[Paper Review] Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator

Xiangang Wan, Ari M. Turner+2 more|arXiv (Cornell University)|Jun 30, 2010

Advanced Condensed Matter PhysicsPhysics and Astronomy1,823 citations

TL;DR

This paper proposes that Y₂Ir₂O₇ is a topological Dirac metal at intermediate electron correlation strength, where Dirac nodes with linear dispersion and Fermi arcs emerge due to spin-orbit coupling and non-collinear all-in/all-out magnetic order. At strong correlations, it transitions to a Mott insulator, while weak correlations yield a magnetic metal; a narrow window of axion insulator with θ=π may also exist.

ABSTRACT

In 5d transition metal oxides such as the iridates, novel properties arise from the interplay of electron correlations and spin-orbit interactions. We investigate the electronic structure of the pyrochlore iridates, (such as Y$_{2}$Ir$_{2}$O$_{7}$) using density functional theory, LDA+U method, and effective low energy models. A remarkably rich phase diagram emerges on tuning the correlation strength U. The Ir magnetic moment are always found to be non-collinearly ordered. However, the ground state changes from a magnetic metal at weak U, to a Mott insulator at large U. Most interestingly, the intermediate U regime is found to be a Dirac semi-metal, with vanishing density of states at the Fermi energy. It also exhibits topological properties - manifested by special surface states in the form of Fermi arcs, that connect the bulk Dirac points. This Dirac phase, a three dimensional analog of graphene, is proposed as the ground state of Y$_{2}$Ir$_{2}$O$_{7}$ and related compounds. A narrow window of magnetic `axion' insulator, with axion parameter $θ=π$, may also be present at intermediate U. An applied magnetic field induces ferromagnetic order and a metallic ground state.

Motivation & Objective

• To understand the electronic phase diagram of pyrochlore iridates (A₂Ir₂O₇) under varying electron correlation strength.
• To determine the role of spin-orbit coupling and magnetic order in stabilizing topological electronic states.
• To reconcile experimental observations—such as metal-insulator transitions and magnetic ordering—with a unified electronic structure framework.
• To investigate the emergence of exotic phases like the topological Dirac metal and axion insulator (θ=π) in correlated 5d iridates.
• To explain the absence of net magnetic moment and the persistence of non-collinear order in Y₂Ir₂O₇ and related compounds.

Proposed method

• Employed density functional theory (DFT) with LDA+U to account for electron correlations in pyrochlore iridates.
• Used effective low-energy Hamiltonians to model the electronic structure near the L-point in momentum space.
• Constructed a k-dependent Hamiltonian H(k) = (Δ + k_z²/2m₁ - k_⊥²/2m₂)τ_z + (βk_z + k_⊥³cos3θ)τ_x + k_⊥³sin3θτ_y to describe Dirac nodes.
• Analyzed the conditions for Dirac node formation by solving A=B=C=0 in the effective Hamiltonian, identifying nodes at specific k_z and θ values.
• Evaluated the role of the effective mass parameter α, showing that α<0 (physically relevant for Y₂Ir₂O₇) stabilizes Dirac nodes only in the small U phase.
• Assessed topological invariants and the axion parameter θ to identify the possibility of a θ=π axion insulator phase.

Experimental results

Research questions

• RQ1 What is the nature of the electronic ground state of Y₂Ir₂O₇ across varying electron correlation strengths?
• RQ2 How does spin-orbit coupling interact with electron correlations to stabilize topological Dirac fermions in 5d iridates?
• RQ3 Can the observed metal-insulator transition in A₂Ir₂O₇ be explained by a correlation-tuned phase transition from Dirac semi-metal to Mott insulator?
• RQ4 What is the role of non-collinear all-in/all-out magnetic order in preserving inversion symmetry and enabling topological surface states?
• RQ5 Is there a narrow window of topological axion insulator phase (θ=π) stabilized by inversion symmetry and intermediate correlations?

Key findings

• For intermediate U, the ground state of Y₂Ir₂O₇ is a topological Dirac metal with six Dirac nodes at the L-point, forming a linearly dispersing band structure.
• The Dirac fermions are two-component and chiral, leading to surface states that form Fermi arcs connecting the bulk Dirac points.
• The system exhibits a vanishing density of states at the Fermi level, consistent with insulating resistivity at low temperatures.
• At strong U, the system transitions to a Mott insulator with all-in/all-out non-collinear magnetic order.
• A narrow window of axion insulator phase with θ=π may exist at intermediate U, protected by inversion symmetry, though LDA+U underestimates the gap.
• The effective Hamiltonian with α<0 (physically relevant) shows Dirac nodes only in the small U phase, and the gap closes at Δ=0, indicating a topological phase transition.