Bohm-Jung Yang

Flat bands have been proposed in various geometrically frustrated lattices, yet their experimental realization has been limited only to the two-dimensional (2D) kagome and three-dimensional (3D) pyrochlore lattices. While synthesizing bulk crystals with desired lattice geometry is generally challenging, the surfaces of 3D bulk materials sometimes naturally host 2D lattice structures hardly achievable in 2D bulk crystals. Thus, the electrons localized on such 2D surfaces can be a new platform for exotic flat bands residing on the unexplored lattice geometry. Here, we report the first experimental observation of singular flat bands with band crossings in the 2D pentagonal lattice on the surface of the 3D ferromagnetic topological semimetal CoS₂. We demonstrate that the coupling between localized surface flat bands and extended bulk topological bands gives rise to the surface non-Fermi liquid behavior characterized by the quasiparticle scattering rate with linear temperature dependence and pronounced quasiparticle broadening. This study of CoS₂ highlights metallic pyrite materials as an ideal platform for exploring the exotic properties of spin-polarized singular flat bands localized on the surface pentagonal lattice, which provides a fresh perspective for investigating correlated electron phenomena in pentagon-based materials.

Moiré superlattices in van der Waals heterostructures are powerful tuning knobs for engineering electronic band structures and emergent phases. Expanding this framework to multi‐moiré architectures enables the discovery of novel quantum states, as hierarchically superposed patterns generate a versatile and sophisticated electronic landscape. Moreover, competition between interlayer interactions and lattice strain can drive structural reconfigurations, forming periodic domains delineated by aperiodic boundaries. Here, anomalous hysteretic charge filling is observed in helical trilayer graphene, where sequential twist angles create a complex moiré‐of‐moiré environment. Transport measurements reveal dual electronic signatures: moiré‐induced minibands in periodic domains, and a distinct hysteretic resistance signal from the aperiodic boundaries. These observations can be interpreted within the framework of partial electron localization driven by the loss of global periodicity in the incommensurate regime. This work provides insights into how spatially inhomogeneous potentials reshape electronic states and establishes a pathway for controlling quantum phases in non‐periodic lattice environments.

For decades, ``geometry" in band theory has largely meant Berry phase and Berry curvature-quantities that reshape semiclassical dynamics and underpin modern topological matter. Yet the full geometric content of a Bloch band is richer and encoded in the quantum geometric tensor (QGT), whose imaginary part is the Berry curvature and whose real part is the quantum metric. Here, we briefly review the recent progress in direct experimental access to the QGT in real crystalline solids using the polarization- and spin-resolved angle-resolved photoemission spectroscopy (ARPES). The extraction of the QGT in momentum space was successfully addressed by two different approaches: One is by introducing quasi-QGT that faithfully represents the QGT and is directly measurable by ARPES. The other is through pseudospin tomography in a material with simple low energy band structure, which successfully retrieved all matrix components of the quantum metric. We discuss the physical meaning of these two recent progresses, their implication/limitation, and open directions.

The localisation of electrons in a lattice potential is an quantum-mechanical phenomenon and is often associated with remarkable physical properties of solids involving electron spins, electric polarisations and topological effects. In particular, even a small amount of distortion of the lattice potential can localise otherwise-delocalised quantum states in low-dimensional electron systems, dramatically influencing their thermodynamic properties and charge-transport behaviour. Study of such electron localisation induced by an aperiodic lattice potential remains exceptionally challenging in solid-state systems, since extrinsic disorders can trivially trap electrons in potential minima near disorders, obscuring the underlying quantum-mechanical origin of localisation phenomena. Van der Waals heterostructures can provide an alternative route for explorations of the phenomena via the emergence of superlattice potentials generated by rotating and stacking individual layers. Here, we report strong signatures of electron localisation in helical trilayer graphene, where the interplay of two moiré patterns gives rise to a moiré-of-moiré superlattice with distinct regions of moiré-periodic and moiré-aperiodic potentials. Remarkably, our measurements reveal the presence of double moiré-induced bands and high-order Brown-Zak oscillations, which are direct reflections of the periodic region with two constituent moiré patterns, and a superimposed anomalous hysteretic signal attributable to the aperiodic region. The data strongly suggest that electron wave functions are partially localised driven by the loss of a periodic lattice potential. Our work provides insight into the effects of spatially inhomogeneous lattice potentials on the low-dimensional electronic states and introduces a promising approach to control electron localisation for practical applications in solid-state devices.

The quantum metric tensor is a central geometric quantity in modern physics that is defined as the distance between nearby quantum states. Despite numerous studies highlighting its relevance to fundamental physical phenomena in solids, measuring the complete quantum metric tensors in real solid-state materials is challenging. In this work, we report a direct measurement of the full quantum metric tensors of Bloch electrons in solids using black phosphorus as a representative material. We extracted the momentum space distribution of the pseudospin texture of the valence band from the polarization dependence of angle-resolved photoemission spectroscopy measurement. Our approach is poised to advance our understanding of quantum geometric responses in a wide class of crystalline systems.

The fundamental characteristics of collective interactions in topological band structures can be revealed by the exploration of charge screening in topological materials. In particular, distinct anisotropic screening behaviors are predicted to occur in Dirac nodal line semimetals (DNLSMs) due to their peculiar anisotropic low‐energy dispersion. Despite the recent extensive theoretical research, experimental observations of exotic charge screening in DNLSMs remain elusive, which is partly attributed to the coexisting trivial bands near the Fermi energy. This study reports the first direct observation of highly anisotropic charge‐screening behavior in the DNLSM SrAs₃. Through atomically resolved conductance measurements, a highly anisotropic charge‐screening pattern around charged impurities on a surface is demonstrated. Moreover, the combination of model studies and first‐principles calculations reveals the unique nature of the screening anisotropy in DNLSMs. The results of this study are expected to pave the way for understanding the profound collective behavior of interacting low‐energy fermions in topological materials.

Understanding the geometric properties of quantum states and their implications in fundamental physical phenomena is at the core of modern physics. The Quantum Geometric Tensor (QGT) is a central physical object in this regard, encoding complete information about the geometry of the quantum state. The imaginary part of the QGT is the well-known Berry curvature, which plays a fundamental role in the topological magnetoelectric and optoelectronic phenomena. The real part of the QGT is the quantum metric, whose importance has come to prominence very recently, giving rise to a new set of quantum geometric phenomena, such as anomalous Landau levels, flat band superfluidity, excitonic Lamb shifts, and nonlinear Hall effect. Despite the central importance of the QGT, its experimental measurements have been restricted only to artificial two-level systems. In this work, we develop a framework to measure the QGT (both quantum metric and Berry curvature) in crystalline solids using polarization-, spin-, and angle-resolved photoemission spectroscopy. Using this framework, we demonstrate the effective reconstruction of the QGT in solids in the archetype kagome metal CoSn, which hosts topological flat bands. The key idea is to introduce another geometrical tensor, the quasi-QGT, whose components, the band Drude weight and orbital angular momentum, are experimentally accessible and can be used for extracting the QGT. Establishing such a momentum- and energy-resolved spectroscopic probe of the QGT is poised to significantly advance our understanding of quantum geometric responses in a wide range of crystalline systems.