Thermal transport in dielectric, non-magnetic crystals is mediated by quantized lattice vibrations, which drift and interact when driven out of equilibrium by a temperature gradient. This phenomenon can be described at multiple theoretical levels, ranging from fully quantum descriptions to semiclassical and mesoscopic continuum approaches. This review rigorously discusses the theoretical steps and approximations connecting these levels, bridging quantum phonon Dyson and Kadanoff-Baym equations and semiclassical Boltzmann transport formalism, and discussing the coarse-graining procedures that yield mesoscopic viscous heat equations for non-diffusive, hydrodynamic heat transport in devices. We show how the Guyer-Krumhansl and dual-phase-lag equations emerge as special linear-isotropic-band and inviscid limits of the viscous heat equations, respectively; most importantly, we demonstrate that these equations predict not only Poiseuille flow and second sound, but also more exotic effects such as negative thermal resistance, steady-state thermal backflow and vortices. We highlight how combining these frameworks with first-principles simulations connects microscopic phonon physics to observable non-diffusive heat-transport phenomena and guides their detection, amplification, and control. We recast the viscous heat equations in terms of Helmholtz and biharmonic equations solved analytically, and use this to discuss similarities and differences between the macroscopic behavior of the phonon fluid and other hydrodynamic systems, such as classical and electron fluids, focusing on compressibility, vorticity, and their influence on phonon hydrodynamics. We conclude with a roadmap to generalize the tools used to describe phonon hydrodynamics to other quasiparticles, motivating future advances in collective quantum transport phenomena in solids.
We highlight recent progress in the study of artificial flat band systems with a threefold focus. First, we discuss single-particle flat band physics, which has advanced through the design of various flat band generators. These generators rely on the classification of flat bands in terms of compact localized states - their fundamental building blocks. A related development is the complete real-space description of flat band projectors. Next, we review studies on perturbations of flat bands, which provide new insights into the effects of disorder and, more importantly, the intricate interplay between many-body interactions and flat band physics. Finally, we survey the growing number of experimental realizations of flat bands across diverse physical platforms.
In this review, we first present compelling evidence from resonant inelastic x-ray scattering data that highlights the significance of the long-range Coulomb interaction in cuprate charge dynamics, particularly around the in-plane momentum q=(0,0). We show that these experimental observations are well-captured by the layered t-J-V model, which extends the standard t-J framework to include the long-range Coulomb interaction V and the layered structure. This new perspective elucidates how charge dynamics renormalizes one-particle excitation properties, leading to several profound and often counterintuitive consequences. We demonstrate that the electron dispersion does not exhibit a sharp kink, and Landau quasiparticles persist in the low-energy limit despite a significant suppression of their spectral weight. We further show that while charge fluctuations alone cannot fully account for the pseudogap, they are a crucial component for understanding its formation. Additionally, we reveal that optical plasmon excitations generate fermionic quasiparticles, known as plasmarons, which give rise to a distinct, incoherent replica band. We argue that accurately describing these plasmonic effects requires a three-dimensional theoretical approach. This perspective on plasmon excitations may offer a critically new clue to a long-standing puzzle: why multi-layer cuprate superconductors, containing more than two CuO2 layers per unit cell, consistently exhibit a higher critical temperature Tc than their single-layer counterparts. Finally, we review the spin-fluctuation mechanism of superconductivity suffers from the "self-restraint effect" and show how important the screened Coulomb interaction is in the spin-fluctuation mechanism to realize high-Tc superconductivity.
The orbital magneto-electric effect (OME), the generation of a steady-state orbital angular momentum (OAM) density by an electric field, is a central component of orbitronics. Nevertheless its microscopic interpretation is complicated by the existence of two qualitatively different contributions: the intra-band Edelstein term stemming from the combined effect of the equilibrium OAM and Fermi surface shift, and the inter-band contribution, stemming from Zitterbewegung induced by the electric field. Here we develop a pedagogical density-matrix formulation of the OME within the framework of the modern theory of Bloch-electron OAM, in which the two contributions naturally emerge from distinct parts of the density matrix, and their distinct quantum geometric structures are clearly seen. In the inter-band contribution, in addition to the local- and itinerant-circulation terms, we show that a band-diagonal displacement, or charge dipole, is present, which is linear in the electric field and governed by the normalized quantum metric. For a tilted massive Dirac cone the Zitterbewegung OME and the Fermi-surface orbital response occur for orthogonal electric-field orientations, providing a route to separate them experimentally. The itinerant-circulation contribution is identical to the dipolar one, so in a two-band model the dipole accounts for exactly half of the inter-band response, both in the doped regime and in the insulating gap. Our recent insights identify quantum-metric engineering as a route for enhancing orbital magneto-electric responses and clarify the relation between modern orbital magnetization, polarization, and orbital torque phenomenology.
