard Interaction
• Correlation Effects in Quantum Spin-Hall Insulators: A Quantum Monte Carlo Study
• Electric Field-Tuned Topological Phase Transition in Ultra-Thin Na3Bi - Towards a Topological Transistor
• Spin-orbit driven band inversion in bilayer graphene by van der Waals proximity effect
• Correlation effects in two-dimensional topological insulators
• The spin Hall effect in a quantum gas
• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• Particle-hole symmetry and interaction effects in the Kane-Mele-Hubbard model
• Mott Physics and Topological Phase Transition in Correlated Dirac Fermions
• Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains
• Quantum phase transitions in the Kane-Mele-Hubbard model
• Observation of a Helical Luttinger-Liquid in InAs/GaSb Quantum Spin Hall Edges
• Intrinsic spin-orbit coupling gap and the evidence of a topological state in graphene
• Quantum Spin Hall Insulators with Interactions and Lattice Anisotropy
• Sparse sampling approach to efficient ab initio calculations at finite temperature
• Theory of single-particle properties of the Hubbard model
• Rashba spin orbit coupling in the Kane-Mele-Hubbard model
• Theory of spin and charge fluctuations in the Hubbard model
• Correlation effects on a topological insulator at finite temperatures
• Optical and DC conductivity of the two-dimensional Hubbard model in the pseudogap regime and across the antiferromagnetic quantum critical point, including vertex corrections
• Magnetic ordering phenomena of interacting quantum spin Hall models
• Mott Physics on Helical Edges of 2D Topological Insulators
• Mott insulators with boundary zeros
• sparse-ir: optimal compression and sparse sampling of many-body propagators
• The effects of interaction on quantum spin Hall insulators
• Topological phase transition in a generalized Kane-Mele-Hubbard model: A combined Quantum Monte Carlo and Green's function study
• Phase Diagram of the Kane-Mele-Hubbard model
• Antiferromagnetism in the Hubbard model on the honeycomb lattice: a Two-Particle Self-Consistent study
• Design and realization of topological Dirac fermions on a triangular lattice
• Development of a two-particle self-consistent method for multi-orbital systems and its application to unconventional superconductors
• Non-Perturbative Treatment of Charge and Spin Fluctuations in the Two-Dimensional Extended Hubbard Model: Extended Two-Particle Self-Consistent Approach
• Nearest-Neighbor Repulsion and Competing Charge and Spin Order in the Extended Hubbard Model
• Effect of non-local correlations on the electronic structure of LiFeAs
• The characterization of topological properties in Quantum Monte Carlo simulations of the Kane-Mele-Hubbard model
• 1/4 is the new 1/2 when topology is intertwined with Mottness
• Competition between charge and spin order in the $t-U-V$ extended Hubbard model on the triangular lattice
• Fate of a topological invariant for correlated lattice electrons at finite temperature
• Superconductivity in correlated BEDT-TTF molecular conductors: critical temperatures and gap symmetries
• Asymmetry of Superconductivity in Hole- and Electron-doped Cuprates: Explanation within Two-Particle Self-Consistent Analysis for the Three-Band Model
• Topological edge Mott insulating state in two dimensions at finite temperatures -bulk and edge analysis-
• Nonequilibrium Two-Particle Self-Consistent Approach
• Hall and Faraday effects in interacting multi-band systems with arbitrary band topology and spin-orbit coupling
• Two-Particle Self-Consistent method for the multi-orbital Hubbard model
• Nonlocal corrections to dynamical mean-field theory from the two-particle self-consistent method
• Enhancement of electron correlation due to the molecular dimerization in organic superconductors $\beta$-(BDA-TTP)${}_{2}X$ ($X$=I${}_3$, SbF${}_6$)
• Analytical approach for the Mott transition in the Kane-Mele-Hubbard model
• Improved effective vertices in the multi-orbital Two-Particle Self-Consistent method from Dynamical Mean-Field Theory
• An Improved Two-Particle Self-Consistent Approach
• Real-space Obstruction in Quantum Spin Hall Insulators
• Dynamical Mean Field Theory extension to the nonequilibrium Two-Particle Self-Consistent approach
• Resilient Fermi liquid and strength of correlations near an antiferromagnetic quantum critical point

Cited by in corpus (4)

• Spin correlations in the bilayer Hubbard model with perpendicular electric field
• Antiferromagnetic pseudogap in the two-dimensional Hubbard model deep in the renormalized classical regime
• Multi-orbital two-particle self-consistent approach -- strengths and limitations
• Incipient quantum spin Hall insulator under strong correlations