Kinetic magnetoelectric effect in topological insulators

The study investigates the kinetic magnetoelectric effect (KME), an orbital analog of the Edelstein effect, focusing on its potential in topological insulators. KME, also known as the orbital Edelstein effect, involves the conversion of charge current into orbital magnetization in low-symmetry crystals. It differs from the magnetoelectric (ME) effect; KME relies on non-equilibrium electron distribution induced by an electric field in metallic systems, while the ME effect stems from equilibrium band structure changes in insulators. The KME's symmetry requirements also differ: inversion symmetry must be broken for both, but time-reversal symmetry can be broken or preserved in KME. Previous KME studies focused on bulk contributions, while this paper examines the boundary and surface effects, crucial due to boundary dependence in orbital magnetization response to an electric field.

The paper reviews existing research on orbital magnetization responses in systems lacking inversion symmetry, highlighting KME and the gyrotropic magnetic effect. Previous studies demonstrated KME in chiral and polar systems, often employing metallic systems. The difference between KME and the ME effect (in insulators) is emphasized, including their distinct mechanisms and symmetry conditions. The authors point to the chirality-induced spin selectivity (CISS) effect as a related phenomenon using organic materials in spintronics. The crucial role of boundaries in magnetoelectric tensors is addressed, emphasizing that while equilibrium orbital magnetization is boundary-independent, the response to electric fields is not.

The study uses a theoretical approach combining analytical calculations and numerical simulations. First, a formulation for KME is developed, calculating orbital magnetization along the z-axis induced by a current along the z-axis in a cylindrical crystal. The Boltzmann approximation is used to describe the non-equilibrium electron distribution due to the electric field. The KME is then calculated for a three-dimensional tight-binding model of a layered Chern insulator with chiral crystal structures, considering a one-dimensional quadrangular prism with xz and yz surfaces. This model allows investigating the effect of boundaries and system size on the KME. A surface theory of KME for a slab is developed using an effective Hamiltonian for the crystal surface, capturing KME's nature through surface states. This surface theory is then extended to a cylinder geometry by considering the individual surfaces of the prism and imposing current conservation at the corners. First-principle calculations using the Vienna ab initio simulation package (VASP) are used for Cu₂ZnSnSe₄, calculating its electronic structure, surface states, and Fermi surfaces to determine the magnetoelectric susceptibility. The scaling behavior of KME in topological insulators versus metals is analyzed by considering surface anisotropic transport coefficients.

The key findings demonstrate that the KME in topological insulators is significantly larger than in metals (5-8 orders of magnitude). This enhancement originates from the confinement of the current to the surface of the topological insulator, creating macroscopic current loops that efficiently induce orbital magnetization. In contrast, in metals, microscopic current loops within the bulk contribute to a much smaller KME. The authors show that the KME in topological insulators is highly surface-dependent and not a bulk property, unlike equilibrium orbital magnetization. The developed surface theory accurately describes the numerical results, confirming the dominant role of surface states in the KME. The analysis reveals that the response coefficient of orbital magnetization to current density in topological insulators scales with the system size (L), unlike in metals where it is size-independent. First-principle calculations on Cu₂ZnSnSe₄ confirm the presence of a significant KME, with different surface terminations exhibiting varying magnetoelectric susceptibilities. The comparison with existing KME measurements in tellurium solidifies the magnitude of enhancement predicted for topological insulators. A detailed analysis comparing the scaling of spin and orbital magnetization in topological insulators versus metals further supports the exceptional nature of the KME in topological insulators. The KME in topological insulators exhibits a unique scaling behavior compared to other magnetization responses, emphasizing the substantial impact of the macroscopic surface current loops.

The findings address the research question by demonstrating the existence and significantly enhanced magnitude of KME in topological insulators compared to metals. This enhanced KME arises from the unique surface-state properties and macroscopic current loops within the surface. The surface-dependent nature of the KME is a significant result, highlighting the importance of considering surface effects in future studies of magnetoelectric phenomena. The theoretical framework developed, combining surface Hamiltonian approach with numerical simulations, provides a powerful tool to investigate and predict KME in various topological materials. The identification of Cu₂ZnSnSe₄ as a potential candidate material opens avenues for experimental verification and exploration of this phenomenon's applications in spintronics and other fields.

The paper successfully demonstrates a significantly enhanced KME in topological insulators compared to metals. The KME is shown to be a surface phenomenon, dependent on the specific surface termination, not a bulk property. The surface theory developed accurately predicts the KME and provides a valuable framework for future research. The identification of promising candidate materials like Cu₂ZnSnSe₄ paves the way for experimental verification and technological applications. Further research should explore KME in other topological materials and investigate the potential for controlling and manipulating this effect for technological advancements.

The study primarily relies on theoretical modeling and first-principle calculations. Experimental verification of the predicted gigantic KME in topological insulators is needed. The surface theory used certain approximations, such as neglecting the finite penetration depth of surface states in early stages, although a fitting function considering this was successfully implemented. The analysis focuses on specific topological insulator types (Chern insulators and Z₂ TIs) and specific crystal structures; future research could expand to other topological materials and explore the influence of diverse crystal symmetries on KME.