Perspective: Strongly correlated and topological states in [111] grown transition metal oxide thin films and heterostructures

We highlight recent advances in the theory, materials fabrication, and experimental characterization of strongly correlated and topological states in [111] oriented transition metal oxide thin films and heterostructures, which are notoriously difficult to realize compared to their [001] oriented counterparts. We focus on two classes of complex oxides, with the chemical formula ABO3 and A2B2O7, where the B sites are occupied by an open-shell transition metal ion with a local moment, and the A sites are typically a rare earth. The [111] oriented quasi-two-dimensional lattices derived from these parent compound lattices can exhibit peculiar geometries and symmetries, namely, a buckled honeycomb lattice, as well as kagome and triangular lattices. These lattice motifs form the basis for emergent strongly correlated and topological states expressed in exotic magnetism, various forms of orbital ordering, topological insulators, topological semimetals, quantum anomalous Hall insulators, and quantum spin liquids. For transition metal ions with high atomic number, spin-orbit coupling plays a significant role and may give rise to additional topological features in the electronic band structure and in the spectrum of magnetic excitations. We conclude the Perspective by articulating open challenges and opportunities in this actively developing field.


I. INTRODUCTION
Physicists undertake a continuous quest for high quality quantum materials in the thin-film form that harbor interesting many-body phases and are tunable by substrate strain, dimensional control, and compositional modulation. Such systems typically allow for the realization of a complex many-body ground state with multiple entwined correlated and topological states that may-in principle-be tuned as a function of external control parameters, such as external electric and magnetic fields, optical excitations, gating, and pressure.
Over the past decade, transition metal oxide interfaces have been a subject of intense investigation with the prime focus on the complex oxides in the ABO 3 perovskite form (here A is typically a rare earth element, B is an open-shell transition metal element, and O is oxygen). These thin films and heterostructures are predominantly grown along the [001] direction [1][2][3][4][5][6][7][8] . As a vivid illustration of the physical possibilities, some of the [001] oriented interfaces composed of two insulating materials show the emergence of a two-dimensional electron gas (2DEG) with electronic states derived primarily from the dorbitals of the transition metal ions [9][10][11] , rather than the more extended and less weakly correlated s, p-orbitals common to semiconductor interfaces. Compared to the extremely high mobility of carriers in GaAs/AlGaAs heterostructures used to study the fractional quantum Hall effect 12 , the 2DEGs at the [001] oxide interfaces have significantly lower mobility but exhibit markedly stronger electron-electron correlations [13][14][15][16][17][18][19] that enable a richer set of compelling phenomena including the a) Electronic mail: jak.chakhalian@rutgers.edu. b) Electronic mail: xiaoran.liu@rutgers.edu. c) Electronic mail: g.fiete@northeastern.edu. quantum Hall effect 20 , the fractional quantum Hall effect 21 , unconventional superconductivity [22][23][24] , and magnetism 24,25 . The large variety of accessible states in these systems can potentially usher in a new era of oxide electronics that exploit these correlated states 26,27 .
In this Perspective, we focus on a new direction which is still in its infancy -transition metal oxide films templated in highindex (e.g. [111]) directions. Compared to the [001] direction, growth along [111] is more difficult due to the lack of readily available lattice-matched substrates, and less favorable and generally little understood thermodynamics of such growth. The first step in this direction was taken with the ABO 3 perovskites, both on the theoretical [28][29][30][31][32] and experimental sides [33][34][35] . An important motivator was the theoretical prediction that correlated topological states, such as the quantum anomalous Hall state, could be realized in ultra-thin films of [111] oriented perovskites 36 , where the transition metal ions in a bilayer system form a buckled honeycomb lattice. This was an important step because the honeycomb lattice has played a pivotal role in the pioneering theoretical studies of topological states on lattices [37][38][39] .
While the perovskite systems are interesting in their own right, in this Perspective we also focus on the interesting class of compounds A 2 B 2 O 7 which brings an additional element of geometrical frustration, compared to the ABO 3 materials. In A 2 B 2 O 7 compounds, the B sites form a pyrochlore latticea network of corner sharing tetrahedra. Viewed along the [111] direction, the lattice consists of alternating kagome and triangular lattice planes. Both the kagome and triangular lattices lead to magnetic frustration, which can support exotic fractionalized states-a major motivation for experimentally achieving high quality materials growth for such systems. The three-dimensional pyrochlore lattice is fully frustrated as well, and can give rise to fractionalized topological insulators 40  This Perspective is organized as follows. In Sec.II we describe several theoretical proposals for novel electronic states and experimental results in the [111] grown ABO 3 perovskite bilayer, which exhibits a buckled honeycomb lattice. In Sec.III we describe theoretical proposals for novel electronic states and experimental results on [111] oriented A 2 B 2 O 7 . We highlight the challenges of the A 2 B 2 O 7 pyrochlore growth compared to the heavily investigated films of the ABO 3 family. Finally, in Sec.IV, we conclude with an outlook towards possible future routes to investigation of these quantum materials.
We note that we do not aim to present a comprehensive review of this fast moving field, but rather provide our perspective of the challenges and opportunities in this direction. We apologize to those whose work is not prominently featured here or inadvertently omitted.

II. [111] GROWN ABO 3 BILAYER: A BUCKLED HONEYCOMB LATTICE
Conventionally, perovskite films and heterostructures are synthesized along the pseudo-cubic [001] direction. As seen in Fig.1, films grown along the [001] direction consist of alternating AO and BO 2 atomic planes. The same perovskite viewed along the [111] direction exhibits alternating AO 3 and B planes. Interestingly, by growing two pseudo-cubic unit cells of ABO 3 along [111], one can generate an entirely new type of lattice with two vertically shifted triangular planes of B sites (see Fig.  1(b)). This artificially assembled buckled honeycomb lattice provides a unique opportunity to explore new phenomena due to the superposition of complex d-orbitals in a graphene-like setting.
What is the reason for such a dramatic change in the many-body ground state caused by the new lattice motif? To start, we note that both tight-binding models and firstprinciples calculations indicate that d-electrons constitute the majority of states at the Fermi level [28][29][30][31][42][43][44] . Here we focus on the partially filled shells with e g electrons. Unlike [001] oriented perovskites that strongly favor real orbitals, in [111] d-orbitals posses d-wave symmetry (e.g. |d ± id = (|d z 2 ± i|d x 2 −y 2 )/ √ 2) in the orbital space, which in a sufficiently weakly interacting regime also favor complex orbital orderings 31 . In addition, for quarter-filing (e.g. low-spin 3d 7 ), the Fermi level lies right at the Γ-point where two bands touch quadratically forming a so called "quadratic band crossing" (QBC) point 28,29,31 . Moreover, six-fold symmetry at the QBC point protects it against splitting into Dirac points 45 . Finally, since in the e g manifold orbital angular momentum is quenched, the spin-orbit interaction only enters via mixing with t 2g -orbitals in the higher-order terms 46 . These features (the orbital structure of the states, along with the electronic band structure) set the stage for non-trivial theoretical possibilities.
Specifically, due to the buckled graphene-like periodic arrangement of atoms, theoretical calculations for [111]-oriented bilayers of nickelates have predicted the realization of several exotic phases unattainable in either bulk or [001]-oriented  heterojunctions [28][29][30][31][42][43][44]48 . For instance, model Hamiltonian calculations in the strongly correlated limit predicted that orbital ordering wins spontaneously over the bulk-like chargeordered phase, whereas in the weakly correlated limit, a number of topological phases, including the Dirac half-metal phase, the quantum anomalous Hall insulator phase, and spin nematic phase with weak ferromagnetism, all driven by interactions without explicitly large spin-orbit coupling, are feasible. 28,29,31 . The details of these theoretical possibilities have appeared earlier in Ref. [36].
Despite numerous predictions of interesting electronic and topological phases, the number of experimentally realized [111] lattice structures is very limited 49 . To understand this situation, first we remind the reader that the majority of popular perovskite substrates (e.g. SrTiO 3 , LaAlO 3 , NdGaO 3 , and YAlO 3 ) are polar along [111] with alternating +4e/-4e (or +3e/-3e) charges per unit cell for each atomic plane. The large surface charges present a challenge, particularly because the process of initial nucleation and epitaxy on such high energy surfaces is not well understood. In addition, [111] grown bi-layers of perovskites readily demonstrate complex combinations of structural, chemical, and electronic reconstructions, which necessarily develop to compensate for the large electric fields from the polarity jump [49][50][51] . It is important to emphasize that unlike bulk crystals or thicker films, these imperfections in morphology and electronic structure are naturally amplified in a graphene-like monolayer of the material. The presence of top and bottom interfaces which are epitaxially coupled to the active monolayer constitutes another often poorly-understood control parameter.
To shed light on those issues, monolayer-by-monolayer growth has been investigated by monitoring in-situ reflection high-energy electron diffraction (RHEED) during the growth progression of LaNiO 3 on SrTiO 3 (a polar interface) and LaNiO 3 on LaAlO 3 (a non-polar interface) for the case of [111]-oriented substrates 52 . The results revealed that in the polar case a non-perovskite La 2 Ni 2 O 5 phase rapidly develops within the first five unit cells followed by a gradual recovery of the desired LaNiO 3 phase. In sharp contrast, high-quality stoichiometric [111] LaNiO 3 was successfully stabilized on the LaAlO 3 [111] surface; these findings imply that a key to successful [111] growth is in a judicious choice of a film/substrate combination to avoid the polar mismatch at the interface 35 .
In close connection, we can conjecture that a few unit cells of a metallic or semiconducting buffer grown next to the ionic polar surface (e.g. SrRuO 3 , SrVO 3 ) may rapidly screen those charges and internal electric fields to enable layer-by-layer synthesis even in the highly polar cases. This attractive approach, however, may cause ambiguity in the detection and interpretation of emerging metallic states in thin film against a trivial contribution from the conducting buffer layer.
The experimental determination of the electronic, magnetic and structural properties of monolayer thick materials is another demanding venue. Following theoretical predictions [28][29][30][31][42][43][44] , the behavior of 3d 7 electrons on the buckled honeycomb lattice was investigated by resonant soft x-ray absorption on a high quality [111] bilayer of NdNiO 3 capped by 4 unit cells LaAlO 3 templated on a LaAlO 3 [111] substrate. A detailed analysis of the angular dependent linear dichroism revealed the presence of a new ground state characterized by antiferromagnetic correlations and orbital ordering, unattainable in either bulk NdNiO 3 or in analogous heterostructures layered along the conventional (001) direction 53 .
Furthermore, electronic band structure characterization by Angle Resolved PhotoEmission Spectroscopy (ARPES) of an active buried monolayer presents an immense technical challenge and yet is highly desired because it is the most direct probe of topological band structures. The main obstacle standing in the way of such measurements is the fact that conventional probes of electronic structure including ARPES or scanning tunneling spectro-microscopy (STM) are severely limited in their applicability to such systems due to the high surface-sensitivity.
Motivated by these challenges, novel bulk-and buriedlayer-sensitive spectroscopic and scattering techniques, such as soft x-ray angle resolved photoemission spectroscopy (SX-ARPES) 54,55 and hard x-ray photoemission spectroscopy (HAXPES) 56,57 , have recently emerged as viable probes for comprehensive investigations of ultrathin buried layers and interfaces due to their enhanced probing depth 58 .
For instance, recently, Arab et al. applied a combination of SX-ARPES and HAXPES to obtain the momentum-resolved and angle-integrated valence-band electronic structure of an ultrathin buckled graphene-like layer of [111] NdNiO 3 confined between two 4-unit cell-thick layers of insulating LaAlO 3 (see Fig.1c) 47 . The direct measurements of the momentumresolved electronic dispersion of the near-Fermi-level Ni 3d valence states via SX-ARPES (shown in Fig.1d) provided an unambiguous evidence of such antiferro-orbital order and revealed a P1 structural symmetry arrangement in a 1×1 unit cell, consistent with the results suggested by the x-ray linear dichroism (XLD) data 53 . Complementary angle-integrated HAXPES measurements of the bulk-sensitive valence-band density of states (shown in Fig.1e) revealed the presence of a small bandgap of 265 meV, consistent with theoretical predictions. These early results suggest an effective strategy for investigating engineered states of matter even in buried structures of only a few atomic layers thick.
The rather thorough experimental investigation of [111] grown bilayers of NdNiO 3 did not provide evidence for a nontrivial topological state, the most likely of which would be a QAHE state 29,30 . The null experimental result for the topological phase detection is somewhat surprising given that even the inclusion of realistic lattice distortions, such as the rotations of octahedral cages of oxygens surrounding the Ni ions, were included in the calculations and showed no important effect on the presence of topological states 30 .
Our best assessment of why the QAHE state was not realized is that the phase requires a rather fine balance of the on-site interaction energy and Hund's exchange coupling on the Ni atoms 29,30 . The precise values of these quantities are difficult to determine since they depend in detail on the way the system is modeled. In particular, theoretical models typically use a "down folding" scheme in which higher-energy bands are "integrated out" but taken into account in the lowenergy models with effective on-site interaction and Hund's coupling 59 . The higher bands result in a screening effect that reduces the effective interaction and exchange values (which are the ones appearing in a few band model) compared to their "bare" values in a model that includes all the bands from all the atoms. The predicted topological phase lies in a rather narrow range of the on-site interaction and Hund's coupling, and the material may happen to fall out of this range. Another possibility is that the relatively small band gap predicted by theory is overwhelmed by disorder effects in the bilayer systems and magnetic domains form instead of a pristine topological state.

III. [111] PYROCHLORE LATTICE
While the ABO 3 perovskite systems are interesting in their own right, the A 2 B 2 O 7 pyrochlore systems bring in an addition element in the form of geometrical frustration. In these materials, the B sites form a pyrochlore lattice -a network of corner sharing tetrahedra. As seen in Fig.2(d), when viewed along the [111] direction the lattice consists of alternating kagome and triangular lattice planes. Both the kagome and triangular lattices give rise to the phenomenon of magnetic frustration, which can result in exotic fractionalized states with quantum numbers of the electron (such as spin and charge) broken apart or broken down into smaller values 40,41,60 .
The bulk crystal pyrochlore systems have gathered significant attention from both the magnetism 61  topological insulator communities 40,65-75 . Of particular interest to this Perspective are the pyrochlore iridates, A 2 Ir 2 O 7 . In this compound the Ir atom has an outer d-shell with 5 electrons, and sits in an approximately cubic environment, leading to a splitting of the 5d orbital into a subset of lower-lying t 2g orbitals and higher lying e g orbitals, as depicted in Fig.2(b). For heavy elements, like Ir, the spin-orbit coupling is sufficiently strong to lock the spin and angular momentum together producing an effective total angular moment J eff = 3/2 and J eff = 1/2 , though there may be some degree of mixing when the spin-orbit coupling is large 46 . Five electrons in the d-shell thus corresponds to a half-filled J eff = 1/2 state, and parallels can be made to spin 1/2 systems. This feature entwined with the frustrated lattice is a major motivator for theoretical studies of the pyrochlore iridates and osmates. An important general consideration for topological states is the spatial dimension of the system. Certain topological states, such as Weyl semimetals exist in three spatial dimensions, but not two 76 . Thus, the film thickness is an important parameter in the realization of topological states. In the ultra-thin limit, the system is effectively two-dimensional and states such as the QAHE (a zero magnetic field quantum Hall state) are possible. For spin systems (local moments on the lattice), the spatial dimension is also important-the lower the dimension, the larger the quantum fluctuations and hence the easier to achieve even more exotic magnetic ground states such as quantum spin liquids 41,77 .
It is important to note that the vast amount of literature over the last 15 years on topological band structures is largely a subset of what are now referred to more generally as "symmetry protected topological" states or SPT states. For example, timereversal invariant topological insulators with a non-trivial Z 2 invariant require the imposition of time-reversal symmetry to provide a sharp distinction from trivial band insulators with a trivial Z 2 invariant [78][79][80] . Topological crystalline insulators require some additional lattice symmetries, such as a mirror symmetry in the lattice that gives rise to a mirror Chern number, to provide a sharp distinction between the topological and non-topological phases 81,82 . There have also been studies of non-symmorphic space groups 83,84 , and many other discrete symmetries 85,86 .
The three-dimensional Weyl and Dirac systems, which have garnered much interest lately also require certain symmetries to be present for their realization and/or stability. Specifically, the Dirac metals require a four-dimensional irreducible representation of the small groups at specific momenta (for symmetry protection) 87,88 , and the Weyl systems entail either inversion symmetry or time-reversal symmetry breaking 76 . Another important way a Dirac metal can occur is at the phase boundary between a time-reversal invariant topological insulator and a trivial insulator 89,90 . These topological semimetals and their other variants, such as nodal line semimetals, have been reviewed recently 76,91 .
On the experimental front, the ability to grow such pyrochlore systems in thin-film form along the [111] direction offers opportunities to "design" interacting topological materials. In particular, en route to the two-dimensional limit from the three-dimensional limit, one may encounter "hidden" topological states 92 in the electronic band structure. There is now a rather vast literature on predicted topological states in [111] grown pyrochlore iridate thin films 92-97 , and other related systems [28][29][30][31]36,[42][43][44][98][99][100][101][102][103][104][105][106][107] . As we mentioned in the introduction, it is not our intent to provide a comprehensive review, but rather highlight the richness of possibilities in this system.
The fabrication of A 2 Ir 2 O 7 thin films and heterostructures remains extremely challenging due to the existence of several closely related critical issues. To understand them, it is necessary to emphasize the structural and chemical peculiarities of the pyrochlore iridates. First, pyrochlore oxides host geometrically frustrated interpenetrating A and B sublattices, such that the pyrochlore structure can be regarded as an anion-deficient fluorite structure (A 2 B 2 O 7 = [AB] 4 O 7 ), whose A and B cations alternatively occupy the fluorite cation sites along the <110> direction, as illustrated in Fig. 2a. The anion vacancies reside in the tetrahedral interstices between adjacent B-site cations. As a result, defects can naturally enter into the structure, forming off-stoichiometric phases A 2±x B 2±y O 7±δ . Unfortunately, the electronic properties of pyrochlore iridates are very sensitive to the non-stoichiometry; For example, in Eu 2 Ir 2 O 7 , approximately ∼4% of extra Ir is sufficient to entirely suppress the metal-insulator transition 108 .
Another formidable issue lies in the oxidation of iridium, which forms highly volatile gaseous iridium oxides (e.g. IrO 3 ) during the growth. This elicits a dramatic loss of Ir inside the film 109,110 . The inherent Ir volatility acts to strongly magnify the formation of defects, further deviating the structure from the pyrochlore phase towards multiple secondary chemical phases. Here we emphasize that these issues are inherent to growth with all platinum metals, including gaseous phases of platinum, rhodium, iridium, ruthenium and osmium oxides 111 .
Therefore, to stabilize high quality films, one may naturally attempt to grow the films in high vacuum and at low temperature. However, this in turn triggers two other problems. First, due to the low reactivity of Ir metal, Ir 4+ oxidation can only be achieved with great difficulty in the vacuum environment. Secondly, growing materials at low temperatures yields samples with very poor morphological quality.
With the growth challenges described above, layer-by-layer growth of [111]-oriented pyrochlore iridate ultra-thin films has yet to be demonstrated. Nevertheless, significant advances in the fabrication of [ 124 have been steadily demonstrated.
The vast majority of the successfully grown A 2 Ir 2 O 7 thin films have been realized via the so-called "solid phase epitaxy". In this method an amorphous film of the proper stoichiometry is first deposited on a [111]-oriented yttria-stabilized zirconia (YSZ) substrate by pulsed laser deposition or sputtering at reduced temperature and under low-oxygen partial pressure of pure O 2 or Ar/O 2 mixture, followed by ex-situ post-annealing at elevated temperatures to crystallize the amorphous film into the desired pyrochlore structure. Such a two-step growth protocol allows for the fabrication of reasonably high-quality A 2 Ir 2 O 7 films down to a few tens of nanometers albeit with mediocre surface roughness. It should be noted that the growth window for each specific compound is rather narrow, lacks universality, and requires dedicated optimization 112,114,121 .
It is noteworthy that the films obtained by the "solid phase epitaxy" technique exhibit distinctly different transport behaviors from their bulk counterparts. In the bulk most of the A 2 Ir 2 O 7 compounds show a metal-insulator transition (MIT) (except for A = Pr and Bi, which are pure metals) 125 . Concurrent with the MIT, the paramagnetic phase transits into an antiferromagnetic phase with the peculiar all-in-all-out (AIAO) spin configuration stabilized on each cation sublattice. Such a spin configuration has two degenerate domain structures -all-in-all-out (AIAO) and all-out-all-in (AOAI) -that are 'switchable' by time-reversal operation 126 .
Strikingly, not found in bulk, an unusual odd-parity fielddependent term in the magnetoresistance, together with a zerofield offset in the Hall resistance were lately discovered in [111] Eu 2 Ir 2 O 7 thin films below the onset of the MIT 114 . Since the Eu 3+ ion is non-magnetic, the observed exotic phenomena directly reflect the magneto-transport response of the carriers coupled to the localized moments of the Ir sublattice. Specifically, it was argued to originate from the formation of the single AIAO domain defined by the direction of the cooling magnetic field. The observed magnetic domains are exceptionally rigid and once established, switching of domains can no longer be realized by sweeping experimentally accessible external fields 115 .
On the other hand, in pyrochore iridates with magnetic A 3+ ions, because of the strong magnetic coupling between 4 f and 5d moments, switching of the Ir domains is easily accomplished by sweeping the external magnetic field along the [111] direction 127 . The proposed mechanism of domain switching has been captured in [111]  thin films -a temperature much higher than the spin-correlation scale due to Pr moments. Based on these results, the enhancement was speculated to originate from the Ir 5d moments. One argument given by Ohtsuki et al. suggests that [111] epitaxial strain may induce the AIAO magnetic order on the Ir sublattice causing a magnetic Weyl semimetal state to appear in the film 118 . However, as no magnetic reflections associated with the AIAO order were detected by resonant scattering, Guo et al. argued that the spontaneous magnetization is likely due to the localization of the Ir moments, which either creates additional spin chirality or strengthens the effective Pr-Pr coupling via the 4 f -5d interaction 119 . Additionally, linear magneto-resistance (MR) linked to the multiple types of charge carriers was found in [111] Bi 2 Ir 2 O 7 thin films, exhibiting striking resemblances to the scale invariant MR in the strange metal state of high Tc cuprates [121][122][123] .
At this point, the conclusion we draw from these findings in A 2 Ir 2 O 7 films is that the magnetic properties are significantly more complex than those of the corresponding bulk systems. The relative abundance of transport data can be contrasted to the challenges of performing other kinds of advanced measurements. For instance, magnetic neutron scattering is difficult because of the small number of scatterers to get a strong scattering signal and the fact that Ir is a strong neutron absorber 129 . The application of ARPES and STM is challenging due to the problem of in-situ preparing clean and atomically smooth surfaces of pyrochlore films. Furthermore, the potentially rich physics of collective excitations in thin films of Ir pyrochlores is almost entirely unexplored. This is primarily due to the low sample volume (e.g. for inelastic neutrons) and lack of momentum information for probes with high energy resolution (e.g. optical probes). One method that may prove to be sufficiently powerful for these systems is the resonant inelastic x-ray scattering (RIXS) which shows a strong response for Ir 130 .

IV. OUTLOOK
In this short Perspective, we have highlighted some of the key theoretical ideas motivating the drive to produce high quality [111] transition metal oxide thin films. One major point is that the material conditions are ripe for exotic many-body quantum states with topological properties or fractionalized excitations. On the experimental side, we have attempted to lay out some of the key materials fabrication challenges facing thin film growth. We hope our discussion will help other researchers to grasp gaps in our current understanding and see them as attractive opportunities to explore.
We will conclude the Perspective by looking into a possible future. From the materials side, while the current focus is mainly on perovskite and pyrochlore [111] oxides with active d electrons, systems dominated by f electrons can potentially lead to striking electronic and magnetic properties, especially where the d-f interaction is strong. In addition, this methodology can also be applied to structures with more interactive degrees of freedom 131 .
One of the promising candidates is the family of spinels AB 2 X 4 , in which both the A and B sites can be either magnetic or non-magnetic, and the X sites may be an element from the chalcogen family (group 16 of the periodic table). In this structure [111] quasi-two-dimensional slab is composed of alternating stacking of kagome and triangular cation planes with magnetic frustration, leading to the potentially rich and exotic magnetism 132 . Following the same line of thought, we can envision that the current scarcity of high quality Kitaev magnets can be mitigated by the designer approach akin to the graphene lattice derived from [111] perovskites. Finally, a large class of frustrated compounds with tri-fold symmetry including jarosites, wurtzites, and garnets await to be stabilized in the thin film form and investigated for interesting quantum and topological phases 133 .
All in all, as sketched in Fig. 3, designer lattices such as the kagome and other thin film systems with geometrical frustration discussed in this Perspective, offer a new framework to explore some of the most interesting frontiers in contemporary condensed matter physics. Among those, the captivating possibilities of interacting topological states, quantum spin liquids, anyonic matter, fractionalized charge and spin fermions, and flat band superconductivity still lie in wait for their realization.