INTRODUCTION

Over the past decade, substantial works have been performed on monolayer FeSe/SrTiO31,2,3, where the cross-interface charge transfer and electron–phonon coupling are suggested to play important roles in enhancing the superconductivity4,5,6,7,8,9,10,11. Exploring similar systems could offer alternative research aspects in understanding the interfacial interactions and to facilitate establishing a general picture. Such efforts in cobalt-based compounds have led to a promising candidate, monolayer CoSb/SrTiO3, which is predicted to adopt a tetragonal phase and similar band structures as monolayer FeSe/SrTiO312. Recently, a combined scanning tunneling microscopy/spectroscopy (STM/STS) and magnetization measurement reports possible superconductivity in two-dimensional (2D) CoSb with orthorhombic lattice13, where the triplet pairing symmetry is proposed14. Therefore, it is necessary to further explore the electronic properties of CoSb-based interface.

Depending on different growth conditions using molecular beam epitaxy (MBE), the CoSb-based interface is shown to be a versatile system not only manifesting as a 2D thin film but nanowire with quasi-one-dimensional (Q1D) stripes, where a gap opening at Fermi level (EF) is also observed13. It thus serves as a rich playground for studying the electronic properties in different dimensions. When the motion of electrons is confined in 1D, the Landau Fermi liquid theory tends to break down because the individual excitation is replaced by the collective mode, which is highly correlated. It leads to the Tomonaga–Luttinger liquid (TLL) model that has succeeded in understanding the distinctive characters of 1D systems, like the power-law-like behavior of various physical properties15,16,17,18,19. In order to understand the electronic properties under dimensional confinement in CoSb-related nanowires, it is critical to experimentally reveal their electronic structure by angle-resolved photoemission spectroscopy (ARPES).

In this paper, we have fabricated CoSb1−x nanoribbons on SrTiO3(001) substrates utilizing MBE. (Here, x is introduced to indicate that the system is likely slightly Sb deficient due to the re-evaporation of Sb. Further studies are required to determine the certain composition.) The Q1D stripes on nanoribbons give rise to straight Fermi surfaces (FSs). CoSb1−x/SrTiO3 is slightly hole doped, where the interfacial charge transfer is opposite to that in monolayer FeSe/SrTiO3. The near-EF spectral weight exhibits power-law-like suppression and obeys a universal temperature scaling, demonstrating the underlying TLL nature. The determined TLL parameter of ~0.21 reveals that CoSb1−x is in the strongly correlated regime. These results establish a model TLL system and provide clues for further studies on the CoSb-related interface.

RESULTS

Surface and structural characterization of as-grown nanoribbons

The surface and structural characterization of CoSb1−x are presented in Fig. 1. Figure 1a–c displays the STM topographic images of Samples I–III, respectively. The surface morphology shows a nanoribbon feature with a typical step height of ~1.2 nm (see Supplementary Fig. 1). Statistics over 35 nanoribbons in Sample III give the ribbon width of 3.9 ± 0.6 nm. In a close-up STM measurement of nanoribbon as in Fig. 1d, parallel stripes with a period of ~1.5 nm are identified, similar to the previous report13. The stripe structure determines the Q1D nature of electronic properties studied later. In ref. 13, a considerable quantity of clusters emerge in the nanowire sample with a nominal amount of 0.45 unit cell (0.45 uc). Whereas here in Sample I, no cluster is observed (Fig. 1a), suggesting the elevated coverage limit. By counting the area and orientations of all the nanoribbons in Fig. 1c, most of the nanoribbons are found to align along two mutually perpendicular directions, i.e., the [100] and [010] axes of SrTiO3 substrate (Fig. 1e).

Fig. 1: Surface morphology and in-plane lattice symmetry of CoSb1−x nanoribbons.
figure 1

a–c STM topographies of Samples I (0.45 uc), II (0.55 uc), and III (1 uc), respectively, measured with Vs = 3 V, I = 30 pA. Clusters of ~4 nm in height form on top of Sample III. d STM image of a [010]-oriented CoSb1−x nanoribbon of Sample III (Vs = 3 V, I = 30 pA). e Counted area and orientations of all the nanoribbons in (c). The definition of θ is shown in the inset. The black curve is the fitting result by two Gaussian peaks and a linear background. f, g RHEED image of Sample II with incident beam along the [100] direction and corresponding RHEED intensity curve along the red cut, respectively. h, i Same as (f, g) with a larger glancing angle and incident beam slightly off the [100] direction. In (g, i), the black curves are the fitting results by Gaussian peaks and quadratic polynomial backgrounds, and the black and red arrows indicate the diffraction signals from CoSb1−x and SrTiO3 substrate, respectively. a (=4.0 Å) is the lattice constant of CoSb1−x. The blue arrows represent the anticipated streak positions of the orthorhombic CoSb phase in ref. 13.

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To determine the in-plane lattice symmetry and lattice constant of nanoribbon, reflection high-energy electron diffraction (RHEED) measurements are performed on Sample II. The RHEED patterns of two different geometries are shown in Fig. 1f–i. In Fig. 1f, the RHEED image only displays CoSb1−x streaks with no noticeable superstructures, as evidenced by the single set of diffraction peaks in Fig. 1g. The absence of reconstruction of CoSb1−x streaks elucidates that the nanoribbon adopts in a lattice close to the tetragonal phase. When the glancing angle is increased and the incident beam is slightly off the [100] direction (Fig. 1h), both the sharp diffraction spots of SrTiO3 substrate and RHEED streaks of CoSb1−x are obtained. Based on the distances between (00) and (02) diffraction peaks from CoSb1−x and SrTiO3 substrate (Fig. 1i), the lattice constant of CoSb1−x is estimated to be 4.0 Å. Moreover, in Fig. 1i, there is no RHEED streak from the orthorhombic CoSb reported in ref. 13, further demonstrating that CoSb1−x nanoribbon possesses a different lattice structure from the orthorhombic phase13. Therefore, the corresponding unit cell should have the lattice constant of tetragonal phase ~4.0 Å along one axis, while having the period of the Q1D stripe ~1.5 nm along the other axis.

Experimental FS topology and band structures

To unravel the electronic properties of CoSb1−x nanoribbons, we have scrutinized the electronic structure by ARPES experiments. The measured FS of Sample III is shown in Fig. 2a, and the schematic FS is sketched in Fig. 2b. The Q1D character of FS topology can be better clarified in Fig. 2c, where we plot the momentum distribution curves (MDCs) of FS mapping in Fig. 2a (indicated by the translucent green rectangle in Fig. 2b). Within experimental uncertainty, the FS forms a straight line with no noticeable lateral dispersions, demonstrating that the electrons are under Q1D confinement. Moreover, since the experimental band structure is mostly a superposition of bands from mutually perpendicular nanoribbons, the detected FS adopts two sets of Q1D features. Based on the FS topologies, the Q1D Brillouin zone (BZ) size along the longitudinal direction of nanoribbon is consistent with the distance between diffraction streaks of nanoribbons in the RHEED measurements.

Fig. 2: FS topology and band structures of CoSb1−x nanoribbons.
figure 2

a Constant-energy ARPES image of Sample III (1 uc) was obtained by integrating the photoemission intensity within EF ± 40 meV. The red and blue cross marks are measured Fermi crossings. b Schematic FS topology of (a). Inset: Sketches of the [100] and [010] oriented CoSb1−x nanoribbons. The black solid and dashed lines in (a) represent the Q1D BZs of [010] and [100] oriented nanoribbons, respectively. The black solid lines in (b) indicate a series of Q1D BZs of [010] oriented nanoribbons, while the BZs of [100] orientation are omitted for better visualization. The solid and dashed schematic FS lines in (b) represent that of [010] and [100] oriented nanoribbons, respectively. c MDC plot of the constant-energy spectra in (a), which is indicated by the translucent green area in (b). The triangle markers are extracted from peak positions. d, e Intensity plot and corresponding MDCs along cut#1 in (b), respectively. f, g Same as (d, e) along cut#2 in (b). The red dashed curves in (d, f) are guides to the eye for the experimental band dispersions. The black markers in (e, g) are extracted peak positions. h Supercell contains an [010]-oriented ribbon of the freestanding tetragonal CoSb with a width of 3 uc (~1.2 nm). i Calculated FSs of the CoSb supercell in (h). The BZ of the supercell represented by the black solid lines shows an aspect ratio of 5: 1. j Calculated band structures of 3-uc-wide CoSb nanoribbon. The red and blue markers are experimental α and γ bands extracted from the MDCs in (g), respectively.

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The near-EF ARPES spectra of Sample III around Γ and X are measured along cuts#1 and #2 in Fig. 2b, respectively (Fig. 2d–g). The hole-like α band and electron-like γ band define the Q1D FSs. Although clusters occur in Sample III (Fig. 1c), their contribution to the band dispersions is not detectable and the resolved bands are the same as that of Samples I and II without clusters (see Supplementary Fig. 2). Further, despite the limited height of nanoribbons, quantum well states are not resolved in experiments; the identified α and γ are two different bands (see Supplementary Fig. 3 and Supplementary Note 1). We carry out band calculations by confining monolayer CoSb to Q1D along [010] direction (Fig. 2h) while retaining the tetragonal crystal structure. Both the calculated FSs (Fig. 2i) and essential band structures (Fig. 2j) resemble our experimental observations. Specifically, the hole bands around Γ correspond to the α band and the electron bands around X correspond to the γ band. By further comparing the 2D calculations in ref. 12 with our Q1D calculations (Fig. 2h–j), connections can be found between CoSb1−x nanoribbon and monolayer CoSb12. Therefore, the CoSb1−x nanoribbon system is likely a close counterpart of monolayer CoSb in a reduced dimension.

By calculating the volumes of both the hole- and electron-like FSs relative to the Q1D BZ size in Fig. 2a, CoSb1−x is found to be slightly hole doped with 0.08 holes/Co based on the Luttinger volume and double degeneracy of the FSs12 (see more discussion in Supplementary Note 2). This doping value is distinct from that of the heavily electron-doped monolayer FeSe/SrTiO3 (0.12 electrons/Fe)2,3, where the significant transfer of electrons from SrTiO3 substrate to monolayer FeSe originates from the large work function difference between them20,21. Therefore, the charge transfer and work function difference in CoSb1−x/SrTiO3 interface should be opposite to that in monolayer FeSe/SrTiO3, leading to hole doping. Further, because of the close connection between CoSb1−x nanoribbon and monolayer CoSb, it is reasonable to expect that the work function of monolayer CoSb is comparable to that of CoSb1−x, and the charge transfer at an interface with SrTiO3 substrate could be similar accordingly. This should serve as a useful piece of information in understanding the properties like potential superconductivity in CoSb-based interface in the future.

TLL origin of the spectral weight suppression

Notably, the ARPES spectral weight of CoSb1−x gradually decreases as approaching EF (Fig. 2d–g and Supplementary Fig. 2). We examine the temperature evolution of energy distribution curves (EDCs) at kF of Sample I (cut#1 in Fig. 2b). As plotted in Fig. 3a, the spectral weight is continuously depleted towards EF, and there is no Fermi edge and well-defined quasiparticle peak. The suppression near EF is clearer by comparing the k-integrated EDCs (cut#1 in Fig. 2b) to a polycrystalline Au spectrum with a steep Fermi edge in Fig. 3b. Although the nanoribbons misaligned from [100] and [010] orientations may give rise to “polycrystallinity” and momentum-averaged spectra with a reduced weight near EF, it would not deplete the density of states (DOS) at EF. As shown in Fig. 3c, similar spectral weight suppression is also observed in the STS spectra obtained on an individual nanoribbon. Therefore, the misaligned nanoribbons have a minor effect on spectral weight suppression near EF. This spectral weight depletion is not likely due to the disorder effect either. As suggested by the Altshuler–Aronov theory22, the DOS near EF of disordered metals is the summation of a finite constant and a power-law-like function23, which is distinct from our observation that the DOS nearly decreases to zero at EF. The similar momentum broadening of α band in Samples I and III indicates a similar level of disorder scattering and similar angular distribution of nanoribbons (see Supplementary Fig. 4), further implying the origin of spectral weight suppression is intrinsic. In a Peierls instability, the Q1D FS topology would induce a large charge density wave (CDW) susceptibility, which may lead to a CDW order or sizable CDW fluctuations24. The CDW order could be excluded in our case as the STS data in Fig. 3c exhibit continuous suppression towards EF without any signature of CDW gap formation, in contrast to the well-defined gap structure in the STS spectra of other typical Q1D CDW systems25,26. On the other hand, the CDW fluctuations could cause a pseudogap opening, which may explain the spectral weight suppression27,28. However, the suppressed spectral weight in a pseudogap would be filled up following a linear function of the temperature29, which is not observed in our case (Fig. 3a).

Fig. 3: Evidence of TLL state in CoSb1−x nanoribbons.
figure 3

a Temperature-dependent EDCs taken at kF (cut#1 in Fig. 2b) of Sample I (0.45 uc). b Integrated spectra (cut#1 in Fig. 2b) at T = 25 K in the range of −0.56 < ky < 0.56 Å−1, compared to a polycrystalline Au spectrum. c dI/dV spectra taken along the black arrow in the inset on an individual nanoribbon, with Vs = 60 mV, I = 100 pA (T = 4.7 K, ΔE ~ 2 mV). For clarity, each spectrum is offset with a constant conductance and the zero is indicated by a horizontal bar. The black curves are the fittings to the TLL model. The asymmetric amplitude of DOS may originate from the local electronic states affected by the size effect of nanoribbons. Inset: STM topography of CoSb1 − x measured with Vs = 0.8 V, I = 30 pA. d Logarithmic plot of the temperature-dependent integrated spectra [same as (b)]. The black line is a linear fit of data at 25 K in the binding energy range of 3–60 meV. e Same as (d) plotted in a linear scale. The spectra are vertically shifted for clarity. The black curves are the fittings to Eq. (1), convolved with Gaussian function of instrumental energy resolution (ΔE ~ 9 meV). f Universal scaling plot of the spectra in (e), where the spectral intensity is scaled as I/T0.74, and energy is normalized to E/kBT. Inset: logarithmic plot of the temperature-dependent spectral intensity at EF, where the data are extracted from (e). The black line is a linear fit, implying the power-law-like behavior with a power index of ~0.74.

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The spectral weight suppression can be well accounted for by the potential TLL state in CoSb1−x. Serving as the spectroscopic fingerprints of TLL, the power-law-like suppression and scaling behavior for low-energy DOS have been observed in several Q1D materials, like (TaSe4)2I17, Li0.9Mo6O1730, Au/Ge(001)31, Bi/InSb(001)32, and K2Cr3As333. By a linear fit to the integrated spectra at 25 K in the double-logarithmic plot (Fig. 3d), the power-law-like manner of DOS can be straightforwardly visualized. Because the finite temperature effect has not been considered, the curves at higher temperatures deviate from the simple power law below the binding energy of ~20 meV, which have also been observed in K2Cr3As333.

To quantitatively model the DOS according to TLL theory with finite temperature effect included, we fit the integrated spectra based on the following formula for photoemission spectral function34,

$$I(\epsilon ,T)\propto {T}^{\eta}\cosh \left(\right.\frac{\epsilon}{2}\left)\right.\,\left|\right.\,{{\Gamma}}\,\left(\right.\frac{1+\eta}{2}+i\frac{\epsilon}{2\pi}\left)\right.\,{\left|\right.}^{2}f(\epsilon ,T),$$
(1)

where ϵ = E/kBT, Γ(ϵ) is the gamma function, which is known as the Euler’s integral of the second kind, is one commonly used extension of the factorial function to complex numbers (see ref. 35 for detailed definitions), and f(ϵ, T) = (eϵ + 1)−1 is the Fermi–Dirac distribution function. After convolved with the Gaussian function of experimental energy resolution (ΔE ~ 9 meV), the fittings well reproduce the experimental spectra at different temperatures (Fig. 3e). The analysis is only done in a low-energy regime with binding energy lower than 60 meV, since at higher energies the β band could be involved in. The obtained power index η shows a temperature renormalization from 0.81 at 25 K to 0.76 at 70 K. A similar renormalization rule has been previously reported in Li0.9Mo6O17, the origin of which is proposed as the interacting charge-neutral critical modes that emerge from the two-band nature of the material30. Here in CoSb1−x, there are also two bands crossing EF (α and γ), we thus suggest that the temperature renormalization of η might be understood in terms of that in Li0.9Mo6O17.

Equation 1 further shows a universal power-law-like scaling relation, i.e., normalize the spectral intensity I(ϵ, T) at different temperatures to Tη and plot I/Tη versus temperature-renormalized energy ϵ = E/kBT, the renormalized spectra at different temperatures should coincide with each other if the scaling factor η is chosen properly. As shown in Fig. 3f and Supplementary Fig. 5, within experimental uncertainty, the corresponding spectra can be well scaled when η = 0.74 ± 0.05. The best scaling behavior is illustrated by comparing the scaling plots with various values of η (see Supplementary Fig. 5); as η departs from 0.74, the scaling becomes increasingly poor. Besides, based on Eq. (1), the spectral intensity at EF should manifest as I(0, T) ∝ Tη, showing the power-law-like scaling as a function of temperature. As plotted in the inset of Fig. 3f, the temperature-dependent I(0, T) follows a power-law-like manner with η ~ 0.74, agreeing well with the above analysis. Similar values of η (0.75–0.80) have also been reproduced by fitting the STS36,37 and ARPES spectra from two different samples (black curves in Fig. 3c and Supplementary Fig. 6, respectively). In the framework of TLL theory38, η is directly related to the TLL parameter K, which characterizes the electron–electron correlation strength, via η = (K + K−1 − 2)/4. We can deduce a value of K ~ 0.21, indicating CoSb1 − x is in the strongly correlated regime compared with K = 1 for the noninteracting Fermi liquid regime. The parameter is also comparable with that of other Q1D systems, for example, single-wall carbon nanotubes (K ~ 0.25)36, MoSe2 mirror twin boundaries (K ~ 0.28)39, SrNbO3.41 single crystals (K ~ 0.2)40, and Li2Mo6Se6 nanowires (K ~ 0.15)41. The strong correlation behavior in the Q1D CoSb1−x is the combined effect of the dimensional confinement and the electron–electron interaction in CoSb itself. As shown by our calculation in Fig. 2j, the overall bandwidth of Q1D CoSb is reduced by approximately half from that of monolayer tetragonal CoSb12, corresponding to a moderate level of correlation enhancement by the dimensional confinement. Another effect of the dimensional confinement is eliminating the quasiparticle weight by inducing the TLL state, which is confirmed by our observation. The correlation strength of CoSb itself is hard to quantify due to the lack of quasiparticle, while the observed dispersion in ARPES is from incoherent features that follow the bare dispersion without correlation effect. Indeed, the dispersions of α and γ bands extracted from MDCs match those in calculations (Fig. 2j). It calls for future experiments on monolayer CoSb films to reveal the underlying correlation strength.

DISCUSSION

It is worth noting that the Coulomb blockade from the size effect has been observed on isolated CoSb-related nanowires13. Statistics of the topography in Fig. 1a gives the total length of 38 ± 6 nm for connected nanoribbon domains, corresponding to an average gap size of ~3–5 meV from the Coulomb blockade studied by STS13. From this perspective, it is only ~10% of the leading edge position (binding energy of ~40 meV) of spectral weight suppression in Sample I (Fig. 3a), indicating that the Coulomb blockade would only have a minor contribution to the spectral weight suppression. Nevertheless, the Coulomb blockade has been observed by photoemission measurements in several interfacial materials and has been suggested as the dynamic final state effect during the photoemission process, which would induce statistical spectra broadening in the energy shifts42,43. Therefore, the Coulomb blockade may have a decoration effect on the spectral shape of Sample I, making a contribution to the spectral weight suppression near EF, while the good agreement of our data with the power-law analysis indicates the dominant role of the TLL state in CoSb1−x nanoribbons.

In summary, we have fabricated CoSb1−x nanoribbons with Q1D stripes on SrTiO3(001) substrates and investigated the electronic structure. The Q1D FS topology is revealed. CoSb1−x/SrTiO3 is slightly hole doped, where the interfacial charge transfer is opposite to that in monolayer FeSe/SrTiO3. The spectral weight near EF shows power-law-like suppression and obeys a universal temperature scaling, suggesting that CoSb1−x belongs to the TLL. The corresponding TLL parameter of ~0.21 uncovers its strongly correlated nature. Our study not only demonstrates a canonical TLL system but also sheds light on the understanding of the physics in CoSb-based interface.

METHODS

Synthesis of nanoribbons

CoSb1−x nanoribbons are fabricated by coevaporating Co (99.995%) and Sb (99.999%) from Knudsen cells on Nb-doped (0.5 wt%) SrTiO3(001) substrates. During the growth of samples with nominal amounts of 0.45 uc, 0.55 uc, and 1 uc, which are denoted as Samples I–III, the substrates are kept at ~130–160 °C, the cell temperatures of Co and Sb are set at 1162 and 337 ∘C, respectively. The corresponding growth rate is 0.02 uc/min.

ARPES and STM/STS measurements

ARPES experiments are performed in situ equipped with Fermi Instruments helium discharge lamp (21.22 eV He-Iα light) and a Scienta R4000 analyzer. The energy and angular resolutions are set to 9 meV and 0.3∘, respectively. During the measurements, the temperature is kept at 40 K if not specified otherwise and the working vacuum is maintained better than 4 × 10−11 mbar. The samples are then transferred to the RHK (data in Fig. 1a–d) and CreaTec (data in Fig. 3c) STM systems via a vacuum suitcase with a base pressure of 3 × 10−10 mbar. STM/STS measurements are conducted at low temperatures with Pt/Ir tips.

Computational methods and details

The energetic calculations and geometrical relaxations are performed using the Vienna ab initio Simulation Package44 within density functional theory. Valence electrons are described using the projector-augmented-wave method45,46. The exchange and correlation functions are treated using the Perdew–Bruke–Ernzerhof47 parametrization of generalized gradient approximation. The kinetic energy cutoff of the plane-wave basis is chosen to be 280 eV. A Γ-centered 15 × 15 × 1 Monkhorst–Pack48k-mesh is used for BZ sampling, and a much denser k-mesh of 45 × 45 × 1 is used for accurate DOS calculations. Electronic minimizations are performed with an energy tolerance of 10−6 eV, and optimized atomic structures are achieved when forces on all the atoms are <0.01 eV/Å. To model the Q1D CoSb nanoribbons, the supercells contain a ribbon of the freestanding tetragonal CoSb with a width of 3 uc (~1.2 nm), and to avoid the interference between neighboring nanoribbons, the ribbons are separated by a 2-uc-wide empty space (~0.78 nm) laterally on each side under periodic boundary conditions. To model a freestanding 2D monolayer CoSb, the supercells contain a slab of the monolayer CoSb with a vacuum region of more than 15 Å. The spin–orbit coupling effect is considered in band structure and DOS calculations.