Emergence of quasiparticle Bloch states in artificial crystals crafted atom-by-atom

Abstract

The interaction of electrons with a periodic potential of atoms in crystalline solids gives rise to band structure. The band structure of existing materials can be measured by photoemission spectroscopy and accurately understood in terms of the tight-binding model, however not many experimental approaches exist that allow to tailor artificial crystal lattices using a bottom-up approach. The ability to engineer and study atomically crafted designer materials by scanning tunnelling microscopy and spectroscopy (STM/STS) helps to understand the emergence of material properties. Here, we use atom manipulation of individual vacancies in a chlorine monolayer on Cu(100) to construct one-and two-dimensional structures of various densities and sizes. Local STS measurements reveal the emergence of quasiparticle bands, evidenced by standing Bloch waves, with tuneable dispersion. The experimental data are understood in terms of a tightbinding model combined with an additional broadening term that allows an estimation of the coupling to the underlying substrate. Atom manipulation by means of STM is a viable way of constructing atomically precise artificial structures [1]. Among others, the technique can be used to engineer atomic scale logic devices [2,3], low dimensional magnetic systems [4][5][6] or atomic data storages [7][8][9]. As our abilities to manipulate atoms on a large scale are improving, the formation of atomically designed artificial crystals becomes of particular interest driven by a demand for new materials where the properties are defined by emerging quasiparticle states [10]. Common approaches to build low-dimensional artificial materials by STM include confinement of electronic surface states through precise assembly of individual atoms and/or molecules [11][12][13][14], self-assembly of molecular networks [15,16] and manipulation of dangling bonds [17] or surface vacancies [18]. The recent development of large-scale fully automated placement of atomic vacancies on a chlorinated copper crystal surface [9] provides an excellent platform to explore various lattice compositions. These vacancies were found to host a localized vacancy state in the surface band gap, similar to dopants in semiconductors, allowing their combined electronic states to be modelled by means of tight-binding approximation [19]. 1SciPost Phys. 2, 020 (2017) Here, we present a study of artificial one-and two-dimensional structures built from Cl vacancies in an otherwise perfect monolayer square lattice formed by chlorine atoms on a Cu(100) surface. Using local electron tunnelling spectroscopy, we demonstrate that we are able to reach system scales where the spectral properties no longer depend on size and which we therefore consider to be in the limit of infinite lattice size. For structures with a sufficiently large vacancy density, we observe quasiparticle Bloch waves that can be simulated by using a tight-binding model. Similar wave patterns were reported previously in assembled chains of Au atoms [14], which were best descr...

Symmetry breaking in molecular artificial graphene

“…The unique physics of Dirac quasiparticles can be mimicked in artificial graphene (AG) systems [1]. These AG systems include cold atom lattices [2][3][4][5][6], phononic crystals [7][8][9][10], photonic crystals [11][12][13][14][15][16], semiconductor nanopatterns [17][18][19][20][21][22] and molecular lattices assembled on metal surfaces, termed as molecular designers [23][24][25][26][27][28][29][30][31][32][33][34]. The tunability of the artificial systems makes them ideal playgrounds to exploit phenomena that are extremely challenging to access in real materials.…”

“…The tunability of the artificial systems makes them ideal playgrounds to exploit phenomena that are extremely challenging to access in real materials. For example, Kekulé structure, graphene pn junctions, deformed graphene, graphene nanoribbons, point and line defects, topological domain wall states, Lieb lattice, quasicrystalline structure, and fractal electronics have been realized in molecular designers [23][24][25][26][27][28][29][30]. These systems exhibit exciting physics such as Gauge field, edge states and flat band [35][36][37][38], to name a few.…”

Creating designer quantum states of matter atom-by-atom

“…One important aspect to mention, is the effect of finite size. This was studied systematically for 1D and 2D Cl vacancy lattices, as well as for CO on Cu(111) 5,14 .…”

“…QWS built bottom-up have been investigated in a variety of manipulated chains derived from coupled adatoms on metallic, nearly insulating, and semiconducting surfaces 2,7,94-99 . Moreover, induced atomic-scale defects, which exhibit a degree of charge localization, have also been utilized to create QWS, for example from dangling bonds derived from dehydrogenated silicon atoms 11 and by controllably coupled Cl vacancies 4,14 . A characteristic example is shown in Fig.…”

Topological states on fractal lattices

“…That the topology of quantum states can be defined in the absence of spatial regularity over long distances opens the door to finding topological phases on fractal lattices, which lack a natural distinction between bulk and boundary, and whose (typically non-integer) Hausdorff dimensions differ from their topological dimensions. Interest in fractal structures, which have a rich history [51][52][53][54][55][56] , has been revived given experimental advances in creating and manipulating synthetic lattices with arbitrary structures, in both photonic and electronic systems [57][58][59][60][61][62] . In particular, fractal lattices have been fabricated using focused ion beam milling 63 , molecular chains [64][65][66] , and scanningtunneling-microscopy (STM) techniques 67 , with theoretical studies primarily focusing on localization and transport phenomena [68][69][70][71][72][73] .…”