Observation of floating surface state in obstructed atomic insulator candidate NiP2 | npj Quantum Materials

npj Quantum Materials volume 9, Article number: 85 (2024) Cite this article

Metrics details

Obstructed atomic insulator is recently proposed as an unconventional material, in which electric charge centers localized at sites away from the atoms. A half-filling surface state would emerge at specific interfaces cutting through these charge centers and avoid intersecting any atoms. In this article, we utilized photoemission spectroscopy and density functional theory calculations to study one of the obstructed atomic insulator candidates, NiP2. A floating surface state with large effective mass that is close to the Fermi level and isolated from all bulk states is resolved on the (100) cleavage plane, implying better catalytic activity in this plane than the previously studied surfaces. Density functional theory calculation results elucidate that this floating surface state is originated from the obstructed Wannier charge centers, albeit underwent surface reconstruction. Our findings not only shed lights on the study of obstructed atomic insulators, but also provide possible route for development of new catalysts.

In the past decades, various topological phases were theoretically proposed and experimentally realized in condensed matter systems, characterized by non-zero topological invariants defined in the reciprocal space. These topological phases include but not limit to topological insulators1,2, quantum anomalous Hall insulators3 and topological semimetals4. Recently, systematic topological classification based on different theoretical methodologies and high-throughput calculations were performed to filter out all possible topological materials from the materials database5,6,7,8. However, even in materials that are classified to be “topologically-trivial” according to k-space invariants, part of them still differs from others in a topological sense. These materials are characterized by non-zero parameters defined in the real space, rendering characteristic electronic structures that cannot be adiabatically evolve to the equivalency of those formed by separated atoms9,10.

One of such unconventional types of materials has been defined as “obstructed atomic insulators” (OAIs), attracting broad scientific attention9,10,11,12,13,14,15. Distinct from the ordinary atomic insulators, there are Wannier charge centers (sites at which the electrical charge spatially localizes and exponentially decays away) located at some empty sites in the crystal of an OAI, which are characterized by non-zero real space invariants9,10. For specific interfaces that only cut through such obstructed Wannier charge centers (OWCCs), fractionalization of charge would occur at the interface, according to the filling anomaly principle16,17,18,19. Ideally, this would result in the emergence of low-bandwidth surface electronic states that floats between the bulk valence and conduction bands and cuts through the Fermi level regardless of electronic occupation. It is these “obstructed surface states (OSSs)” that contribute predominantly to the catalytic activity of OAIs. High-throughput first-principles calculations have screened out hundreds of OAI candidates from the current material database10,11,15. These candidates can be identified as various functional materials, including electrides20,21,22,23, thermoelectric materials, hydrogen evolution reaction (HER) electrocatalysts10,24, etc. The diversity of OAI candidates paves the way for investigation and application of them in the future.

Currently, the theoretical description of OAIs has been well developed, while the experimental study on them is still rare. A recent study verified the catalytic active sites in HER of several OAI candidates24; another work observed the in-gap soliton state at the domain boundary on Si 2 × 1 (111) surface, which can be manipulated by electric pulse discharged from the tip25. These results support the theoretical predictions of OAIs, elucidating the relation between novel phenomena and localized OWCCs, and revealing the application potential of OAIs on catalysis. Noticeably, spectroscopic experiments reveal that the OSSs in OAI candidates are subject to significant modifications in realistic surfaces that undergo structural reconstructions. Such reconstructions would remedy the fractionalization of charges, causing an energy split of the OSSs to the level that the two branches locate at both sides of the Fermi level. In the case of SrIn2P2, the upper branch of the modified OSSs on the \(\sqrt{3}\,\times \,1\) (0001) plane shows signatures of charge localization, yet locating far above EF26. On the other hand, the lower branch in both SrIn2P2 and Si (111) are found to be not only highly dispersive, with small effective masses and large bandwidths, but also connect to the bulk valence bands at high binding energies25,26. These features hamper the catalytic application of these electronic states. Thus, finding OWCC-originated SSs in OAI candidates that have small bandwidth and are separated from bulk states is demanded to complement the knowledge about this type of unconventional materials and instruct the development of new catalysts.

In this article, we systematically study the electronic structure of monoclinic NiP2 (denoted as m-NiP2) using angle-resolved photoemission spectroscopy (ARPES)27 and density functional theory (DFT) calculations. The dispersion of bulk bands and a global flat band in the three-dimensional Brillouin zone (3D BZ) are observed. Importantly, a floating SS (fSS) with large effective mass that is separated from other bands is resolved on the (100) surface near the Fermi energy, and it evolves to be even flatter at the surface BZ (sBZ) boundary. The temperature dependence of band structures is also studied, which is found to be in line with the temperature evolution of the electrical conductivity. The DFT calculation results reproduce the dispersion of bulk states and the fSS on the (100) plane. Our findings elucidate the relation between the fSS and the OWCCs in m-NiP2, highlighting the importance of small-bandwidth, fully separated SSs on OAI candidates, and providing an explanation of the termination-dependent catalytic activity from the electronic structure point of view.

As one of the OAI candidates10, m-NiP2 crystallizes in space group C2/c. The nickel and phosphorous atoms form a single atomic layer within the bc plane, and the neighboring layers are coupled via P-P chains along the a axis [Fig. 1a, b]28. The theoretically predicted OWCCs locate at Wyckoff positions 4d (between two neighboring phosphorous atoms within a single atomic layer) and 4e (between two neighboring phosphorous atoms along the P-P chain), while Ni and P atoms locate at Wyckoff positions 4c and 8 f, as shown in Fig. 1. Both the (100) and (11-1) cleavage plane cut through the OWCCs without intersecting any atoms. (Here, the Miller indexes of these planes are defined in the conventional cell, rather than the primitive unit cell.) According to the theoretical prediction, fractional charge and OSS would emerge once the crystal is terminated at these planes. Moreover, as seen in Fig. 1a, the cleavage along the (100) plane not only cut through the OWCCs at 4e (magenta spheres), but also expose the OWCCs at 4d (orange spheres) to the vacuum. In principle, the fully occupied spatially-localized charge centers (OWCCs at 4d) could also serve as sites for potential ligand adsorption and charge transfer, and contribute to the interface catalysis. In a recent study, the (100) surface of m-NiP2 shows much higher catalytic activity than other terminations in HER29, which supports this hypothesis and implies the essential role of OWCCs in interface catalysis.

a, b Illustration of crystal structure of m-NiP2 and location of OWCCs along (010) and (100) planes (side view and top view). c Single crystal X-ray diffraction results of m-NiP2 terminated at the (100) and (11-1) planes. Inset: photographs of single crystals of m-NiP2 with different terminations. d The photoemission core level measurement results. Core levels of nickel and phosphorous are clearly resolved. The peak at EB ~ 154 eV corresponds to electrons with kinetic energy of about 845 eV, which should be ascribed to be the Auger electron spectroscopy peak of nickel40. Another peak at EB ~ 137 eV is the 4 s peak of tin, which originates from the residual flux on the sample. e The 3D BZ and high symmetry points (black points). f The DFT-calculated bulk bands along the high symmetry path defined in (e).

We start from the data collected on samples cleaved along the (100) surface measured using soft X-ray photons at 80 K. The normal vector of the in-plane BZ is determined to be the [1-10] direction, in units of primitive unit vectors in the reciprocal space (Supplementary Section I). The ARPES EB-kx band dispersion near the Fermi level, which cuts through different positions in the 3D BZ, are shown in Fig. 2. It’s easy to find one relatively flat, wave-like floating band that tops at EB ~ 0.2 eV (denoted as the floating surface state, fSS), separating from other bands in energy. It disperses as heavy hole-like pockets at the \(\bar{\Gamma }\), X1 and X2 points, and the global bandwidth is found to be less than 260 meV. The bandwidth estimated from data shown in Fig. 2 (~260 meV) is slightly larger than the DFT calculation results (220 meV). This discrepancy may be ascribed to the intrinsic worse energy resolution at the soft X-ray range and thermal broadening due to higher measurement temperature (see the Methods section). Signals from multiple domains could also introduce broadening of the bandwidth. This band shows almost identical dispersion along kx in several sBZs [Fig. 2(a)], as well as along kz at several out-of-plane BZs [Fig. 2(c),(d)], signifying its surface origin. There is also an electron-like band at the \(\bar{\Gamma }\) point whose bottom locates at EB ~ 1.8 eV (denoted as e1), which appears to be the same at different kzs. This is also a surface band. On the other hand, two hole bands whose band tops locate at EB ~ 0.8 and 1.3 eV (denoted as h1 and h2, respectively) are observed at the \(\bar{\Gamma }\) point. These pockets show strong dispersion across several sBZs and different kzs, implying their bulk origin. Besides these dispersive bands, one could also notice a nearly flat band that locates at EB ~ 2.0 eV at different kzs. As discussed later, this band is a bulk global flat band that appears in the whole 3D BZ.

a1-a3 The band structure along \(\bar{\Gamma }\)-X at kz = 11.2 (the bulk Γ point), 11.8 and 12.3 Å−1 (the bulk Z point), respectively. The data within −0.6 to 0.5 eV is plotted using a narrower color scale to highlight the fSS. b The DFT calculation results for bulk states (blue dots) and the fSS (red dots) along the kx direction. c1,c2 The EB-kz dispersion collected at the \(\bar{\Gamma }\) point of the second and the first sBZ (\({\bar{\Gamma }}_{+1}\), kx = 1.119 Å−1 and \({\bar{\Gamma }}_{0}\), kx = 0). The red dots represent the DFT calculation results for the bulk bands. d1-d3 The constant energy contours in the kz-kx map at EB = 0.35, 1.10 and 1.6 eV, respectively. From Fig. 2, we see that the (100)-cleaved m-NiP2 processes a surface state at EB ~ 0.3 eV that has a narrow bandwidth of <260 meV and is completely separated from the bulk bands, together with a flat bulk band at EB ~ 2 eV.

The photon-energy-dependent map was performed for direct visualization of the out-of-plane dispersion [Fig. 2(c1),(c2)]. The out-of-plane momentum is calculated via \({k}_{z}=\sqrt{2m/{{{\hslash }}}^{2}\left({E}_{k}{\cos }^{2}\theta +{V}_{0}\right)}\), where the inner potential V0 is determined to be 12 eV. The EB-kz dispersion collected at the \(\bar{\Gamma }\) point of the first and the second sBZ (corresponds to kx = 0 and 1.119 Å−1, respectively) verifies that both the fSS and the bulk flat band show no kz dispersion over the entire 3D BZ. On the other hand, the h1 band shows well-defined periodic kz dispersion within the first sBZ. It is identified as a single hole pocket near the Γ point and evolves to a “M”-shaped band near the Z point. The periodicity in the second sBZ reveals a π phase shift compared with that in the first sBZ. Such feature coincides with the in-plane BZ evolution behavior at different kzs (Supplementary Section I), suggesting the bulk nature of the h1 band. Upon a global energy shift of −0.28 eV which accounts for possible charged defects, the DFT calculation results agree well with the observed dispersion of the h1 band and the flat band, further confirming their bulk nature. The fSS and the e1 pocket are absent in the bulk-band calculation results, but are present in the DFT calculation based on an 8-unit-cell slab model, which further elucidates their surface nature.

To study the band dispersion along the in-plane directions, kx-ky maps are performed at selected photon energies. The constant energy contours (CECs) at EB = 0.4 eV collected with 116 eV incident photons reveal a spot-like feature between two adjacent fSS pockets along the ky direction [indicated by the black arrow in Fig. 3(a)]. In the EB-ky dispersion that crosses the \(\bar{\Gamma }\) point at 116 and 83 eV (correspond to kz = 5.694 Å−1, close to the Z point, and 4.875 Å−1, close to the Γ point, respectively), it’s easy to identify it as another hole pocket [Fig. 3(b),(c)]. This pocket is not clearly resolved in the data collected within the soft X-ray energy range, possibly due to the reduced photoemission cross-section at higher photon energies (Supplementary Section III). Both hole pockets of the fSS show no kz-dispersion from 24 to 120 eV (corresponds to kz = 2.892 to 5.785 Å−1, over an entire 3D BZ), indicating that it should be a SS (Supplementary Section II). The effective masses of the two pockets of fSS are estimated to be −4.85 me and −1.45 me, respectively (Supplementary Section IV).

a ARPES constant energy contour at EB = 0.4 eV of m-NiP2 collected at hν = 116 eV (kz = 5.694 Å−1). The black dashed lines indicate the boundary of the sBZ on the (100) plane of m-NiP2. b–g ARPES band maps along in-plane directions marked in (h), collected with (b), d, f 116 eV (kz = 5.694 Å−1) and (c), e, g 83 eV (kz = 4.875 Å−1) photons. h Schematic illustration of the sBZ, along with the high symmetric points. i, j DFT calculation results along the high symmetric paths defined in (h), based on an 8-unit-cell slab model. k, l The EDCs corresponding to the spectra shown in d, e, respectively. The curves are collected from ky = −1.2 to 1.2 Å−1, each integrated within a momentum range of 0.04 Å−1. From Fig. 3, it is seen that the fSS of m-NiP2 has a narrow global bandwidth of ~220 meV, which becomes even flatter at the edges of the sBZ, agreeing well with the calculated results [Figs. 2(b), 3(i)-(j)].

Apart from the previously mentioned spot-like feature, a ribbon-like, faint trace that connects the fSS hole pockets between neighboring sBZs along the kx direction also presents in the constant energy contours, as indicated by the white arrow and white dashed lines in Fig. 3(a). Thus, we examine the dispersion of the fSS near the boundary of the sBZ. From Fig. 3(d)–(g), it is easy to find that the fSS evolves to be an almost flat band at the M-X-M cuts along ky [Fig. 3(d), (e)], and a single hole pocket centered at the Y point at the M-Y-M cuts along kx [Fig. 3(f), (g)]. All of the energy distribution curves (EDCs) tracked from the spectrum collected at 116 eV reveal a peak feature at a constant binding energy EB = 0.55 eV, which further confirm its flat band nature. The spatially-localized OWCCs at the interface would yield surface bands that disperse with low group velocity, i.e., these bands possess relatively large effective mass. Thus, the large effective mass of the hole pocket at the center of the sBZ also reflects the relation between the fSS and OWCCs. Our DFT calculation results on an 8-unit-cell slab model reveal a floating SS within the bulk band gap, well reproducing the observed dispersion of the fSS along both the kx and ky directions [Fig. 3(i), (j)]. The two closely situated bands of the fSS below EF shown in Fig. 3(i), (j) originate from the artificial finite size effect due to the finite-sized slab applied to the DFT calculation. In experimental conditions which is better modeled by a semi-infinite slab, only one surface band would be present, and that is what we observed by ARPES. The fSS yields anisotropic and periodic dispersion in the momentum space, and is reproduced by DFT calculations based on an 8-unit-cell slab model without the consideration of impurities. The charge distribution of the fSS is found to locate periodically around the Ni atoms or above the P atoms at the interface, rather than locating randomly around the impurities (Fig. 5). These features rule out the possibility that the fSS is introduced by impurities. The fSS found in our ARPES measurements and DFT calculations originates from the OWCCs, albeit underwent an energy splitting possibly due to surface structural reconstruction, similar to the case in SrIn2P2 and Si25,26. Important differences between the OSSs in these materials are that (1) the OSS in m-NiP2 exhibit much smaller bandwidth than that in SrIn2P2, implying better localization condition, (2) the OSS in m-NiP2 locates in general closer to EF than that in SrIn2P2 and Si, and (3) the lower branch of the reconstructed surface band remains separated from the bulk bands in m-NiP2, while merges to the bulk states in the cases of SrIn2P2 and Si. These features make the OSS-originated fSS in m-NiP2 more relevant to its transport properties and thus more related to the enhancement of the catalytic activity in the (100) surface.

To investigate the correspondence between the band structure and the electrical transport, we studied the temperature-dependence of the bands on the (100) plane of m-NiP2 from T = 8 to 150 K, with hν = 42 eV. The EDCs collected at the \(\bar{\Gamma }\) point at different temperatures were shown in Fig. 4(a). Here, we set the band position at 20 K as a reference, and the band shift of the fSS and the e1 pocket are obtained by fitting the EDC peaks at different temperatures. Both the fSS and the e1 pocket are found to shift upward upon heating, and recover to previous energy upon cooling. These two pockets shift with temperature at the same pace, revealing a rigid band shifting behavior. We argue that the energy shift of bands comes from intrinsic characteristics of the system rather than extrinsic reasons such as surface degrading or gas molecule deposition during the ARPES experiments. It is seen in Fig. 4(b), (c) that the band positions are reversable within the large-range heating and cooling cycle, and the system basically returns to its original stage when the temperature is returned. Thus, no apparent degradation appears on the sample surface. Such band shift may be ascribed to the intrinsic residual carriers, which were thermally excited and shifts the chemical potential as temperature increases. For realistic semiconducting materials, intrinsic residual carriers may exist, and the Fermi level may locate closer to one side of the gap (through e.g. weak impurity states that are invisible by ARPES). In this case, these residual carriers would be excited as temperature increases, which could cause the energy shift of the chemical potential and the energy bands. The positive correlation between the temperature evolution of the conductance and that of the band shift [Fig. 4(b)] suggests a close relationship between the transport behavior and the electronic structure, especially the fSS, in the m-NiP2 (100) surface.

ARPES data is collected at hν = 42 eV. a EDCs at different temperatures collected within 0.05 Å−1 range near the \(\bar{\Gamma }\) point. The temperature cycle starts from 20 K, slowly heats up to 150 K and then cools back down to 8 K. Similar overall shape of the EDCs suggests a rigid-band shift scenario. b The band shift of the fSS and the e1 pockets in the heating-cooling cycle (red and blue markers, left axis). The band shifts are obtained by fitting the EDC peaks at different temperatures using Lorentzian functions. The temperature dependence of electrical conductance (black markers, right axis) from T = 5 to 150 K is also plotted in the figure, which corresponds positively to the band shifts. c1-c5 The ARPES EB-ky maps collected at 20 K (heating), 50 K (heating), 150 K (heating), 50 K (cooling) and 15 K (cooling), respectively. The common trend of temperature evolution between the conductivity of the system and the rigid shifts of the bands shown in Fig. 4 indicates a close relationship between the transport behavior and the electronic structure, especially the fSS which evolves closer to EF at ambient temperatures.

To further discuss the relation between the surface electronic structure and the termination-dependent catalytic activity, the band structure of m-NiP2 that cleaved along the (11-1) plane was also studied (Supplementary Figs. 7 and 8). Although faint traces of possible electronic states are found to cross EF after second-order curvature analysis30, it is not certain whether these are the SSs of the m-NiP2 (11-1) cleavage plane. Nonetheless, the divergent surface electronic structures on different cleavage planes of m-NiP2 are likely responsible for the previously reported termination-dependent catalytic activity29.

According to theoretical prediction, both the (100) and (11-1) planes would cut through the OWCCs in m-NiP2 without intersecting any atoms, yielding fractional charges and metallic SSs at the interface. However, in realistic situations, the fractional charges localized at the interface may not be energetically stable, and are subject to surface reconstruction. The spontaneous surface reconstruction upon cleavage would change the charge distribution on the surface, reshaping or even eliminating the theoretically predicted half-occupied OSSs. In previously reported ARPES studies on OAI candidates, the OSSs evolved to a fully-occupied branch and a fully-unoccupied branch to lower the total energy of the surface25,26. The fSS on the (100) surface of m-NiP2 should also be ascribed to this situation. In this paper, we simulate the surface reconstruction process by fully relaxing an 8-unit-cell slab model (Supplementary Section VIII). DFT calculation results based on this relaxed model well reproduced our ARPES results, providing evidence that this surface reconstruction is driven by energy-favorable spontaneous evolution of surface atoms. The displacement of topmost-layer atoms other than P2 is smaller than 0.2 Å (Supplementary Section VIII), which elucidates the limited effect of the surface reconstruction on the surface topography. Since the real space topological invariants defined within the bulk material is preserved, the bulk-boundary correspondence between the fSS and the OWCCs was maintained even after the surface reconstruction. Compared with the SSs in previously reported OAI candidates, the fSS of m-NiP2 yields a much smaller bandwidth and locates closer to the Fermi energy. The localization of electrons would benefit the formation of the chemical bonds between the surface and the adsorbents, whose electronic density of states is also spatially localized. Being close to EF ensures that the conducting electrons are originated overwhelmingly from the fSS, providing numerous active sites for the adsorption process.

In Fig. 5, we investigate the electrical charge distribution of the fSS by performing DFT calculation on an 8-unit-cell slab model, and mapping the charge distribution of the bands within EB = 0 to 0.5 eV (where the occupied fSS locates in energy) to the real space [Fig. 5(b)]. From Fig. 5(a), one realized that the original OWCC-induced OSS indeed split into two branches via surface reconstruction. Both branches float within the bulk band gap and isolate from all the bulk states. From Fig. 5(b), we found that the electrical charges (yellow bubbles) mainly locate either around the Ni atoms or just above the P atoms at the interface, which provides solid evidence that the OWCCs localized at 4e are mainly responsible for the observed fSS near the Fermi level. Meanwhile, the observed temperature dependence of the fSS suggests that the lower branch of the fSS would get closer to the Fermi energy at higher temperatures. In principle, these features benefit for the charge transfer in room-temperature catalytic processes. On the other hand, considering the atomic sites in m-NiP2, the surface structure of the as-cleaved (11-1) plane is more complex than that of the (100) plane. Thus, the surface relaxation upon cleavage along the (11-1) plane would modify the atomic sites and charge distribution of several topmost atomic layers to a greater extent than that in the (100) plane, which may even eliminate the theoretically predicted OSSs. This distinction can explain the emergence of the fSS near the Fermi energy on the (100) surface rather than the (11-1) surface of m-NiP2. Moreover, the (100) surface not only cuts through the OWCCs at 4e, but also expose the OWCCs at 4d to the interface. Those charge centers can also serve as sites for charge transfer and ligand adsorption, and contribute to the surface catalysis. Our study on the electronic structure of two different surfaces of a single OAI candidate provides evidence for the relation between the catalytic performance and the surface electronic structure.

a The fully relaxed, surface projected DFT-calculated band structure on an 8-unit-cell slab model. The fSS hole pockets at the \(\bar{\Gamma }\) point and the Y point, and the e1 pocket at EB ~ 1.5 eV, are identified as surface states. b The DFT-calculated electrical charge distribution (yellow bubbles) of the bands within EB = 0 - 0.5 eV [marked by dashed rectangles in (a)] on an 8-unit-cell slab model. The electrical charge mainly locates either around the Ni atoms or above the P atoms at the interface (correspond to OWCCs at 4e). From Fig. 5, it is inferred that the fSS, together with an additional, unoccupied surface state revealed above EF [Panel (a)], correspond to the occupied and unoccupied branches of the OWCC-induced obstructed surface states that are split due to surface reconstruction.

In conclusion, we combine ARPES and DFT calculations to study the electronic structure of m-NiP2. A fSS that is separated from the bulk bands in energy is observed on the (100) plane, which features a low global bandwidth of ~220 meV, and locates only ~0.3 eV below EF at 20 K. At elevated temperatures, the fSS is found to evolve even closer to EF, which indicates an important role the fSS plays in the transport process in devices that are functional at room temperature. Our DFT calculation results reproduce the dispersion of both the bulk bands and the fSS, and point out that the observed fSS is the lower, occupied branch of the energy-split SSs that originated from the OWCC-induced OSS. Our findings confirm an isolated, relatively flat SS in one of the OAI candidates, give an explanation on the catalytic performance of m-NiP2 from the surface electronic structure point of view, and offer a novel idea for the development of new catalysts.

Single crystals of m-NiP2 were grown using the Sn-flux method28. The Ni powder (99%), P powder (Alfa Aesar, 99%) and Sn shots (Aladdin, 99.5%) was mixed with a molar ratio Ni : P : Sn = 1 : 2 : 20 in an alumina crucible, and then flame sealed in quartz ampoule under Argon protection. The sealed ampoule was set in a box furnace. The furnace was heated from room temperature to 1373 K in 10 h, maintained at this temperature for 25 h and slowly cooled down to 773 K in 72 h. After another 24 hours the ampoule was centrifugalized. The obtained crystals after centrifugation were treated with a 1:1 HCl/H2O solution for 5 h to remove the redundant tin flux. The single crystal X-ray diffraction was performed with Cu Kα radiation at room temperature using a Rigaku Miniex diffractometer.

The soft X-ray ARPES measurements on m-NiP2 (Fig. 2) were performed at Beamline 25SU of the SPring-8 synchrotron light source31, which is equipped a Scienta DA30 electron analyzer. The overall energy and angular resolution were set to be better than 80 meV and 0.2°, respectively. The samples were cleaved in-situ by top-post method along the (100) plane at 80 K. During the measurement, the temperature of the sample was kept at 80 K, and the pressure was maintained at less than 2.5 × 10−8 Pa. The incident beam is left-circular polarized. The incident angle of photons is set to be 5°. This grazing incidence setup would not only increase the photon-electron interaction cross section in the soft X-ray energy range32, but also introduce larger spot size of the incident beam, which may cause simultaneous collection of ARPES signal from multiple crystallographic domains.

VUV ARPES measurements on m-NiP2 were performed at Beamline 13U of the National Synchrotron Radiation Laboratory (NSRL) and Beamline 03U of the Shanghai Synchrotron Radiation Facility (SSRF)33,34, both equipped with Scienta DA30 electron analyzers. The overall energy and angular resolution was set to be better than 30 meV and 0.2°, respectively. For experiments at NSRL, the samples were cleaved in-situ by top-post method along the (100) plane. The base temperature was set to 8 K and the base pressure was better than 6 × 10−11 torr. For experiments at SSRF, the samples were cleaved in-situ by top-post method along both the (11-1) and (100) planes. The temperature was set to 26 K for samples cleaved along the (11-1) plane and 35 K for those cleaved along the (100) plane. The base pressure was better than 6 × 10−11 torr. The temperature-dependent ARPES study was performed at NSRL from T = 8 K to 150 K, and the pressure was maintained at less than 1.5 × 10−10 torr. The incident beams at the two beamlines were both p-polarized.

The electronic structure calculations were carried out by the DFT method encoded in the Vienna Ab-initio Simulation Package (VASP)35,36 based on the projector augmented wave (PAW) method37. The Perdew–Burke–Ernzerhof (PBE) approximation was used for the exchange-correlation function38. The plane-wave cutoff energy was set to be 520 eV, and the DFT-D3 method was also included for the van-der-Waals correction39. GGA + U correction was applied to the Ni 3d orbitals, and U was set to be 3.0 eV. The k-point sampling is 11 × 11 × 6 with the Γ scheme for the bulk structure. To study the surface states of the crystal, we constructed a slab structure with the thickness of 8 unit cells. The in-plane lattice constants were set to be a = 5.629 Å and b = 5.616 Å. The whole Brillouin zone was sampled by a 6 × 6 × 1 Monkhorst-Pack grid. The experimental values were used for cell parameters28. Atomic positions were fully relaxed until the force on each atom was smaller than 1 × 10−3 eV/ Å, and the total energy convergence criterion was set to be 1 × 10−7 eV.

The data that support the findings of this study are available from the corresponding authors on request. Correspondence and requests of data are addressed to C.L.

Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045 (2010).

Article ADS Google Scholar

Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057 (2011).

Article ADS Google Scholar

Chang, C.-Z., Liu, C.-X. & MacDonald, A. H. Colloquium: quantum anomalous Hall effect. Rev. Mod. Phys. 95, 011002 (2023).

Article ADS Google Scholar

Lv, B. Q., Qian, T. & Ding, H. Experimental perspective on three-dimensional topological semimetals. Rev. Mod. Phys. 93, 025002 (2021).

Article ADS Google Scholar

Bradlyn, B. et al. Topological quantum chemistry. Nature 547, 298–305 (2017).

Article ADS Google Scholar

Tang, F. et al. Comprehensive search for topological materials using symmetry indicators. Nature 566, 486–489 (2019).

Article ADS Google Scholar

Zhang, T. T. et al. Catalogue of topological electronic materials. Nature 566, 475–479 (2019).

Article ADS Google Scholar

Jorrit, K. et al. Topological classification of crystalline insulators through band structure combinatorics. Phys. Rev. X 7, 041069 (2017).

Google Scholar

Song, Z. D., Elcoro, L. & Bernevig, B. A. Twisted bulk-boundary correspondence of fragile topology. Science 367, 794–797 (2020).

Article ADS MathSciNet Google Scholar

Xu, Y. et al. Three-dimensional real space invariants, obstructed atomic insulators and a new principle for active catalytic sites. arXiv:2111.02433 (2021).

Gao, J. et al. Unconventional materials: the mismatch between electronic charge centers and atomic positions. Sci. Bull. 67, 598–608 (2022).

Article Google Scholar

Po, H. C., Watanabe, H. & Vishwanath, A. Fragile topology and Wannier obstructions. Phys. Rev. Lett. 121, 126402 (2018).

Article ADS Google Scholar

Bouhon, A., Black-Schaffer, A. M. & Slager, R.-J. Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time-reversal symmetry. Phys. Rev. B 100, 195135 (2019).

Article ADS Google Scholar

Khalaf, E., Benalcazar, W. A., Hughes, T. L. & Queiroz, R. Boundary-obstructed topological phases. Phys. Rev. Res. 3, 013239 (2021).

Article Google Scholar

Xu, Y. F. et al. Filling-enforced obstructed atomic insulators. Phys. Rev. B 109, 165139 (2024).

Article ADS Google Scholar

Song, Z. D., Fang, Z. & Fang, C. (d-2)-dimensional edge states of rotation symmetry protected topological states. Phys. Rev. Lett. 119, 246402 (2017).

Article ADS Google Scholar

Rhim, J. W., Behrends, J. & Bardarson, J. H. Bulk-boundary correspondence from the intercellular Zak phase. Phys. Rev. B 95, 035421 (2017).

Article ADS Google Scholar

Benalcazar, W. A., Li, T. H. & Hughes, T. L. Quantization of fractional corner charge in Cn-symmetric higher-order topological crystalline insulators. Phys. Rev. B 99, 245151 (2019).

Article ADS Google Scholar

Schindler, F. et al. Fractional corner charges in spin-orbit coupled crystals. Phys. Rev. Res. 1, 033074 (2019).

Article Google Scholar

Wagner, M. et al. An electride with a large six-electron ring. Nature 368, 726–729 (1994).

Article ADS Google Scholar

Dye, J. L. Electrons as anions. Science 301, 607–608 (2003).

Article Google Scholar

Lee, K. et al. Dicalcium nitride as a two-dimensional electride with an anionic electron layer. Nature 494, 336–340 (2013).

Article ADS Google Scholar

Nie, S. M. et al. Application of topological quantum chemistry in electrides. Phys. Rev. B 103, 205133 (2021).

Article ADS Google Scholar

Li, G. W. et al. Obstructed surface states as the descriptor for predicting catalytic active sites in inorganic crystalline materials. Adv. Mater. 34, 2201328 (2022).

Article Google Scholar

Liu, Z. et al. Massive 1D Dirac line, solitons and reversible manipulation on the surface of a prototype obstructed atomic insulator, silicon. arXiv2406:08114 (2024).

Liu, X.-R. et al. Spectroscopic signature of obstructed surface states in SrIn2P2. Nat. Commun. 14, 2905 (2023).

Article ADS Google Scholar

Sobota, J. A., He, Y. & Shen, Z. X. Angle-resolved photoemission studies of quantum materials. Rev. Mod. Phys. 93, 025006 (2021).

Article ADS Google Scholar

Owens-Baird, B. et al. NiP2: A story of two divergent polymorphic multifunctional materials. Chem. Mater. 31, 3407–3418 (2019).

Article Google Scholar

Owens-Baird, B. et al. Crystallographic facet selective HER catalysis: exemplified in FeP and NiP2 single crystals. Chem. Sci. 11, 5007–5016 (2020).

Article Google Scholar

Zhang, P. et al. A precise method for visualizing dispersive features in image plots. Rev. Sci. Instrum. 82, 043712 (2011).

Article ADS Google Scholar

Senba, Y. et al. Upgrade of beamline BL25SU for soft x-ray imaging and spectroscopy of solid using nano- and micro-focused beams at SPring-8. AIP Conf. Proc. 1741, 030044 (2016).

Article Google Scholar

Strocov, V. N. et al. Soft-X-ray ARPES facility at the ADRESS baemline of the SLS: concepts, technical realisation and scientific applications. J. Synchrotron Rad. 21, 32–44 (2014).

Article Google Scholar

Sun, Z. P. et al. Performance of the BL03U beamline at SSRF. J. Synchrotron Rad. 27, 1388–1394 (2020).

Article Google Scholar

Yang, Y. C. et al. High-resolution ARPES endstation for in situ electronic structure investigations at SSRF. Nucl. Sci. Tech. 32, 31 (2021).

Article Google Scholar

Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).

Article ADS Google Scholar

Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comp. Mater. Sci. 6, 15–50 (1996).

Article Google Scholar

Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758 (1999).

Article ADS Google Scholar

Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).

Article ADS Google Scholar

Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132, 154104 (2010).

Article ADS Google Scholar

McGuire, G. E. Auger electron spectroscopy reference manual. Springer Science + Business Media New York. ISBN 978-1-4757-1702-0.

Download references

This work was supported by the National Key R&D Program of China (Grant Nos. 2022YFA1403700, 2021YFB3501201 and 2023YFA1406304), the National Natural Science Foundation of China (NSFC) (Nos. 11934007, 12074161, 12204221), NSFC Guangdong (Nos. 2016A030313650, 2020KCXTD001, 2022A1515012283), and the Guangdong Innovative and Entrepreneurial Research Team Program (No. 2016ZT06D348). The ARPES experiments were performed at BL03U of Shanghai Synchrotron Radiation Facility under the approval of the Proposal Assessing Committee of SiP.ME2 platform project (Proposal No. 11227902) supported by NSFC. The DFT calculations were performed at Center for Computational Science and Engineering of Southern University of Science and Technology. D.S. acknowledges support from NSFC (No. U2032208). C.L. acknowledges support from the Highlight Project (No. PHYS-HL-2020-1) of the College of Science, SUSTech.

These authors contributed equally: Xiang-Rui Liu, Ming-Yuan Zhu, Yuanwen Feng.

Department of Physics and Shenzhen Institute for Quantum Science and Engineering (SIQSE), Southern University of Science and Technology (SUSTech), Shenzhen, Guangdong, China

Xiang-Rui Liu, Ming-Yuan Zhu, Meng Zeng, Xiao-Ming Ma, Yu-Jie Hao, Yue Dai, Rong-Hao Luo, Yu-Peng Zhu & Chang Liu

Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, Liaoning, China

Yuanwen Feng & Bing Li

School of Materials Science and Engineering, University of Science and Technology of China, Shenyang, Liaoning, China

Yuanwen Feng & Bing Li

International Quantum Academy, and Shenzhen Branch, Hefei National Laboratory, Shenzhen, Guangdong, China

Xiao-Ming Ma

Japan Synchrotron Radiation Research Institute (JASRI), Hyogo, Japan

Kohei Yamagami

National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei, Anhui, China

Yi Liu, Shengtao Cui, Zhe Sun & Dawei Shen

National Key Laboratory of Materials for Integrated Circuits, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai, China

Jia-Yu Liu & Yu Huang

Shanghai Synchrotron Radiation Facility, Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai, China

Zhengtai Liu & Mao Ye

School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, Anhui, China

Dawei Shen

You can also search for this author in PubMed Google Scholar

C.L. and B.L. conceived and designed the research project. X.-R.L., Y.F., and B.L. grew and characterized the single crystals. X.-R.L., M.Z., X.-M.M., Y.-J.H., Y.D., R.-H.L., Y.-P.Z., K.Y., Y.L., S.C., Z.S., J.-Y.L., Y.H., Z.L., M.Y., D.S., and C.L. performed the ARPES measurements. M.-Y.Z. performed the DFT calculations. X.-R.L. and C.L. wrote the paper, with the help from all authors.

Correspondence to Bing Li or Chang Liu.

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

Reprints and permissions

Liu, XR., Zhu, MY., Feng, Y. et al. Observation of floating surface state in obstructed atomic insulator candidate NiP2. npj Quantum Mater. 9, 85 (2024). https://doi.org/10.1038/s41535-024-00699-3

Download citation

Received: 16 June 2024

Accepted: 19 October 2024

Published: 02 November 2024

DOI: https://doi.org/10.1038/s41535-024-00699-3

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative