Angle-resolved photoemission spectroscopy for the study of two-dimensional materials

3.1 2H-MoS\(_2\), WS\(_2\), MoSe\(_2\), WSe\(_2\)

The semiconducting 2H-phase TMDCs MX\(_2\) (M = Mo, W; X = S, Se) are arguably the most studied 2D materials beyond graphene. They have attracted intense interest since the observation of much enhanced photoluminescence in monolayer MoS\(_2\) [7, 8], which is interpreted in terms of a transition from an indirect gap semiconductor to a direct band gap semiconductor when the thickness is reduced to the monolayer. The interesting physical property is not limited to the band gap transition and potential applications based on that, such as photoharvesting [85, 86] and photodetection [87] devices. It includes the spin-splitting of the valence band (VB) [88, 89], a well-pronounced valley degree of freedom [90–93], a charge density wave (CDW) state at the mirror twin domain boundaries [94], as well as the gigantic exciton binding energy that governs their optical spectra [95–97].

ARPES can directly show the changes in electronic structure when the thickness is varied from monolayer to thicker layers. Figure 3 summarize the results from Ref. [98], in which the layer-by-layer band structure evolution is directly mapped using in situ ARPES on MBE grown MoSe\(_2\) samples on bilayer graphene substrate. The main feature of the band structure variation is the change in the number of the \(\varGamma\) point branches and concomitant change of the VB maximum from K to \(\varGamma\) when thickness increases from monolayer to bilayer. With the conduction band being at the K point regardless of the number of layers, as probed by chemical potential shift through surface potassium doping, this immediately indicates a transition from a direct band gap semiconductor to an indirect band gap semiconductor. These observations match well with the first principle calculations [88, 98], although exact position of the conduction band minimum varies depending on the calculation methods [99]. Another important aspect is the spin splitting at the K point ~180 meV for MoSe\(_2\) and \(\sim\)470 meV for WSe\(_2\) [100]. The latter is larger due to the stronger SOC induced by a heavier element W. ARPES studies on epitaxial grown 2H-MX\(_2\) films can be found for WSe\(_2\) on bilayer graphene [100], MoS\(_2\) on Au(111) [101, 102], and WS\(_2\) on Au(111) [103]. They also report the effect of surface potassium doping, which is not only shifts the chemical potential but modifies the band structure [104, 105] allowing yet another parameter to control the electronic structure of semiconducting TMDCs.

There have been quite a few ARPES studies on the bulk samples of 2H-MX\(_2\) samples [104, 106–111]. The issue here is to determine the band parameters precisely, such as the size of the electron removal gaps at the \(\varGamma\) and K points and the size of the spin-splitting at the K point, and to figure out the origin of apparent discrepancies among the values from different probes and different theory calculations. One notable finding is that the size of the band gap and the position of the conduction band minimum is extremely sensitive to the c / a ratio [99, 110] of the lattice constants.

Mechanically exfoliated samples and CVD grown samples of 2H-MX\(_2\) and their heterostructures with other 2D materials have been successfully measured with nano-ARPES [99, 106, 112–118]. While the spectra from nano-ARPES do show the essential features expected from the band structure of few-layer 2H-MX\(_2\), they also suffer from the limited resolution by allowing maximum photon flux to compensate the loss caused by the focusing optics. On the other hand, nano-ARPES gives a much more flexibility in studying the heterostructures of 2D materials, expanding the boundary of sample preparation for ARPES measurements. Of particular interest, nano-ARPES studies on the graphene/MoS\(_2\) heterostructure [114, 115] report a strong hybridization between MoS\(_2\) and graphene, which is evidenced from the opening of hybridization gaps in the bands located at high binding energies. This is not consistent with the ARPES data on MBE grown MoSe\(_2\) on graphene [98], for which such hybridization has not been found, suggesting that the interaction between 2D materials in MBE-grown and mechanically-produced heterostructures may not be exactly the same. The work in Ref. [118] focuses the band alignment between MoSe\(_2\) and WSe\(_2\) bands in a monolayer MoSe\(_2\)/monolayer WSe\(_2\) heterostructure, which provides essential information for the understanding of the charge transfer process in a device made with such heterostructures [119].

A distinct valley degrees of freedom with completely flipped spin textures between K and \(K'\) points of the hexagonal BZ is the basis of the valleytronic applications in MX\(_2\). Spin-ARPES must provide a direct view of the spin texture and the spin flip between different valleys. Earlier spin-ARPES works are essentially measured on bulk samples of MX\(_2\), such as bulk inversion symmetry broken 3R phase of MoS\(_2\) [120] and spin polarization induced by the space charge residing in the overlayer [121]. Riley et al. [122] report spin polarized signal just from a regular bulk WS\(_2\), and interprets their results in terms of strong electron localization at the K/\(K'\)-point of WS\(_2\). Spin-ARPES data on MBE grown MoSe\(_2\) and WSe\(_2\) [123] find a mostly out-of-plane spin polarization and confirm that the splitting at the K point is indeed a spin-splitting (Fig. 4). However, the spin-flip between K and \(K'\) was not clearly exhibited due to the intricate interplay among spin, orbital, and spin-ARPES matrix elements.

There are only handful of tr-ARPES data on 2H-MX\(_2\) systems since the development of XUV probe is still in its early stage. The tr-ARPES data on the bulk 2H-MoS\(_2\) [124] found multiple decay channels of optically populated electrons in the conduction band with largely different time scales \(\sim\)1 to \(\sim\)15 ps. The tr-ARPES work on the epitaxially grown MoS\(_2\) on Au(111) [125] and on graphene [126] report a renormalized band gap size depending on the interaction of electrons with the substrate as well as much faster electron dynamics compared to that in bulk.

3.2 \(1T'\)-MoTe\(_2\), WTe\(_2\), MoSe\(_2\), WSe\(_2\)

\(1T'\) phase TMDCs in their bulk form has been studied intensely in recent years since the discovery of non-saturating linear magnetoresistance (MR) in WTe\(_2\) [127] and the prediction of the type-II Weyl semimetals [128, 129]. There have been a surge of research following these discoveries including ARPES data from multiple groups, either focusing on the large anomalous MR [130–133] or their topological properties [134–142]. The competing pictures to explain anomalous MR are electron-hole carrier compensation [143] and topological protection [144, 145]. The latter is closely related to the topological classification of \(1T'\) TMDCs. ARPES measurements should in principle provide an unambiguous answer to these issues by deciding the sizes of electron and hole Fermi surfaces (FS) and revealing the surface Fermi arcs. However, a rather closely packed multiple Fermi pockets in a narrow momentum region near \(\varGamma\) [131] and the Fermi arc being slightly above \(E_\mathrm{F}\) [128] hinder a clear observation of various pockets and arcs. Furthermore, it has been noted that the classification of arc-like features and assignment of Weyl nodes and their projection on the surface are closely dependent on the theoretical models, which in turn is very sensitive to the parameters such as lattice constants [136].

The 2D limit of \(1T'\) phase of TMDCs hold interesting theoretical proposal that it may host a large gap quantum spin Hall (QSH) insulator phase [146], suggesting a thickness dependent changes in the topological nature of these materials. A band gap opening, with a size similar to the theoretical prediction, in the optical and transport measurements of MoTe\(_2\) alluded that such proposal may be true [147]. Recent transport measurements suggesting an edge conduction below critical temperature in WTe\(_2\) may further provide evidences of the existence of QSH insulator phase in monolayer \(1T'\) TMDCs [148]. Up to now, there has not been any ARPES data on the QSH aspects of monolayer \(1T'\) phase TMDCs. A direct observation of the band gap opening at the low temperature, the orbital characters of inverted bands, and the momentum resolved electronic structure would benefit a development of a comprehensive picture for this intriguing material class.

3.3 NbSe\(_2\), TiSe\(_2\)

TMDCs with transition metal elements such as Nb, Ti, Ta, and V share a common theme of physics stemming from the coexisting collective orders of charge density wave (CDW) and superconductivity (SC) [149]. Whether these orders compete or cooperate, particularly at a few layer limit, is an interesting question with significant implications, for example, to the physics of high temperature superconductivity in cuprates [150].

2H-NbSe\(_2\) is a prototypical system to study the coexisting CDW and SC orders with \(T_\mathrm{CDW}\) \(\,=\,33\) K and \(T_\mathrm{C}\) \(=\) 7.2 K in its bulk form. There have been multiple ARPES studies on the bulk NbSe\(_2\) [151–154], focusing mostly on the mechanism of the CDW order formation. A combined ARPES and scanning tunneling microscopy/spectroscopy (STM/STS) study on a MBE grown monolayer NbSe\(_2\) on bilayer graphene reveals that the band structure fundamentally changes when the thickness is reduced to the monolayer going from a multi-band FS to a single-band FS (Fig. 5) [155]. While the band structure changes, the 3 \(\times\) 3 CDW order remains intact in both ordering q-vector and the transition temperature. The SC order is still present but the \(T_\mathrm{C}\) is suppressed down to 1.9 K. This makes a contrasting case with the Raman study [156] on exfoliated NbSe\(_2\), for which a large increase of the CDW transition temperature was observed with a similar suppression of \(T_\mathrm{C}\). It is also in discord with the interpretation of transport data under magnetic field [157] and the spin-ARPES measurement on bulk [158], both of which assumes the spin-momentum locking based on the preservation of the same band structure around K-point even in the monolayer limit. A possible origin of such discrepancy could be the role of substrate, which should be demonstrated by further studies. Recent MBE \(+\) ARPES measurements on NbSe\(_2\) report that it is possible to isolate either 2H or 1T phase depending the substrate temperature during the growth process [159].

1T-TiSe\(_2\) makes a 2 \(\times\) 2 \(\times\) 2 CDW order below \(T_\mathrm{CDW}\) \(\approx 200\) K and the superconductivity can be induced by suppressing CDW order through, e.g., electric field, doping or pressure [160–162]. Despite multiple ARPES studies and theoretical scenarios to explain the nature of the bulk CDW phase [161–166], the microscopic origin still remains elusive. ARPES studies on few-layer samples should provide a systematic evolution of the CDW by suppressing and reinstating the order along the c axis. Chen et al. report [167, 168] an enhanced CDW transition temperature \(T_\mathrm{CDW}\) \(=\) 232 K from the monolayer TiSe\(_2\) grown on bilayer graphene with 2 \(\times\) 2 superstructure. The layer-by-layer ARPES investigation also find that there exist two distinct transition temperatures in the bilayer, one which is similar to that of monolayer and the other similar to that of bulk. These two transition temperatures conform to the bulk value \(\approx\)200 K for the films thicker than 3 layers. Their findings are in contrast to the similar study by Sugawara et al.  [169], in which an essentially the same \(T_\mathrm{CDW}\) has been reported in the monolayer TiSe\(_2\) on graphene. It is worthwhile to note that the bulk 1T-TiSe\(_2\) and TiS\(_2\) have been the model system to study the dynamics of CDW order using tr-ARPES [170, 171]. The time scale for the melting of the CDW order was found to be extremely small \(\sim\)20 fs, which has been attributed to the screening by the transient generation of free charge carriers [170].

4.1 Silicene

Silicene is a graphene analog of silicon in a low-buckled honeycomb lattice [172, 173]. Since the theoretical studies that predict [174, 175] the existence of a stable silicene phase with a massless Dirac fermion and a Dirac point at \(E_\mathrm{F}\), it received a large amount of interest. The freestanding silicene has not been isolated experimentally, yet a few layer silicon films on various substrates, such as Ag(110) [176], Ag(111) [177–181], ZrB\(_2\) [182, 183], Ir(111) [184], and MoS\(_2\) [185], have been synthesized. Care should be taken in the interpretation of the ARPES data since the silicon layer itself forms various reconstructed phases depending on the growth conditions and the interaction with the substrate could affect the electronic structure.

The most studied silicene structure is monolayer Si on Ag(111) surface. A combined ARPES and STM study by Vogt et al.  [177] reported a Dirac cone like linear band structure from a (4 \(\times\) 4) Si overlayer on Ag(111). The estimated \(v_\mathrm{F}\) is similar to that of graphene, although there exists an electron removal gap opening \(\sim\)0.3 eV resulting from the interaction with the substrate. Such interpretation was later challenged by ARPES studies [180, 181] that showed a saddle point like dispersion rather than a conical one at the K point of Si monolayer at which the Dirac cone was reported in the previous studies. Conflicting ARPES data were also reported for Si multilayer on Ag(111). De Padova et al. [186] reported a growth of Si multilayers with (\(\sqrt{3} \times \sqrt{3}\))R\(30^{\circ }\) reconstruction and ARPES data that shows linear dispersion with a Dirac point at 0.25 eV binding energy. Mahatha et al. [187] argued that such band should be attributed to the Si-modified Ag(111) interface state and the Si films of a few monolayer thickness on Ag(111) are \(sp^3\) diamondlike Si rather than multilayer silicene. Similar opening of the gap and deviation from the Dirac dispersion due to the buckling and a substrate interaction have been observed for silicene on ZrB\(_2\) [182, 183].

4.2 Germanene

Germanene is a sister material of silicene with a similar low-buckled honeycomb lattice structure [173, 175]. Compared to silicene, the study on germanene is in its early stage due to the sample availability. Synthesis of germanene on metal substrates have only been reported recently—on Pt(111) [188], Al(111) [189, 190], Ag(111) [191], and Au(111) [192]. A report has been made on the synthesis of germanene on MoS\(_2\) [193]. Most of the studies utilize STM and STS to identify structural properties with local electronic structure. Up to now, ARPES measurement has been rare. Few layer germane on Au(111) is reported to possess Dirac cone like linear dispersions in ARPES spectra [192].

4.3 Stanene

Out of group IV elemental 2D materials, stanene, a single layer of tin, is expected to possess the largest SOC. This implies, with the buckling structure of honeycomb lattice, a more textured topological properties are possible, including the prediction of a large gap QSH insulator [194, 195] with a gap size larger than 100 meV for room temperature applications [196].

Few layer \(\alpha\)-Sn films have been grown on InSb substrate and investigated using ARPES [197, 198]. Both results confirm the existence of topological surface state with a linear dispersion of Dirac cone. They also directly observe the spin polarization in the topological surface state through spin-ARPES measurements. Barfuss et al. find that the role of strain is essential to realize the topological insulator phase by density functional and GW calculations. Ohtsubo et al. report that the topological character in \(\alpha\)-Sn depends on thickness and it becomes a topological insulator only within a small range of thickness.

Stanene, a 2D structure of \(\alpha\)-Sn(111), has only recently been realized by MBE on Bi\(_2\)Te\(_3\)(111) substrate [199]. The crystal structure has been identified in STM as that of stanene. The electronic structure was investigated by ARPES (Fig. 6). The measured band structure bears a close resemblance with the DFT calculation that includes a contribution from Bi\(_2\)Te\(_3\) substrate. However, the measured band structure shows a complete disappearance of \(p_z\) band near the K-point, which indicate that \(p_z\) orbitals are fully saturated by an interaction with the substrate or an inclusion of adsorbates [195, 199]. At the same time, the chemical potential is shifted to bring the hole bands around the \(\varGamma\)-point to cross \(E_\mathrm{F}\). This makes the identification of the predicted QSH phase [194, 195], a band inversion and an opening of a gap, impossible for ARPES.

5.1 Phosphorene

Phosphorene is a 2D atomic crystal made of black phosphorus [200]. It can be exfoliated from the bulk crystal and retains the direct band gap ranging 0.3–1.7 eV. The size of the band gap fills the gap between those of graphene and semiconducting TMDCs. The gap size can be controlled through the number of layers, strain, and electric field [200–202]. The atomic structure of black phosphorus is highly puckered, armchair shape in one direction and zigzag shape in the perpendicular direction. This results in an unusual mechanical properties and makes phosphorene a ideal template for an atomic chain [200].

There have been a number of ARPES studies [202–206] on bulk black phosphorus. Han et al. [204] made a wide range photon energy dependence to decide the \(k_z\) dispersion and find that the valence band maximum occurs at the Z-point of BZ. They also found that experimental electronic structure from ARPES is more two-dimensional compared to the theoretical calculations. Kim et al. [205] made interesting observations when potassium is dosed on the surface of black phosphorus (Fig. 7). With the increasing amount of potassium on the surface, the band structure of black phosphorus can be tuned from a direct band gap semiconductor with variable gap size into a band-inverted semimetal. At the critical point of such transition, the electronic state becomes highly anisotropic, with a linear Dirac dispersion along the armchair direction and nearly parabolic dispersion along the zigzag direction. Theoretical studies predict [207] that further surface doping on few-layer black phosphorous would turn the system into a Dirac semimetal with linear dispersion in all three momentum directions.

Until now, the investigation of electronic structure on few-layer black phosphorus has been lacking on the ARPES side. The main bottleneck has been the difficulty in sample preparation due to the fast degradation of the material [200]. Encapsulation of exfoliated samples, a technique readily available to, for example, optical measurements [208], is not compatible with ARPES due to the short escape depth of the photoelectrons.

5.2 Arsenene, antimonene, and bismuthene

Down the row in the periodic table from phosphorus, arsenene, antimonene, and bismuthene are the 2D forms of arsenic (As), antimony (Sb), and bismuth (Bi), respectively. These materials are expected to assume a stable form of atomic structure out of multiple allotropes of their bulk counterpart and to stay stable in room temperature and ambient environment [209, 210]. Shared themes of material properties of these 2D crystals are the semimetal to semiconductor transition with reduced dimension with variable gap size through strain and other parameters [209, 210] and the diverse topological phases that is particularly pronounced for antimonene and bismuthene [210, 211]. While the isolation of arsenene is yet to be realized, antimonene and bismuthene has been successfully exfoliated [212, 213] and grown by epitaxial methods [214–218].

ARPES measurements have been performed on a single layer Sb grown on Sb\(_2\)Te\(_3\)(111) and Bi\(_2\)Te\(_3\)(111) [215]. It has been shown that the band structure of Sb overlayer is strongly modified due to the substrate effect. A single layer Bi has attracted interest as a candidate material for the realization of a QSH insulator [216, 217, 219]. STM combined with ARPES measurements on Bi(111) single layer grown on Bi\(_2\)Te\(_3\)(111) [216] reported signatures of the topological edge state albeit \(E_\mathrm{F}\) has been shifted deep into the valence band. STM measurements on the step edge of Bi single crystals [219] also found an edge state above \(E_\mathrm{F}\). More recent study on Bi(111) single layer grown on SiC(0001) [217] with STM and ARPES indeed observed an edge state lying in a band gap as large as ~0.8 eV. A sizable tensile strain of 18% is identified as essential to realize a large band gap QSH phase, which stress the importance of substrate in realizing desired physical properties.