Disappearance of Superconductivity and a Concomitant Lifshitz Transition in Heavily-Overdoped Bi2Sr2CuO6 Superconductor Revealed by Angle-Resolved Photoemission Spectroscopy

TL;DR

This study uses ARPES to reveal a Lifshitz transition from hole-like to electron-like Fermi surface in heavily overdoped Bi2Sr2CuO6, coinciding with the loss of superconductivity, thus linking Fermi surface topology changes to superconducting suppression.

Contribution

It provides direct experimental evidence of a Lifshitz transition in heavily overdoped cuprate superconductors and connects Fermi surface topology change with the disappearance of superconductivity.

Findings

Lifshitz transition occurs at doping level ~0.35.

Fermi surface changes from hole-like to electron-like.

Superconductivity vanishes as Fermi surface undergoes transition.

Abstract

By partially doping Pb to effectively suppress the superstructure in single-layered cuprate Bi2Sr2CuO6+{\delta}(Pb-Bi2201) and annealing them in vacuum or in high pressure oxygen atmosphere, a series of high quality Pb-Bi2201 single crystals are obtained with Tc covering from 17 K to non-supercondcuting in the overdoped region. High resolution angle resolved photoemission spectroscopy (ARPES) measurements are carried out on these samples to investigate the evolution of the Fermi surface topology with doping in the normal state. Clear and complete Fermi surface are observed and quantitatively analyzed in all these overdoped Pb-Bi2201 samples. A Lifshitz transition from hole-like Fermi surface to electron like Fermi surface with increasing doping is observed at a doping level of ~0.35. This transition coincides with the change that the sample undergoes from superconducting to non-superconducting states. Our results reveal the emergence of an electron-like Fermi surface and the existence of a Lifshitz transition in heavily overdoped Bi2201 samples. They provide important information in understanding the connection between the disappearance of superconductivity and the Lifshitz transition in the overdoped region.

Full text

The normal state of high temperature cuprate superconductors, characterized by their unusual and distinct temperature dependence in the transport propertiesATFiory1987MGurvitch ; WFPeck1994HYWang ; KKitazawa1995JMHarris , is markedly different from the usual metals that can be well described in terms of the Fermi liquid theory. The scattering process of the electrons around Fermi surface dominates the macroscopic physical properties of materials, therefore, the shape and size of Fermi surface play key roles in understanding the anomalous normal state properties of cuprate superconductors. In the underdoped, optimally-doped and even slightly overdoped regions, due to the existence of pseudogapBStatt1999TTimusk , the quantitative determination of Fermi surface topology is complicated from the debate between Fermi arc (gapless Fermi surface section) and Fermi pocket (small closed Fermi pocket)ZXShen1996DSMarshall ; DGHinks1998MRNorman ; ZXShen2005KMShen ; JCCampuzano2006AKanigel ; ZXShen2007WSLee ; GDGu2008HBYang ; LTaillefer2007NDLeyraud ; NEHussey2008AFBangura ; JRCooper2008EAYelland ; XJZhou2009JMeng . Meanwhile, the pseudogap is suppressed or absent in the heavily overdoped regionJCCampuzano2011UChatterjee ; JZaanen2015BKeimer and it makes it possible to obtain complete Fermi surface in the samples that still exhibit unusual normal and superconduting propertiesYShimakawa1992TManako ; CTLin1996APMackenzie ; XJZhou2010LZhao . Assuming that the same superconductivity mechanism operates inside the superconducting dome, the study of the overdoped region provides an alternative and less complicated route in understanding the evolution between the superconducting state and non-superconducting state with doping. In (La2-xSrx)CuO4 system, it was reported that its Fermi surface topology in the normal state changes from a hole-like pocket (centered at ($\pi$,$\pi$)) in the underdoped and optimally-doped regions to an electron-like pocket (centered at (0,0) in the overdoped regionXJZhou_JESRP2002 ; SUchida2006TYoshida . It is natural to ask whether this transition is universal or not, and whether there is a connection between the Fermi surface topology change and the disappearance of superconductivity in the heavily overdoped region in other cuprate superconductors. In the Bi2Sr2CaCu2O8 (Bi2212) system that has been most extensively studied by angle resolved photoemission spectroscopy (ARPES), such a study has not been possible because it remains difficult to get Bi2212 samples with high enough doping that approaches the superconducting to non-superconducting transition. In comparison, the single-layer Bi2Sr2CuO6 (Bi2201) system provides another desirable candidate for such a purpose. It contains a single CuO2 plane within one structural unit (half unit cell), giving a single band and a single Fermi surface sheet that avoid band structure complications from multi-layered compounds where there is a band splittingZXShen2001DLFeng ; SIUchida2001YDChuang ; SMaekawa2003SEBarnes . In particular, it has been found that by partially substituting Bi with Pb in Bi2Sr2CuO6+δ (Pb-Bi2201), together with annealing under different conditions, the samples can be pushed to the overdoped and heavily overdoped regions to become even non-superconductingXJZhou2010LZhao . Furthermore, the Pb-substitution can also suppress the incommensurate superstructure formation in Bi2201, thus removing the electronic structure complications from the superstructure bands that occur in Bi2212 and other multi-layered bismuth systems. Therefore, Pb-Bi2201 provides an ideal system to investigate the electronic structure evolution with doping in the heavily overdoped region.

In this paper, a series of Pb-Bi2201 single crystals have been prepared that covers the overdoped region (with a Tc at 17 K) to heavily overdoped region, and to extremely overdoped region where the samples become non-superconducting. ARPES measurements are carried out to investigate the evolution of their Fermi surface topology with doping in the normal state. Clear and complete Fermi surfaces have been observed and quantitatively analyzed for all the samples. With the increase of doping accompanying the decrease of Tc, the Fermi surface of Pb-Bi2201 undergoes a Lifshitz transition changing from a hole-like pocket in the overdoped region to electron-like pocket in the extremely overdoped region. Our results reveal the emergence of electron-like Fermi surface in extremely overdoped Bi2201. They also provide important information in understanding the connection between the disappearance of superconductivity and the Lifshitz transition in the overdoped region..

High quality Bi1.74Pb0.38Sr1.88CuO6+δ (Pb-Bi2201) single crystals were grown by floating-zone techniqueXJZhou2010LZhao . Plate-like single crystals with a size up to 5mm$\ast$10mm were obtained. The as-grown single crystals were post-annealed in different atmospheres, including in vacuum, flowing Ar, flowing air and high pressure oxygen at different temperatures (400∘C $\sim$ 600∘C) and for different times to change the doping level and to make the samples more homogeneous. All of the samples were quenched in liquid nitrogen right after the post-annealing in order to get sharp superconducting transition. The annealed samples were characterized by X-ray diffraction (XRD), magnetic susceptibility and electrical resistivity measurements, and the results for five representative samples with different superconducting transitions are shown in Fig.1. They are marked as OD17K for overdoped Tc =17 K sample, OD11K for overdoped Tc =11 K sample, OD7K for overdoped Tc=7 K sample, OD3K for overdoped Tc=3 K sample, ODNS for overdoped non-superconducting sample, respectively. The OD11K and OD17K samples were obtained by annealing the as grown Pb-Bi2201 sample in flowing Ar atmosphere and in vacuum, respectively, which can effectively remove extra oxygen to increase Tc. The OD3K sample was obtained by annealing in air and the non-superconducting ODNS sample was obtained by annealing in high pressure oxygen atmosphere which can put more oxygen into sample to increase the hole doping.

High resolution angle-resolved photoemission measurements were performed on our photoemission system equipped with a Scienta R4000 electron-energy analyzer and a helium-discharge lamp, which gives a photon energy of h$\nu$ =21.218 eVXJZhou2008GDLiu . The light on the sample is partially polarized. The energy resolution is set at 10$\sim$20 meV and the angular resolution is $\sim$ $0.3^{\circ}$ corresponding to 0.008 ${\AA}^{-1}$ momentum resolution at the photon energy of 21.218 eV. All of the samples were cleaved in situ at a low temperature of 30 K and measured in ultrahigh vacuum with a base pressure better than 5$\times$10*-11* mbar and at a temperature of 20 K in the normal state. The Fermi level is referenced by measuring on the Fermi edge of a clean polycrystalline gold that is electrically connected to the sample.

Figure 1(a) shows X-ray diffraction (XRD) patterns for some typical annealed Pb-Bi2201 single crystal samples which were measured by using a rotating anode x-ray diffractometer with Cu Kα radiation ($\lambda$=1.5418$\AA$). All the observed peaks can be indexed to the (00$l$) peaks of Bi2201, indicating a pure single-phase of the single crystals. The peaks are sharp, as exemplified from the (008) peaks in the top-left inset of Fig. 1(a) which have a width of $\sim$ 0.2∘ (full width at half maximum), indicating high crystallinity of the single crystals. The c axis lattice constant is shown in the top-right inset of Fig.1(a) which exhibits a monotonous decrease with Tc but totally only 0.04% change is observed from the OD17K sample to the ODNS sample. This indicates the annealing process has a negligible effect on the lattice constant. Instead, it mainly changes the extra oxygen content in Pb-Bi2201. Figure 1(b) shows the temperature dependence of the magnetization for these Pb-Bi2201 single crystals measured under a magnetic field of 1 Oe. All the samples show narrow superconducting transition width within 1$\sim$2 K. Figure 1(c) shows the temperature dependence of in-plane resistivity for the ODNS sample, measured using the standard four-probe method. The resistivity is found to be metallic with a concave shape that is commonly observed in heavily-overdoped samples such as La1.7Sr0.3CuO4NEHussey2003SNakamae .

Figure 2 shows the Fermi surface evolution of a series of Pb-Bi2201 samples with different dopings and different Tcs measured at a temperature of 20 K. Figures 2(a)-2(e) show the Fermi surface mappings for five representative overdoped Pb-Bi2201 samples from OD17K, OD11K, OD7K, OD3K to ODNS samples, respectively. They are obtained by integrating the photoemission spectral weight within [-5, 5] meV energy window with respect to the Fermi level as a function of kx and ky. Fig. 2(f) shows the schematic Fermi surface that includes the main Fermi surface (black solid lines) and shadow Fermi surface (dashed lines) that are symmetrical with respect to the (0,$\pm\pi$)-($\pm\pi$,0) lines in the Brillouin zoneJFink2004AKoitzsch ; KHirota2006Nakayama ; MSGolden2006AMans . All the samples show clear main Fermi surface (marked by red dashed lines in Figures 2(a)-2(e)) and shadow Fermi surface,and the spectral weight of the shadow Fermi surface is much weaker than that of the main Fermi surface. All the observed features can be assigned to either the main Fermi surface or shadow Fermi surface with no sign of Fermi surface from superstructure modulation which are commonly observed in Bi2212. This further confirms that the incommensurate superstructure is well suppressed by Pb substitution in Pb-Bi2201XJZhou2010LZhao . For the OD17K sample (Fig.2(a)), its Fermi surface is hole-like with barrels centered around the ($\pi$,$\pi$) and its equivalent points. The typical feature is that two separated Fermi surface sheets cross around the (-$\pi$,0) antinodal region and its equivalent points nearly in parallel without any touching. With the increase of doping and decreasing of Tc, the overall Fermi surface topology changes gradually and the major topology change occurs around the antinodal region. From OD17K to OD7K samples (Fig.2(b) and 2(c)), the two Fermi surface sheets near (-$\pi$,0) get closer and closer, but their separation is still clear which indicates that they still have hole-like Fermi surface topology. For the OD3K sample (Fig.2(d)), these two Fermi surface sheets nearly touch at (-$\pi$,0) point. For the ODNS sample (Fig.2(e)), it is clear that these two Fermi surface sheets merge together before approaching (-$\pi$,0) which indicates an electron-like Fermi surface topology with barrels centered around the (0,0) point. These results indicate that there is a critical doping between OD3K and ODNS samples, where a lifshitz transitionLifshitz1960 occurs with the Fermi surface topology changing from a hole-like to an electron-like topology.

To reveal the Fermi surface topology transition in more detail, we focus our attention on the antinodal region around (-$\pi$,0). Figure 3 shows the Fermi surface and band structures around the antinodal regions for the OD17K and ODNS samples. For each sample, we carried out detailed momentum-dependent measurements around (-$\pi$,0) point (A1-A6 in Fig.3(a) for OD17K sample and B1-B6 in Fig.3(b) for ODNS sample). For the OD17K sample, small electron-like bands with the band bottom below the Fermi level can be observed for all the six momentum cuts (Fig.3(c)). Two-peak features are obvious in all their corresponding momentum distribution curves (MDCs) at the Fermi level in Fig.3(d). Especially for the key momentum cut A2,which crosses the (-$\pi$,0) point, both the measured band and the MDC at the Fermi level clearly indicate the existence of two Fermi momenta kFs. These have provided clear evidence that the OD17K sample has a hole-like Fermi surface topology. On the other hand, for the ODNS sample, the situation is different. Small electron bands can only be observed for the bands of momentum Cut B4 to B6(Fig.3(e)). Their corresponding MDCs also exhibit two-peak feature in Fig.3(f). However, for the spectral images of Cut B3 to B1 (Fig.3(e)), which cover (-$\pi$,0) point, only a small patch is observed and the corresponding MDCs exhibit one peak feature. This provides clear evidence of an electron-like Fermi surface in the ODNS sample.

For the Bismuth-based cuprate superconductors, the band structures around the antinode region determine the Fermi surface topology. It is also essential to locate the Fermi momentum kF precisely at the nodal region to get an accurate carrier concentration of the sample. Figure 4(a) shows the band structures along (-$\pi$,-$\pi$)-($\pi$,$\pi$) nodal direction crossing (0,0) point measured at 20 K for OD17K, OD11K and ODNS samples, respectively. These three images cover two main bands which should be centrosymmetric to the $\Gamma$(0,0) point. Their corresponding MDCs at the Fermi level are shown in Fig.4(b). The MDC peak positions determine the Fermi momentum kF along the nodal direction and the results are shown in the inset of Fig.4(b). Within our experimental uncertainty, the nodal kF exhibits only a slight change within our measured doping range. Figures 4(c) and 4(d) summarize the photoemission images measured crossing the (-$\pi$,0) point and the corresponding MDCs at the Fermi level for all the five samples. With the increase of doping, the photoemission images evolve from an electron-like band to a small patch-like feature, and the corresponding two-peak MDCs change into a single peak feature. This is consistent with the evolution of the Fermi surface topology from the hole-like to the electron-like. Figure 4(e) summarizes all the Fermi surfaces quantitatively determined in the first Brillouin zone. The corresponding carrier concentration (obtained according to the area of the Fermi surface) increases from $\sim$ 0.3 holes/Cu for OD17K to $\sim$ 0.4 holes/Cu (the inset in Fig.4(e)). Around the antinodal region, it is clear that there is a Lifshitz transition with increasing doping at $\sim$0.35 doping level.

It is well known that there is a close relationship between the Lifshitz transition and superconductivity, such as Lifshitz transition at the onset of superconductivityAKaminski2010CLiu , collapse of the normal-state pseudogap at a Lifshitz transitionAForget2015SBenhabib and enhancement of superconductivity at a Lifshitz transitionHDing2017XShi . Our results indicate that the Lifshitz transition occurs at a critical doping somewhere between the OD3K and ODNS samples. For the OD3K sample at the antinode, the two Fermi surface sheets almost touch. For the ODNS sample, they already merge and the Fermi surface becomes electron-like. It is interesting to note that the Lifshitz transition observed in Pb-Bi2201 occurs at a critical doping where the superconductivity also disappears. This observation may provide a possible connection between the disappearance of superconductivity and the Lifshitz transition in the Bi2201 system.

Our present results pose an interesting and challenging question on the origin of superconductivity in cuprate superconductors. Compared with another prototypical single-layer La2-xSrxCuO4 (LSCO) system, Pb-Bi2201 is unique in two aspects. First, for the LSCO, the Fermi surface change from the hole-like to the electron-like occurs at a doping level of $\sim$0.16 holes/Cu which is only slightly overdopedXJZhou_JESRP2002 ; SUchida2006TYoshida . For the Pb-Bi2201 system, such a transition occurs at a much higher doping level $\sim$0.35. Second, when the Lifshtz transion occurs in LSCO, the sample is still superconducting. However, in Pb-Bi2201 system, the Lifshitz transition happens at the doping level where the sample becomes non-superconducting. It is generally believed that superconductivity in cuprate superconductors is dictated mainly by doping the CuO2 planes. For the same single-layer systems, the doping dependence of superconductivity is very different between the LSCO and Pb-Bi2201 systems. The origin of such a dramatic difference is interesting and requires further investigation.

In summary, by carrying out high resolution angle-resolved photoemission spectroscopy measurements on Pb-Bi2201 to investigate the evolution of the Fermi surface topology with doping in the normal state, we have revealed a Lifshitz transition from a hole-like Fermi surface topology to an electron-like Fermi surface topology with increasing doping in the heavily overdoped Pb-Bi2201 system. The Lifshitz transition coincides with the disappearance of superconductivity. Our results provide a possible connection between the disappearance of superconductivity and Lifshitz transition in Bi2201 system. They also provide important information to understand the superconductivity in the overdoped region of high temperature cuprate superconductors.