Electronic Quantum Materials Simulated with Artificial Model Lattices

Abstract

The band structure and electronic properties of a material are defined by the sort of elements, the atomic registry in the crystal, the dimensions, the presence of spin−orbit coupling, and the electronic interactions. In natural crystals, the interplay of these factors is difficult to unravel, since it is usually not possible to vary one of these factors in an independent way, keeping the others constant. In other words, a complete understanding of complex electronic materials remains challenging to date. The geometry of two-and one-dimensional crystals can be mimicked in artificial lattices. Moreover, geometries that do not exist in nature can be created for the sake of further insight. Such engineered artificial lattices can be better controlled and fine-tuned than natural crystals. This makes it easier to vary the lattice geometry, dimensions, spin−orbit coupling, and interactions independently from each other. Thus, engineering and characterization of artificial lattices can provide unique insights. In this Review, we focus on artificial lattices that are built atom-by-atom on atomically flat metals, using atomic manipulation in a scanning tunneling microscope. Cryogenic scanning tunneling microscopy allows for consecutive creation, microscopic characterization, and band-structure analysis by tunneling spectroscopy, amounting in the analogue quantum simulation of a given lattice type. We first review the physical elements of this method. We then discuss the creation and characterization of artificial atoms and molecules. For the lattices, we review works on honeycomb and Lieb lattices and lattices that result in crystalline topological insulators, such as the Kekuléand "breathing" kagome lattice. Geometric but nonperiodic structures such as electronic quasi-crystals and fractals are discussed as well. Finally, we consider the option to transfer the knowledge gained back to real materials, engineered by geometric patterning of semiconductor quantum wells.

Formation of an Extended Quantum Dot Array Driven and Autoprotected by an Atom-Thick h-BN Layer

“…Considering that h -BN is known to induce an upshift of the Cu(111) surface state by about 0.11 eV due to the weak interaction with the h -BN overlayer, , our observed onset (∼ −0.32 V) of the confined states fits well to the suggestion that Cu(111) surface state electrons are confined beneath the protecting h -BN. We state that the corrugated CuS reconstruction, defining the QD array, is the scatterer responsible for the confinement, analogous to traditional surface state scattering by steps, corrals ,,, and surface reconstructions . This is further assured by high-resolution STM images of previously studied CuS reconstructions on Cu(111), where clear standing wave patterns were displayed. , …”

“…The most prominent target for this has been the Shockley surface state at coinage metal surfaces. Common strategies to fabricate confining nanostructures on these surfaces, in ultrahigh vacuum (UHV), rely on atom-by-atom/molecule-by-molecule manipulation by the tip of a scanning tunneling microscope (STM) , at low temperature (<10 K) or on self-assembly protocols offered by, e.g., supramolecular chemistry principles …”

Size effects on atomic collapse in the dice lattice

“…The present study is motivated by the experiments with electronic lattices such as Lieb [25] and honeycomb with sp hybridization [26,27], which might serve as potential platform to realize also the dice lattice. The artificial lattices of such kind have approximately ten times larger lattice constant that atomically-thin materials and thus much weaker electronelectron interactions.…”

“…In addition, one should note the typical sample size difference between atomic samples and electronic artificial lattices. The latter have a size of order of 10 sites along each side [25][26][27], making the role of edges significant in any studied effect. To analyze the role of size effects on the possibility of observation of atomic collapse we consider quantum dots of circular shape made of dice lattice.…”

Halide Perovskite Artificial Solids as a New Platform to Simulate Collective Phenomena in Doped Mott Insulators

“…The paradigm of quantum simulations , has been pioneered by the development of ultracold-atom systems − and extended to the solid state via nano- and heterostructured ,− devices and, more recently, twisted bidimensional materials. − An additional promising path consists in coupling a quantum material with the photons of a cavity, , which opens the possibility to optically drive and control the emergence of collective phenomena and long-range coherence. Intense efforts are currently being dedicated to the development of photonics-based platforms aimed at replicating the many-body physics of quantum correlated materials.…”