Negative flat band magnetism in a spin–orbit-coupled correlated kagome magnet

Ever since its discovery, the Berry phase has permeated through all branches of physics. Over the last three decades, it was gradually realized that the Berry phase of the electronic wave function can have a profound effect on material properties and is responsible for a spectrum of phenomena, such as ferroelectricity, orbital magnetism, various (quantum/anomalous/spin) Hall effects, and quantum charge pumping. This progress is summarized in a pedagogical manner in this review. We start with a brief summary of necessary background, followed by a detailed discussion of the Berry phase effect in a variety of solid state applications. A common thread of the review is the semiclassical formulation of electron dynamics, which is a versatile tool in the study of electron dynamics in the presence of electromagnetic fields and more general perturbations. Finally, we demonstrate a re-quantization method that converts a semiclassical theory to an effective quantum theory. It is clear that the Berry phase should be added as a basic ingredient to our understanding of basic material properties.

The understanding of strongly-correlated materials, and in particular unconventional superconductors, has puzzled physicists for decades. Such difficulties have stimulated new research paradigms, such as ultra-cold atom lattices for simulating quantum materials. Here we report on the realization of intrinsic unconventional superconductivity in a 2D superlattice created by stacking two graphene sheets with a small twist angle. For angles near \(1.1^\circ\), the first `magic' angle, twisted bilayer graphene (TBG) exhibits ultra-flat bands near charge neutrality, which lead to correlated insulating states at half-filling. Upon electrostatic doping away from these correlated insulating states, we observe tunable zero-resistance states with a critical temperature \(T_c\) up to 1.7 K. The temperature-density phase diagram shows similarities with that of the cuprates, including superconducting domes. Moreover, quantum oscillations indicate small Fermi surfaces near the correlated insulating phase, in analogy with under-doped cuprates. The relative high \(T_c\), given such small Fermi surface (corresponding to a record-low 2D carrier density of \(10^{11} \textrm{cm}^{-2}\) , renders TBG among the strongest coupling superconductors, in a regime close to the BCS-BEC crossover. These novel results establish TBG as the first purely carbon-based 2D superconductor and as a highly tunable platform to investigate strongly-correlated phenomena, which could lead to insights into the physics of high-\(T_c\) superconductors and quantum spin liquids.

Tunneling spectroscopy played a central role in the experimental verification of the microscopic theory of superconductivity in the classical superconductors. Initial attempts to apply the same approach to high-temperature superconductors were hampered by various problems related to the complexity of these materials. The use of scanning tunneling microscopy/spectroscopy (STM/STS) on these compounds allowed to overcome the main difficulties. This success motivated a rapidly growing scientific community to apply this technique to high-temperature superconductors. This paper reviews the experimental highlights obtained over the last decade. We first recall the crucial efforts to gain control over the technique and to obtain reproducible results. We then discuss how the STM/STS technique has contributed to the study of some of the most unusual and remarkable properties of high-temperature superconductors: the unusual large gap values and the absence of scaling with the critical temperature; the pseudogap and its relation to superconductivity; the unprecedented small size of the vortex cores and its influence on vortex matter; the unexpected electronic properties of the vortex cores; the combination of atomic resolution and spectroscopy leading to the observation of periodic local density of states modulations in the superconducting and pseudogap states, and in the vortex cores.