Buried double CuO chains in YBa$_2$Cu$_4$O$_8$ uncovered by nano-ARPES

TL;DR

This study uses nano-ARPES to uncover the electronic structure of buried double CuO chains in YBa2Cu4O8, revealing metallic dispersions and Fermi surfaces that are highly one-dimensional but lack strong electron correlations.

Contribution

First observation of the electronic structure of buried double CuO chains in YBa2Cu4O8 using spatially-resolved nano-ARPES, clarifying their metallic nature and surface termination effects.

Findings

Buried CuO chains exhibit sharp metallic dispersions.

Fermi surfaces are highly one-dimensional.

No evidence of strong electron correlations or Luttinger liquid behavior.

Abstract

The electron dynamics in the CuO chains has been elusive in Y-Ba-Cu-O cuprate systems by means of standard angle-resolved photoemission spectroscopy (ARPES); cleaved sample exhibits areas terminated by both CuO-chain or BaO layers, and the size of a typical beam results in ARPES signals that are superposed from both terminations. Here, we employ spatially-resolved ARPES with submicrometric beam (nano-ARPES) to reveal the surface-termination-dependent electronic structures of the double CuO chains in YBa$_2$Cu$_4$O$_8$. We present the first observation of sharp metallic dispersions and Fermi surfaces of the double CuO chains buried underneath the CuO$_2$-plane block on the BaO terminated surface. While the observed Fermi surfaces of the CuO chains are highly one-dimensional, the electrons in the CuO-chains do not undergo significant electron correlations and no signature of a Tomonaga-Luttinger liquid nor a marginal Fermi liquid is found. Our works represent an important experimental step toward understanding of the charge dynamics and provides a starting basis for modelling the high-$T_c$ superconductivity in YBCO cuprate systems.

Tables

Table 1. Table 1: Interchain and itrachain hopping parameters ( t a subscript 𝑡 𝑎 t_{a} and t b subscript 𝑡 𝑏 t_{b} ), and hopping anisotropy | t b / t a | subscript 𝑡 𝑏 subscript 𝑡 𝑎 |t_{b}/t_{a}| of the inner and outer CuO 2 -chain bands (CH inner and CH outer ) for CuO-terminated and BaO-terminated surfaces, obtained by fitting tight-binding model to experimental Fermi surfaces.

		$t_a$ [eV]	$t_b$ [eV]	$\left|t_b/t_a\right|$
CuO	CHinner	0.003	0.20	66.7
BaO	CHinner	0.004	0.12	30.0
	CHouter	-0.004	0.17	42.5

Equations

$$E_k=-2t_a\cos (k^a\cdot a)-2t_b\cos (k^b\cdot b)-\mu ,$$

Full text

Identifying the role of the CuO chains is fundamentally important to understand superconductivity in high-$T_{\rm c}$ yttrium-barium-copper-oxide (YBCO) superconductors, in which quasi-one-dimensional (1D) CuO chains and two-dimensional (2D) CuO2 planes coexist. Due to the low dimensional electronic nature of the CuO chains, the electrons are generally expected to be strongly correlated because their motion is confined along the atomic chains Voit95 . Such electron dynamics in the coupled CuO chains was calculated using a variation of the dynamical mean field theory (DMFT) where all the 1D chains except for one-site are treated as a self-consistent bath (ch-DMFT), demonstrating a possible splitting of the 1D Fermi surface into Fermi pockets due to diverging self-energy in the chains Berthod95 .

Many experimental efforts using angle-resolved photoemission spectroscopy (ARPES) have been devoted on the single CuO-chain system, YBa2Cu3O7-δ (Y123), while the results and interpretations of the electronic structure has been not straightforward Schabel98 ; Lu01 ; Nakayama07 ; Zabolotnyy07 ; Hossain08 ; Okawa09 ; Fournier10 . This is mainly due to the coexistence of multiple CuO- and BaO-terminated surfaces on the cleaved surface Edwards92 ; Iwasawa18 . On the other hand, Kondo et al. succeeded in disentangling complex electronic structures originated in the CuO-chains and CuO2 planes in the double CuO-chains system, YBa2Cu4O8 (Y124), by utilizing spatially-resolved ARPES with sub-hundred micrometer beam (micro-ARPES) Kondo07 ; Kondo09 ; Kondo10 . It is noteworthy that they observed a spectral weight distribution at the Fermi surface that resembles those predicted by ch-DMFT calculations Kondo10 , suggesting strong electron correlations in the CuO chains.

These micro-ARPES results demonstrated that one of the CuO chains exposed on the CuO-terminated surface is insulating, while the other (subsurface) CuO chain is conducting. Although the mechanism of the electronic reconstruction resulting in the insulating chains is unknown, the reported CuO-chain states are representative of surface properties and distinct from those in the bulk, in which they are conductive and contribute to superconductivity Basov95 ; Hussey97 . Consequently, the electronic states of the 1D CuO chains related to the bulk superconducting properties has been not clarified yet.

In this Letter, we present the state-of-the-art ARPES study utilizing sub-micrometer probe spot (nano-ARPES) to clarify the termination-dependent electronic structure of the CuO chains in Y124. We observe the metallic dispersions of double CuO chains, buried underneath the CuO2 plane on the BaO-terminated surface, for the first time. The metallic behaviour of these double CuO chains is consistent with the bulk transport properties Basov95 ; Hussey97 , and quite different from the surface reconstructed structures observed in the CuO-terminated surface as in the previous micro-ARPES reports Kondo07 ; Kondo10 . In addition, we observe a highly 1D Fermi surfaces with a tiny warping due to the interchain coupling, while seeing no evidence of strong electron correlations nor characteristic 1D electronic behaviour. Our experimental data thus show the intrinsic electronic properties of the native CuO chains of Y124 in full.

High-quality single crystals of Y124 ($T_{c}$ = 82 K) were grown by the flux method at ambient pressure Song07 . Experiments were performed using the newly-developed nano-ARPES instrument at beamline I05 of the Diamond Light Source with a spatial resolution better than 500 nm (see the Supplementary Note 1 and Note 2 SM ). Nano-ARPES data were collected at a photon energy of 60 eV with linear horizontal polarization using a DA30 electron analyser (Scienta-Omicron). Samples were cleaved in situ under ultra-high-vacuum conditions ($\sim$1\times$$10^{-10} mbar) and kept at a temperature of 30 K. The total instrumental energy resolution including the light, analyser, and thermal broadening were set to be better than 50 meV for spatial mapping, and 35 meV for measuring band dispersions and Fermi surfaces. The angular resolution was better than 0.13∘, estimated by fitting angular distribution curves at the Fermi level ($E_{\rm F}$) using a Voigt function.

Figure 1(a) illustrates setup for nano-ARPES experiments, where a submicrometric beam can be provided by utilizing focusing optics in close vicinity to the sample. For polar angular scans ($\theta$), a deflector scan of the electron analyser lens ($\theta_{a}=\pm 10^{\circ}$) was used against the detector slit in the vertical direction. This does not require changing the geometry between the light and sample, thus ensuring stable illumination of and data acquisition from a microscopic spot of the material.

Figure 1(b) shows a scanning photoemission microscopy (SPEM) image of Y124 obtained by integrating the valence bands (VB) intensity in a fixed energy window [shaded areas in Fig. 2(e)] and scanning the sample along two in-plane directions ($X$ and $Y$). The overall topography shown in Fig. 1(b) is consistent with the ex-situ optical microscope (OM) images [Fig. 1(c)]. As the cleaved surface of Y124 is generally expected to contain multiple surface terminations due to either CuO-chains or BaO-layer [Figs. 1(d)-(f)]. In the following, to reveal intrinsic intensity modulations related with different surface terminations, we focus on a small area on the sample surface [red square in Fig. 1(b)] where height fluctuations are small ($<$1-3 $\mu$m), well below the focal depth of the nano-ARPES setup.

In Fig. 2, we use nano-ARPES to identify the different surface terminations on the cleaved (001) plane of Y124, and characterize the electronic structure in each case. Figure 2(a) shows the spatial mapping image of total ARPES intensity near $E_{\rm F}$ along the high-symmetry Y-$\Gamma$-Y line [see Fig. 2(c)]. As seen in the calculated band dispersions [Fig. 2(d)], the electronic structure along the $\Gamma$Y direction near $E_{\rm F}$ consists of two bands, in each case of double CuO chains and bilayer CuO2 planes bands Yu91 . To reveal the separate contributions of the CuO chains and CuO2 planes, we performed an analysis of the spatial mapping data by utilizing narrow integration windows in both energy and momentum. First, the integration windows were determined so as to be sensitive to either bands from CuO chains or CuO2 planes as indicated by red and blue boxes in Fig. 2(e), which yields the two-dimensional intensity maps ($I_{\rm CH}$ and $I_{\rm PL}$, respectively). Secondly, we deduced the intensity ratio of the mean deviation between the CuO chains and CuO2 planes as $(I_{\rm CH}-\overline{I_{\rm CH}})/(I_{\rm PL}-\overline{I_{\rm PL}})$, where the $\overline{I_{\rm CH}}$ and $\overline{I_{\rm PL}}$ are the mean value of $I_{\rm CH}$ and $I_{\rm PL}$, respectively. The resulting image shown in Fig. 2(d) highlights the dominant signal from to the CuO chain bands in red and the CuO2 plane bands in blue. Thirdly, core level spectra in each domain displayed in Fig. 2(e) show significant differences, particularly in the binding energies of Ba 5$p$ core levels. This chemical shift is unambiguously found in the two types of domains and attributed to different surface terminations of CuO-chains or BaO-layer Iwasawa18 (see also Supplementary Note 3 SM ). In what follows, we focus on ARPES features that are attributed to the CuO chains but are probed on the two different surface terminations CuO and BaO.

Having thus characterized the CuO-chain or BaO-layer terminated surface regions, we perform nano-ARPES measurements on each termination [red region for the CuO-terminated surface and the blue region for the BaO-terminated surface in Fig. 2(d)]. Owing to its strong surface sensitivity, we can expect the ARPES spectra to be dominated by emission from the top-most surface layer: a CuO chains layer for the CuO-terminated surface and a CuO2 plane layer for the BaO-terminated surface as seen in the schematic drawings of the possible stacking layer along the $c$-axis [Figs. 3(a), (g)]. The BaO layer itself is not expected to contribute to the electronic structure near $E_{\rm F}$ due to its insulating nature. Figures 3(b), (h) show the ARPES data along the high-symmetry direction Y-$\Gamma$-Y on CuO-chain and BaO-layer terminations, respectively. Consistent with previous micro-ARPES results on the CuO-terminated surface Kondo07 ; Kondo10 , two strong dispersive features derived from CuO-chains near the surface (${\rm CH_{CuO}^{TS}}$) are observed centred at the $\Gamma$ point. The inner-chain band dispersion crosses $E_{\rm F}$, while the outer-chain band does not cross $E_{\rm F}$, but rather reaches only up to a maximum point located at $\sim$0.12 eV below $E_{\rm F}$. Similarly, for the BaO-terminated surface, two bands exist centred at the $\Gamma$ point besides the broad CuO2 plane bands dispersing from the $\Gamma$ point towards the Y point at $k^{a}=\pm\pi/a$ [blue dashed line in Fig. 3(j)]. Here, observed for the first time in our data, we find sharp metallic dispersions for the both states of the double CuO chains. It is worth stressing that these observed CuO chains states on the BaO-terminated surface must arise from sub-surface CuO-chains layer (${\rm CH_{BaO}^{SS}}$) beneath the CuO2 planes and these states are significantly different from those observed in ${\rm CH_{CuO}^{TS}}$.

The observed distinct behaviours between the ${\rm CH_{CuO}^{TS}}$ and ${\rm CH_{BaO}^{SS}}$ are also visualised in the momentum distribution curves (MDCs) in Figs. 3(c), (i), and MDC-derived band dispersions in Figs. 3(d), (j). Astonishingly, the MDC dispersions (red circles) can be fitted very well by a simple shift of the band dispersions calculated by density functional theory (DFT) Yu91 (grey lines) along the energy axis as shown in Figs. 3(d), (j). This implies a small effect of mass renormalization due to electron correlations on either surface termination. An analysis of effective masses relative to the free electron mass $m_{e}$ gives $m^{*}=0.92~{}m_{e}$ for the outer and $m^{*}=0.49~{}m_{e}$ for the inner CuO chain bands, irrespective of surface terminations.

The constant energy planes shown in Figs. 3(e), (k) highlight again the difference between the ${\rm CH_{CuO}^{TS}}$ and ${\rm CH_{BaO}^{SS}}$, which can be confirmed not only along the high-symmetry line but also in a wider region across the Brillouin zone. Either ${\rm CH_{CuO}^{TS}}$ and ${\rm CH_{BaO}^{SS}}$ are dominant in the maps, while the bands of the CuO2 plane are less visible [Figs. 3 (e), (k)]. We then determine the quasi-1D CuO-chain Fermi surfaces precisely by fitting MDCs as shown in Figs. 3(f), (l), where a very small but finite warping along the $k^{a}$ is observed. This is assigned to finite interchain coupling. To evaluate the in-plane charge transfer due to interchain and intrachain couplings, we fit the Fermi momentum plots using a simple tight-biding model for one-dimensional chain Nicholson17 given by

[TABLE]

where $\mu$ is the chemical potential, and $t_{a}$ and $t_{b}$ are hopping parameters across and along the chain, respectively (see also Supplementary Note 4 SM ). The quasi-1D dispersions can be well reproduced by the model with the parameters summarized in Table 1. We found that the interchain hopping $t_{a}$ is consistently small compared to the intrachain hopping for all CuO-chain bands, resulting in the large hopping anisotropy given by $|t_{b}/t_{a}|$.

Meanwhile, the tight-binding fit of the Fermi surface also provides an estimation of the carrier concentration. We confirmed that the carrier concentration is almost maintained for the CuO-terminated surface while extra hole-doping is present in the case of the BaO-terminated surface (see Supplementary Note 5 SM ). Despite the hole-doping difference, we interpret that the metallic CuO-chain states ${\rm CH_{BaO}^{SS}}$ on the BaO-terminated surface is more representative of bulk properties because (1) they are free from exotic surface insulation effects seen in the top-most CuO-chain exposed on the CuO-terminated surface and (2) the inner CuO-chain bands on both surface-terminations show a rigid-band shift as well as the similar Fermi surface warping.

Our experimental observations of the metallic ${\rm CH_{BaO}^{SS}}$ states provide important insights into the in-plane charge dynamics on the 1D CuO chains in the Y124 system. According to ch-DMFT calculations for the coupled 1D chains Berthod95 , the 1D chain Fermi surface shows a strong anisotropy due to the interchain coupling with an intermediate coupling strength ($t_{a}^{c1}<t_{a}<t_{a}^{c2}$, where $t_{a}^{c1}$ and $t_{a}^{c2}$ are some critical hopping parameters). This may lead to a formation of Fermi pockets which are disconnected at ($k^{a}$, $k^{b}$) = (0, $\pi/2b$) because of the divergence of the self-energy. Indeed, the calculated intensity distributions were similar to what were observed in the previous micro-ARPES results Kondo10 . However, this scenario must be inapplicable to the present system because the interchain hopping is found to be critically small ($t_{a}<0.03t_{b}\ll t_{a}^{c1}$). This interpretation is also supported by the experimental observation of the continuous Fermi surface with a finite spectral weights at $E_{\rm F}$ around ($k^{a}$, $k^{b}$) = (0, $\pi/2b$) [Figs. 3(e), (k)].

The observed strong hopping anisotropy in the CuO chain, on the other hand, should enhance the 1D directionality of the CuO-chain electronic states, which may lead to characteristic 1D electronic excitations of a Tomonaga-Luttinger liquid (TLL). However, we did not observe the power-law depletion of spectral weight in the vicinity of $E_{\rm F}$ Voit95 , given by $\rho(\omega)\propto|\omega|^{\alpha}$. Furthermore, we did not observe any steep broadening of quasiparticle lifetime near $E_{\rm F}$ with a linear $\omega$-dependence Varma96 expected for a marginal Fermi liquid (FL) nor the significant effective mass enhancement due to electron correlations. We therefore see that the electrons on CuO-chains behave like 1D Fermi gas along the CuO chain in Y124. Meanwhile, we also predict that a longitudinal hopping ($t_{c}$) may exist. An orbital hybridization between the CuO chain $3d_{y^{2}-z^{2}}$ orbitals and CuO2 plane $3d_{3z^{2}-r^{2}}$ orbitals via apical oxygen 2$p_{z}$ orbitals was predicted based on more bulk sensitive experiments on the analogous Y123 system using x-ray absorption spectroscopy (XAS) and resonant inelastic x-ray scattering (RIXS) Magnuson14 . This interpretation is also in line with the 3D metallic transport properties of Y124 Hussey97 . Further studies on the $t_{c}$ hopping would be of interest to address this point.

In summary, we present the termination-dependent electronic structure of Y124 using nano-ARPES. The observed electronic properties of the CuO chains are quite different between the CuO- and BaO-terminated surfaces. The exposed CuO chains (${\rm CH_{CuO}^{TS}}$) on the CuO termination show gapped features reflecting significant surface effects, consistent with the earlier reports using micro-ARPES results Kondo07 ; Kondo10 . In contrast, we observe the double metallic dispersions for the CuO chains (${\rm CH_{BaO}^{SS}}$) buried underneath the CuO2 plane on the BaO-terminated surface for the first time. The uncovered metallic ${\rm CH_{BaO}^{SS}}$ bands on the BaO-terminated surface exhibit a highly 1D Fermi surface with a very small warping due to interchain coupling ($t_{a}<0.03t_{b}$) as well as a hopping anisotropy between inter- and intra-chain couplings ($|t_{b}/t_{a}|>30$). Nevertheless, we do not find any signature of neither the 1D TLL nor marginal FL, and the electrons in the CuO-chains do not undergo significant electron correlations as represented by their small effective masses and un-renormalized band width. These findings should be implemented in a future theoretical framework, which may help to understand the high-$T_{c}$ superconductivity in YBCO cuprate systems.