Research
Emergent Orders from Corrected Electrons
My research focuses on emergent orders in strongly correlated electron systems. In crystalline solids, electrons experience the Coulomb force both from the (nearly) stationary lattice and from other electrons. A simplified approach is to consider a single electron moving in a background of others, as done in conventional Fermi gas and liquid models. However, in strongly correlated electron systems, this simplification fails. Fermi liquid theory assumes electrons can move freely throughout the solid, but in many materials, electron motion is localized due to strong Coulomb repulsion, which dominates over their kinetic energy and limits their mobility. In reciprocal space, these localized electrons appear as flat bands, which correspond to highly delocalized electrons in momentum space—a concept easily understood through Fourier transform arguments.
There are several ways to realize strongly correlated systems, including: (a) 2D electron gases (2DEG) with extremely low carrier density: In these systems, the potential energy from electron-electron interactions decreases more slowly than the kinetic energy as the charge density decreases. (b) Crystalline solids with small atomic orbitals, such as 3d and 4f transition metal oxides: The smaller radii of the transition metal ions restrict electron hopping between sites. Although these materials have partially filled bands and should theoretically be conductive from a single-electron perspective, they act as insulators, known as Mott insulators. (c) Systems with localized scattering centers: In these systems, electrons interact with localized particles, such as spins, creating a hybridization gap between localized and itinerant electrons, effectively localizing the latter. These are referred to as Kondo insulators or heavy Fermion systems. (d) Engineered flat bands near the Fermi surface: By carefully tuning the crystal structure, flat bands can be created near the Fermi surface, and the strong correlation effects arise from these flat bands. Magic-angle twisted bilayer graphene, as well as kagome metals, belong to this category.
One of the defining features of strongly correlated systems is the emergence of various collective orders, such as magnetism, charge and spin density waves, and unconventional superconductivity. For instance, in Mott insulators, although electrons are largely localized due to strong Coulomb repulsion, they can still tunnel to neighboring sites through quantum tunneling. Electrons with opposite spins are not constrained by the Pauli exclusion principle, allowing their wave functions to spread out more. The reduced momentum and energy arising from the more delocalized wavefunctions result in effective antiferromagnetic exchange couplings, which ultimately lead to the formation of antiferromagnetic order. Studying these emergent orders in correlated electron systems has been a central focus in condensed matter physics. It provides critical insights into electron behavior in crystalline solids, advancing the development of more efficient electronic materials and technologies.
Experimental Probes: Neutrons and more
In solids, multiple degrees of freedom—such as spin, charge, orbital, and lattice—are interrelated through electron correlations. To detect the emergent orders associated with these degrees of freedom, we must use probes that interact effectively with each. For example, the electronic band structure is commonly explored using ARPES, while neutron scattering is ideal for investigating magnetic structure and dynamics. Phonon excitations can be examined through techniques like neutron scattering, inelastic X-ray scattering (IXS), and Raman scattering. By combining these probes, we can gain a more comprehensive understanding of the electronic behaviors in strongly correlated systems.
My primary focus is using neutron scattering spectroscopy to probe lattice and spin dynamics in these systems. Neutrons, having no charge and a spin of 1/2, are sensitive only to lattice vibrations (phonons) and magnetic excitations (magnons). Moreover, at typical interatomic distances (1Å–10Å), neutron energies are well-matched to the energy scales of these excitations (0.1~100meV), making them an ideal tool for such studies. Neutron interactions with matter are relatively weak and nearly linear, which has several important consequences:
The neutron cross-section directly reflects the internal correlations of the solid, modulated only by a constant related to neutron-matter interactions.
Neutron scattering minimally disturbs the system, such as avoiding significant sample heating, making it suitable for low-temperature measurements.
Neutrons penetrate deeply into materials, probing bulk properties rather than just surface layers, though this requires a significant amount of sample material.
Because neutron experiments often require large quantities of sample material, I have developed expertise in sample synthesis and characterization, and I frequently collaborate using these samples. In addition to my work with neutrons, I have gained hands-on experience with Inelastic X-ray Scattering (IXS/RIXS) and Raman scattering through fruitful collaborations.
