Metallic delafossite thin films for unique device applications

Metallic delafossites (ABO2) are layered oxides with quasi-two dimensional conduction layers. Metallic delafossites are among the most conducting materials with the in-plane conductivity comparable with that of elemental metals. In this perspective, we will discuss basic properties and future research prospects of metallic delafossites, mainly focusing on thin films and heterostructures. We exemplify the fascinating properties of these compounds such as high conductivity and surface polarity and discuss how it can be utilized in thin films and heterostructures.


INTRODUCTION
Research on quantum materials has deepened our knowledge of condensed matter physics and expanded the choice of materials for future thin-film devices.2][3] In the rigid oxide framework shown in Figure 1, metallic delafossites demonstrate intriguing physical properties driven by high electron mobility and surface polarity.These compounds are also chemically inert and thermally stable, with a decomposition temperature of ~800°C or higher in air. 1 The high stability of metallic delafossites give them great potential for use in thin-film devices.
After an overview of the basic properties of metallic delafossites (section 2), this paper will focus on two important characteristics of these materials with respect to device applications: high mobility/conductivity, which give rise to intriguing transport phenomena (section 3 and 4), and surface polarity, which leads to a large work function and emergent spin polarized surface states (section 5 and 6).While high mobility/conductivity and surface polarity are essentially independent properties, metallic delafossites in characteristic layered crystal structures demonstrate these properties.The physical properties of metallic delafossites have mainly been revealed through the study of bulk single crystals 4 , with limited research on thin films.For metallic delafossites to be used for device applications, it will be crucial to accelerate research on thin films, which includes making heterostructures by design (section 6).For this purpose, as described in section 7, we emphasize the importance of direct imaging of metallic delafossite thin films using spectroscopic imaging scanning tunneling microscopy (SI-STM).

PHYSICAL PROPERTIES OF METALLIC DELAFOSSITES
In this section, a brief overview is given on the physical properties of metallic delafossites.For details, the reader can refer to existing reviews on single crystals, 4,5 thin films, 6 and theory. 7As shown in Figure 1 79 Reprinted with permission from ACS (Copyright 2008, American Chemical Society) electrical conduction: PdCoO2, PdCrO2, PdRhO2, PtCoO2, and AgNiO2. 4Here, we will focus on the first four compounds, in which A + (Pd + or Pt + ) ions mediate electrical conduction, and will refer to them collectively as metallic delafossites.[10] In each layer, A + ions or BO6 octahedra form 2D triangular lattices (Fig. 1(a)-(c)).The A + layers are 2D conductive sheets while the [BO2] − layers are insulating in nature.Because of this layered crystal structure, metallic delafossites show quasi-2D electrical conduction.Conductivity in the ab-plane (ab) of metallic delafossites is generally orders of magnitude higher than along the caxis (c).In the case of PdCoO2 at room temperature, ab ~ 3.8 × 10 7 S/m while c ~ 9.3 × 10 4 S/m.At cryogenic temperatures, the conductivity of PdCoO2 increases by a factor of ~400 for ab, 11 resulting in an electron mean free path length l ~ 21.4 m. 4,12 4][15][16][17][18] The band structure and Brillouin zone of PdCoO2 is shown in Figures 1(d) and (e).The dispersive band that crosses the Fermi level is predominantly attributed to Pd 4d and Pd 5s states. 19These electronic states form the nearly cylindrical Fermi surface shown in Figure 1(f), reflecting the quasi-2D electrons in the Pd layers.
Regarding magnetic properties, PdCrO2 shows antiferromagnetic transition with the Néel temperature TN ~ 37.5 K while the bulk states of PdCoO2, PdRhO2, and PtCoO2 are nonmagnetic. 4In PdCrO2, the Cr 3+ ions have localized spins with S = 3/2. 20,21 s shown in Figure 1(c), the CrO6 octahedra form geometrically frustrated 2D spin triangular lattices, which influence the high-mobility electrons in the Pd sheets and cause an unconventional anomalous Hall effect. 20[24] 3. HIGH MOBILITY AND HIGH DENSITY QUASI-2D ELECTRONS As described in section 1, one of the most remarkable characteristics of metallic delafossites are their high electrical conductivity.Figure 2 compares the metallic delafossites and various high-mobility 2D electronic systems: 2D materials, quasi-2D materials, and 2D electrons at surfaces/interfaces (Figs 2(a)-(c)).As shown in Fig. 2(d), currently known high mobility electronic systems have relatively low carrier densities of n2D < 10 14 cm -2 .In contrast, metallic delafossites, plotted in red in Fig. 2(d), are high mobility quasi-2D systems with comparably high carrier densities of n2D ~ 10 15 cm -2 .Thus, metallic delafossites are unique and ideal for exploring mesoscopic electrical transport phenomena in high mobility, high carrier density materials (Fig. 2(d)).
To compare the cleanness of 2D conduction channels, mean free path l is plotted in Fig. 2(e) for the same set of data as Fig. 2(d).The mean free path of metallic delafossites compares well with most of high-mobility materials, showing exceptional cleanness of the conduction channels of metallic delafossites (Fig. 2(e)).As demonstrated by PdCoO2 single crystals at cryogenic temperatures, the 2D electrons in Pd sheets have impressively long electron scattering lengths, with an electron mean free path length l ~ 21.4 m 12 and a phase coherence length l > 10 m. 17 An interesting consequent phenomenon observed for the high-mobility electrons in PdCoO2 is hydrodynamic electron flow. 13The flow of electrons in solids is normally far different from the hydrodynamic flow of an ordinary fluid like water.In ordinary conductors, electrons are scattered by phonons and impurities, resulting in momentum relaxation and the generation of resistance.On the other hand, if the total momentum of electrons is conserved inside a conductor and is predominantly relaxed at the edges, electrical transport resembles the hydrodynamic motion of a fluid.To achieve this, the rate of momentum-relaxing scattering inside a conductor (electron-impurity, electron-phonon, and Umklapp scattering) should be minimized.In this situation, the channel resistance is partly given by the viscosity of electron fluid.The viscosity of electron fluid is governed by the rate of momentum-conserving electronelectron scattering.This was recently demonstrated by Moll and colleagues who fabricated microchannels in PdCoO2 single crystals using a focused ion beam (FIB) technique. 13The low rate of momentum-relaxing scattering in ultrapure PdCoO2 single crystals results in electrical transport through these microchannels that can be described as hydrodynamic motion. 13,25 urthermore, various mesoscopic high mobility electrical transport phenomena, such as ballistic 16,18,26 or phase-coherent transport 17 , have been demonstrated in high-purity single crystals of PdCoO2.
Along with the above-mentioned transport phenomena, the high carrier density in metallic delafossites is predicted to cause additional physical effects.Because of the high carrier density, the Fermi surfaces of metallic delafossites are considerably larger than other quasi-2D systems, such as semiconductor heterostructures (Fig. 1(f)).This can cause the many-body effects, such as quasiparticle formation and/or an anisotropic Fermi surface shape, to appear with the high mobility transport phenomena.For example, because of the large hexagonal cylindrical Fermi surface, the trajectory of ballistic transport is not isotropic as in ordinary 2D systems but highly directional and dominantly oriented in six directions (Fig. 3(a), (b)). 16,18,26 Intifying exotic consequences of many-body effects in mesoscopic electrical transport is an intriguing challenge, which may be facilitated by real-space probing techniques (section 7).
While mesoscopic electrical transport phenomena in metallic delafossites have been mainly studied in FIBpatterned bulk single crystals, these fascinating transport properties are motivating thin-film researchers to grow high-purity PdCoO2 in order to make mesoscopic devices using conventional lithography techniques.Once realized, exotic transport in thin films could be expanded to the study of spin transport or the superconducting proximity effect by making thin-film heterostructures, as will be discussed in section 6 and 7. Signatures of phase-coherent transport in PdCoO2 thin films have already been reported in mesoscopic structures. 27Although the l and l of thin-film mesoscopic structures are currently l ~ 100 nm and l ~ 10 nm, 27 improving thin film quality could extend these scattering lengths.

TOWARD THIN FILMS WITH HIGH ELECTRON MOBILITY
In this section, we will discuss the possibility of achieving high electron mobility metallic delafossite thin  80,81 Quasi-2D materials: bulk single crystals of PdCoO2 (red circle), PtCoO2 (red square), and PdCrO2 (red diamond) at 4 K 12 and graphite (green hexagon) at 4.2 K 82, 83 or 3 K. 84 Semiconductor interfaces: (Al,Ga)As/GaAs heterostructures (black diamonds), 85,86 SiGe/Si quantum wells (QW, brown open circles) at 0.3 K, 87 (Mg,Zn)O/ZnO heterostructures (purple uppointing triangles) at 500 mK or ≤ 100 mK, 88 (Al,Ga)N/GaN heterostructures (green down-pointing triangles) at 20 K 89 or 0.3 K, 90 and SrTiO3-based heterostructures (blue circles) at low temperature. 91Surfaces of topological insulators: the surface states (SS) of Bi2Se3 at 1.5 K. 92 For the quasi-2D systems, the sheet carrier density for a single conductive layer is calculated as n2D = NdML using the carrier concentration N and the interlayer distance dML schematically shown in (b).
The carrier mobility of PdCoO2, PtCoO2, and PdCrO2 are calculated as  = 1/eN, where e is elemental charge and  is resistivity.The reported ab-plane resistivity is used for .(e) Mean free path l of charge carriers in the same materials as (d).2]84 For the other materials, the mean free path l is calculated using the formulas for circular Fermi surfaces around valleys:  = where ℏ is the reduced Planck constant, kF is the Fermi wave vector, gs is the spin degeneracy, and gv is the valley degeneracy.For SrTiO3 heterostructures, the non-circular 2D Fermi surface could result in deviation from the calculated l.We also note that the mean free path is proposed to be limited by the sample size for the graphene data. 80,81 .Metallic delafossite thin films were first fabricated in the 1980s by annealing amorphous precursors deposited by sputtering. 28Recently, several groups have reported the fabrication of c-axis oriented thin films of PdCoO2, [29][30][31][32][33] PdCrO2, [33][34][35] and PtCoO2 33 by pulsed laser deposition (PLD), 29,31,34 molecular beam epitaxy, 30,32 and solutionbased processes. 33s it possible to increase the electron mobility of thin films to the level of single crystals?With the exception of metallic delafossites, studies on the resistivity of thin metal films have a long history.Studies on elemental metals such as Au, 36 Pt, 37 Co, 38 and Cu 39,40 have shown that the resistivity of metals scales with thin film thickness and generally increases as thickness is reduced down to a few nanometers, which can be explained by the surface scattering of electrons.According to theory, the resistivity,  of three-dimensional metals is expected to increase as the thickness, d, decreases, with  ∝ 1/[dln(lbulk/d)], 41,42  ∝ 1/d, 40 or  ∝ 1/d 2 , [43][44][45] depending on the model, where lbulk is the bulk mean free path.
Because of the quasi-2D nature of PdCoO2, a reduction in thickness may not cause a serious surface scattering effect since electron mobility could be maintained, as seen in other quasi-2D systems like graphite.The directional transport effect found in single crystals of PdCoO2 is an encouraging result that supports this hypothesis.According to transport measurements of PdCoO2 single crystals, 16,18,26 the ballistic transport of electrons is highly anisotropic, reflecting the hexagonal cylindrical shape of the Fermi surface.The spherical Fermi surfaces of alkali metals are compared with those of PdCoO2 in Figure 3(a) and (b).
The velocity of electrons, vn, is expressed as, , where n is the band index, k is the wavevector, ħ is the reduced Planck constant, and n(k) is the energy of an electron with k in the n-th band. 46The Fermi velocity, vF, is therefore perpendicular to the Fermi surface and is isotropic in alkali metals that has additional one electron to the closed-shell configuration.In contrast, the vF of PdCoO2 is dominantly oriented in six directions in the abplane (Fig. 3, top).Because of the directional ballistic transport, c-axis oriented thin films of metallic delafossites may not be significantly affected by surface scattering (Fig. 3, bottom).Although the warping in the Fermi surface of PdCoO2 causes a finite component of vF and sets a limitation to the above discussion, 47 the nearly cylindrical Fermi surface of PdCoO2 should be a predominant advantage for achieving long mean free path in thin films.Table 1 summarizes the challenges toward highmobility thin films of metallic delafossites and reported approaches.So far, PdCoO2 is most studied for thin films among the metallic delafossites.For MBE growth, the substrate temperature ranges in 300-480°C under atomic oxygen plasma 30 or distilled ozone.32 The room-temperature ab-plane resistivity ab of the PdCoO2 thin films reported to date is about 2-5 times higher than that of the bulk single crystal (ab = 2.6 cm). 6,29 he low-temperature resistivity has been reported for these thin films.The largest residual resistivity ratio (RRR) for PdCoO2 of 16 has been reported in a thick (~180 nm) MBE-grown PdCoO2 thin film that is postannealed at 800 °C in oxygen. 30The RRR of 16 in the PdCoO2 thin film is still small compared with the bulk value (RRR~400). 11o improve the thin-film quality, dominant scattering sources should be clarified.One of the possible dominant scattering sources is twin boundaries.For c-axis oriented thin-film growth of metallic delafossites, Al2O3 substrates are widely used.As the surface of Al2O3 substrates is effectively 6-fold symmetric, the reported thin films have crystal twins that are 180°-rotated from each other. 29,30,32 Tse twin boundaries can scatter electrons.Growing single crystal thin films without twin boundaries could dramatically improve electron mobility.Although various promising approaches, as listed in Table 1, to achieve this using single crystal substrates with delafossite structures 48 or twin-free delafossite buffer layers 49 have been reported, twin-free thin films have not realized.Toward twin-free thin films, stacking faults need to be also suppressed.
Other possible scattering sources include point defects caused by impurities, cation off stoichiometry, and oxygen vacancies.As the RRR of thin films have not been significantly dependent on the purity of the material sources (PLD targets, MBE sources), 32, 50 impurity scattering seems not a dominant scattering mechanism in the current metallic delafossite thin films.Increase of RRR by post annealing could be due to the reduction of oxygen vacancies as well as improved atomic ordering in the crystal.Post-annealing temperature is limited by the decomposition temperature of metallic delafossites (800-925°C).Alternative approach such as thin-film growth techniques based on chemical reactions could be promising to improve atomic ordering as they may mimic the bulk synthesis of pure single crystals. 33,51  a potentially low-cost and wide-area deposition technique that is important for application, solution-based growth on 2-inch wafers has been reported for PdCoO2, PdCrO2, PtCoO2. 33Regarding device fabrication, PdCoO2 has been successfully patterned into submicron scales by conventional electron beam lithography and Ar-ion Substrates with low symmetry surfaces -Ga2O3 (-201) (ref. 55) SrTiO3 (111) (ref. 49) Buffer layers: CuCrO2 (ref. 34,49 Delafossite-type substrates: CuFeO2 (ref. 48

PdCoO2
Oxygen vacancies Post annealing in air or O2 improves RRR (ref. 30) MBE in atomic oxygen plasma 30 or ozone 32

PdCoO2
Atomic ordering Post annealing in air or O2 improves RRR (ref. 30)

Chemical growth method
Solution-based growth 33 Atomic layer deposition 51

PdCoO2
Table 1.Challenges in growth and processing of metallic delafossite thin films and tested approach milling. 27As discussed in the sections 5 and 6, search for novel heterostructures is important to find a possible application of metallic delafossites.

POLAR SURFACES FOR DEVICE APPLICATIONS
Along with high electron mobility/conductivity, the surface polarity of metallic delafossites is also highly significant as it permits an exceptionally large work function, which is beneficial for device applications.According to the classification by Tasker, 52 the c-plane surfaces of metallic delafossites are classified as type-3 polar surfaces. 6As a result, the surface properties of metallic delafossites strongly depend on the termination layer of the surface (e.g., Pd or CoO2 layer).Recent surface measurements of cleaved PdCoO2 showed that the work function of a Pd-terminated surface (m Pd ) was ~4.7 eV while a CoO2-terminated surface (m CoO2 ) was ~7.8 eV, indicating that the work function of PdCoO2 is highly dependent on the termination layer. 53The large difference between m Pd and m CoO2 is due to the polar surface.A work function of ~7.8 eV is very large for a metallic compound and far exceeds the Pt work function (~5.65 eV), which is the largest value found in elemental metals. 54e large work function of PdCoO2 should be of great value for various device applications, such as for electrodes for semiconductor devices.In Figure 4, the work function of PdCoO2 (m Pd and m CoO2 ) is compared with the conduction band minimum (CBM) and valence band maximum (VBM) of various semiconductors.In semiconductor devices, Schottky junctions formed at metal/semiconductor interfaces often play key roles in device operation.According to the Schottky-Mott relationship, the ideal Schottky barrier height of metal/ntype semiconductor interfaces, b,n, is estimated to be b,n = m − , where m is the work function of a metal and  is the electron affinity of a semiconductor.As shown in Figure 4, the difference between m CoO2 and  of various semiconductors is as large as several eV.Therefore, large Schottky barrier heights can be achieved in PdCoO2/n-type semiconductor polar interfaces, as demonstrated by PdCoO2/-Ga2O3 [55][56][57] and PdCrO2/-Ga2O3 junctions. 35he large Schottky barrier height would be useful for diodes for high-temperature operation and Schottky gates for transistors.Careful control of the initial growth layer would be important to generate an interface with a homogeneous Schottky barrier height.

FIG. 4.
The band alignment of semiconductors compared with the work function of Pd-terminated (m Pd ) 53,55 and CoO2-terminated (m CoO2 ) 53 PdCoO2.The valence and conduction bands of the various semiconductors are shown in green and blue, respectively.For Si, the electron affinity (), the bandgap (Eg), the conduction band minimum (CBM), and the valence band maximum (VBM) are noted.The band alignment is drawn based on the reported bandgap and the electron affinity for Si, 93 GaAs, 93 ZnO, 93,94 4H-SiC, 95 GaN, 96 -Ga2O3, 97,98 and oxidized diamond surfaces. 99,100  ZnO and GaN, the CBM and VBM are shown with bars, which are reported to depends on the surface termination. 94,96 neral, ohmic contacts with low contact resistance are important to reduce power loss in wide bandgap semiconductor devices.Making low resistance contacts to p-type wide bandgap semiconductors is often a challenge, particularly when the hole concentration is low.In the Schottky-Mott relationship, the Schottky barrier height of a metal/p-type semiconductor interface is b,p =  + Eg − m, where Eg is the bandgap of the semiconductor.To achieve a true ohmic contact (b,p < 0), one needs a metal with m >  + Eg.For wide bandgap semiconductors such as 4H-SiC (Eg ~ 3.2 eV) and GaN (Eg ~ 3.4 eV),  + Eg is well above 6 eV, and there is no elemental metal electrode that satisfies m >  + Eg.As shown in Figure 4, PdCoO2 with a CoO2 initial layer is a promising candidate for a true ohmic contact for wide bandgap semiconductors since m CoO2 is larger than the  + Eg of semiconductors with ptype doping (Si, GaAs, ZnO, 4H-SiC, GaN, and diamond).

SURFACE SPIN STATES
Surface polarity also causes emergent spin polarized surface states.In general, to electrostatically stabilize the polar surface, charge compensation occurs. 52,58,59 Tis causes the electron density at the surface to differ from that of the inner bulk.Recent experiments have indicated that charge compensation changes the surface of the inherently nonmagnetic PdCoO2 to have spin-dependent electronic states.
The surface electronic states of PdCoO2 have been calculated using a density functional theory (DFT)-based method. 60Owing to the electronic reconstruction induced by the surface polarity, a Pd-terminated surface of PdCoO2 was proposed to have surface magnetism. 60The calculation also predicted that the Co-derived bands at a CoO2-terminated surface are split because of the spin-orbit interaction. 60unko and colleagues observed the BO2-terminated surfaces of PdCoO2, PtCoO2, and PdRhO2 by angleresolved photoemission spectroscopy (ARPES) and discovered Rashba-like spin splitting, 22 which is caused by strong inversion symmetry breaking on the BO2terminated surface.Spin splitting is comparable to atomic spin-orbit coupling of B-site cations.Mazzola et al. reported the surface ferromagnetic states at Pd-terminated surfaces of PdCoO2 by ARPES. 23Ferromagnetism has also been detected in PLD-grown PdCoO2 thin films by ARPES and the anomalous Hall effect. 24From the magnetoresistance measurements under the in-plane magnetic field, the Pd-terminated surface of PdCoO2 also has Rashba-spin splitting with a Rashba coefficient ~ 0.75 ± 0.3 eV. 61Possible coexistence of ferromagnetism and Rashba spin-orbit coupling will be an interesting subject for future studies in the context of spin-orbitronics. 62ere we will discuss the prospects of using the Rashba ferromagnetic surfaces of metallic delafossites.We performed DFT calculations of a Pt-terminated PtCoO2 surface (Fig. 5) and found similar properties to that of PdCoO2.In the nonmagnetic calculation, Rashba-like split bands were observed around the  point.Furthermore, the flat region of the conduction band shifted close to the Fermi level, which may cause Stoner splitting, as with PdCoO2. 23n the calculation considering collinear spin polarization, the bands around the  point were spin-split.The Rashba effect visible in the nonmagnetic calculation was more pronounced in PtCoO2 compared with that in PdCoO2 because of the larger atomic spin-orbit coupling in Pt than in Pd (Fig. 5(a)).
Surface spin-split electronic states can be utilized in heterostructures to induce exotic electronic states.For example, making a heterostructure with a superconductor may be interesting.As a model system that could show topological superconductivity, a 2D electronic system with relatively large spin-orbit coupling, effective Zeeman coupling, and proximity-induced superconductivity has been proposed. 63,64 he model Hamiltonian can be written as H(k) = H0(k) + HR(k) + HZ + HS, where H0 is kinetic energy, HR is the Rashba spin-orbit interaction, HZ is the effective Zeeman interaction, and HS is the spin-singlet swave pair potential. 64At the surface of PtCoO2 or PdCoO2, there can be a relatively large spin-orbit coupling HR(k) and Including spin-orbit interaction can give rise to noncollinear spin textures and require larger supercells for calculation.A symmetric slab model containing nine Pt and eight CoO2 layers with a vacuum gap of 15 Å is employed for the calculation, following a report on PdCoO2. 23The inner five Pt and four CoO2 layers are fixed to have the lattice constants of bulk single crystals. 4The outer four Pt and four CoO2 layers were relaxed.For both (a) and (b), the generalized gradient approximation and Perdew-Burke-Ernzerhof (GGA-PBE) functionals are used, and the Hubbard U is not taken into account.
Stoner splitting (i.e., effective Zeeman coupling, HZ) in a nearly 2D conduction channel.Inducing superconductivity HS by the proximity effect and applying a magnetic field to adjust HZ might induce topological superconducting states.

REAL SPACE PROBING OF ELECTRONIC STATES
To search for exotic electronic states in metallic delafossite, it is important to understand the external magnetic field dependence of electronic states.An ideal experimental approach for this purpose is SI-STM, which has a unique capability to resolve differential conductance (dI/dV(r,E,B)) that is proportional to the density of state bellow and above EF, as a function of position r with atomic precision, energy E, and magnetic field B. [65][66][67][68][69][70] SI-STM has been applied to the polar surfaces of PdCoO2 bulk single crystals.On CoO2-terminated surfaces of PdCoO2, long-lived quasiparticle states have been visualized as extended six-fold standing waves. 53This observation is consistent with the anisotropic hexagonal cylindrical Fermi surface of high mobility electrons (Fig. 3(b)).The observed standing waves have been interpreted by considering the large Rashba-like band splitting driven by strong inversion symmetry breaking. 53On Pd-terminated surfaces of PdCoO2, SI-STM has revealed the formation of charge density waves 71 and renormalized electronic states that are coupled with magnons. 72o further understand the electronic states of PdCoO2 surfaces, SI-STM under external magnetic fields would be informative.As discussed in section 6, metallic delafossites are expected to contain characteristic surface spin states.On Pd-terminated surfaces of PdCoO2 (and possibly in PtCoO2), the possible coexistence of and HZ may give rise to spin-momentum coupled electronic structures with a HZ-derived gap at the band crossing point (Fig. 5).Such spin-momentum coupled band structures with surface ferromagnetism could respond to external magnetic fields with controlled magnitude and direction. 73,74 Fr example, studies on magnetic-field dependent standing wave patterns and spatially averaged dI/dV(E) shapes could reveal the spin-momentum coupled states of PdCoO2.As SI-STM can visualize spin texture with atomic resolution in real space [75][76][77][78] , searching for topological magnetism on the surface of metallic delafossites is an exciting prospect.
To the best of our knowledge, all SI-STM studies reported to date were performed on cleaved surfaces of single crystals.By applying SI-STM to metallic delafossite thin films (Fig. 6), we would be able to investigate the electronic states of heterostructures with other materials, such as the superconductors discussed in section 6.Furthermore, as with other layered materials, monolayerthick metallic delafossites may also be an interesting system for SI-STM study.
Finally, another important task is to identify the scattering sources that limit electron mobility of thin films.The electronic scattering response to twin-domain boundaries and point defects could be visualized by SI-STM, which would provide feedback for thin-film growth optimization.The combination of thin-film growth and real-space imaging techniques may lead to high-mobility thin films, facilitating research into unexplored phenomena in ultrathin films and heterostructures.

CONCLUSION
In this article, we have provided an overview of the physical properties of metallic delafossites and discussed the perspectives of thin-film research.Inherent high mobility and surface polarity make metallic delafossites fascinating materials for both basic and application studies.In particular, mesoscopic electrical transport, many-body effects derived from Fermiology, and the interplay of these may lead to intriguing unexplored phenomena.Thin film growth of metallic delafossites would provide tremendous research possibilities for the design of heterostructures and functional devices.The author would like to thank Prof. A. Tsukazaki and all collaborators for their contributions to this work on metallic delafossites.This work was supported by a Grantin-Aid for Scientific Research (B) (20H02611), a Grant-in-Aid for Challenging Research (exploratory) (20K21138) from the Japan Society for the Promotion of Science (JSPS), MEXT Leading Initiative for Excellent Young Researchers (JPMXS0320200047), JST PRESTO (JPMJPR20AD), Izumi Science and Technology Foundation, and the Foundation for The Promotion of Ion Engineering.

FIG. 6.
A conceptual figure for spectroscopic imaging scanning tunneling microscopy (SI-STM) on metallic delafossite thin films and heterostructures.SI-STM is able to visualize electronic states with ultra-high spatial and energy resolution under controlled external magnetic fields.
FIG. 1.(a) The crystal structure of metallic delafossites ABO2.The A + and [BO2] − layers are noted.(b) The crystal structures of A + layers and (c) the [BO2] − layers.(d) The electronic band structure, (e) the Brillouin zone of the hexagonal unit cell, and (f) the Fermi surface of PdCoO2 calculated by density-functional theory (DFT) in the generalized gradient approximation (GGA). 79Reprinted with permission from ACS (Copyright 2008, American Chemical Society)

FIG. 3 .
FIG. 3. (a) A spherical Fermi surface (top) and a schematic of electrons travelling with vF in a thin film with thickness d (bottom).(b) A schematically drawn hexagonal Fermi surface of PdCoO2 (top) and electrons travelling with vF along the conductive layer of Pd (bottom).The total thickness of the thin film is noted as d.We note that the warping in the PdCoO2 Fermi surface results in finite component of vF perpendicular to the conductive layer.

FIG. 5 .
FIG. 5.The electronic structure of the slab model for a Ptterminated PtCoO2, calculated by density functional theory (DFT) using the CASTEP package.The vertical axis is the energy relative to the Fermi level (EF).(a) The nonmagnetic calculation result considering spin-orbit coupling (SOC).(b) The calculation result considering collinear spinpolarization.The red and blue lines correspond to the spinup and spin-down states, respectively.For (b), SOC is not included because of the limitation of our computer setup.Including spin-orbit interaction can give rise to noncollinear spin textures and require larger supercells for calculation.A symmetric slab model containing nine Pt and eight CoO2 layers with a vacuum gap of 15 Å is employed for the calculation, following a report on PdCoO2.23The inner five Pt and four CoO2 layers are fixed to have the lattice constants of bulk single crystals.4The outer four Pt and four CoO2 layers were relaxed.For both (a) and (b), the generalized gradient approximation and Perdew-Burke-Ernzerhof (GGA-PBE) functionals are used, and the Hubbard U is not taken into account.