Absence of a BCS-BEC crossover in the cuprate superconductors

Uezono Y., Otsuka T., Hagisawa S., Taniguchi H., Matsukawa M., Fujii T., Watanabe T.

Tromp W.O., Benschop T., Ge J., Battisti I., Bastiaans K.M., Chatzopoulos D., Vervloet A.H., Smit S., van Heumen E., Golden M.S., Huang Y., Kondo T., Takeuchi T., Yin Y., Hoffman J.E., et. al.

AbstractThe cuprate high-temperature superconductors exhibit many unexplained electronic phases, but the superconductivity at high doping is often believed to be governed by conventional mean-field Bardeen–Cooper–Schrieffer theory1. However, it was shown that the superfluid density vanishes when the transition temperature goes to zero2,3, in contradiction to expectations from Bardeen–Cooper–Schrieffer theory. Our scanning tunnelling spectroscopy measurements in the overdoped regime of the (Pb,Bi)2Sr2CuO6+δ high-temperature superconductor show that this is due to the emergence of nanoscale superconducting puddles in a metallic matrix4,5. Our measurements further reveal that this puddling is driven by gap filling instead of gap closing. The important implication is that it is not a diminishing pairing interaction that causes the breakdown of superconductivity. Unexpectedly, the measured gap-to-filling correlation also reveals that pair breaking by disorder does not play a dominant role and that the mechanism of superconductivity in overdoped cuprate superconductors is qualitatively different from conventional mean-field theory.

Shi T., Zhang W., Sá de Melo C.A.

Abstract We discuss the evolution from Bardeen-Cooper-Schrieffer (BCS) to Bose superconductivity vs. carrier density n in two-dimensional (2D) gated superconductors and address the fundamental role that the interaction range plays in the Berezinskii-Kosterlitz-Thouless transition. We investigate the density dependence of the critical temperature (T c ), superfluid density, order parameter modulus, chemical potential and pair size. Our most important finding is that it is absolutely essential to include classical and quantum phase fluctuations, as well as finite-ranged interactions to explain the non-monotonic behavior of T c vs. n and to guarantee that the upper bound on T c is not exceeded in 2D superconductors, as experimentally observed in (Nakagawa Y. et al., Science, 372 (2021) 190), a lithium-intercalated layered nitride, and in magic-angle twisted trilayer graphene (Park J. M. et al., Nature, 590 (2021) 249). Furthermore, we show that we can extract, from measurements of T c and the order parameter modulus, the effective mass of charge carriers and their interaction strength and range.

Harrison N., Chan M. .

Specific heat measurements show the existence of a crossover between the superconducting pairing state (Bardeen-Cooper-Schrieffer) and a lower temperature superfluid condensate state (Bose-Einstein Condensate) in high-temperature cuprate superconductors.

Chen S., Hashimoto M., He Y., Song D., He J., Li Y., Ishida S., Eisaki H., Zaanen J., Devereaux T.P., Lee D., Lu D., Shen Z.

In conventional superconductors, the phase transition into a zero-resistance and perfectly diamagnetic state is accompanied by a jump in the specific heat and the opening of a spectral gap1. In the high-transition-temperature (high-Tc) cuprates, although the transport, magnetic and thermodynamic signatures of Tc have been known since the 1980s2, the spectroscopic singularity associated with the transition remains unknown. Here we resolve this long-standing puzzle with a high-precision angle-resolved photoemission spectroscopy (ARPES) study on overdoped (Bi,Pb)2Sr2CaCu2O8+δ (Bi2212). We first probe the momentum-resolved electronic specific heat via spectroscopy and reproduce the specific heat peak at Tc, completing the missing link for a holistic description of superconductivity. Then, by studying the full momentum, energy and temperature evolution of the spectra, we reveal that this thermodynamic anomaly arises from the singular growth of in-gap spectral intensity across Tc. Furthermore, we observe that the temperature evolution of in-gap intensity is highly anisotropic in the momentum space, and the gap itself obeys both the d-wave functional form and particle–hole symmetry. These findings support the scenario that the superconducting transition is driven by phase fluctuations. They also serve as an anchor point for understanding the Fermi arc and pseudogap phenomena in underdoped cuprates. A high-precision angle-resolved photoemission spectroscopy (ARPES) study on the superconductor Bi2212 resolves the spectroscopic singularity associated with the superconducting transition temperature, and indicates that the transition is driven by phase fluctuations.

Ma L., Nguyen P.X., Wang Z., Zeng Y., Watanabe K., Taniguchi T., MacDonald A.H., Mak K.F., Shan J.

Excitonic insulators (EIs) arise from the formation of bound electron–hole pairs (excitons)1,2 in semiconductors and provide a solid-state platform for quantum many-boson physics3–8. Strong exciton–exciton repulsion is expected to stabilize condensed superfluid and crystalline phases by suppressing both density and phase fluctuations8–11. Although spectroscopic signatures of EIs have been reported6,12–14, conclusive evidence for strongly correlated EI states has remained elusive. Here we demonstrate a strongly correlated two-dimensional (2D) EI ground state formed in transition metal dichalcogenide (TMD) semiconductor double layers. A quasi-equilibrium spatially indirect exciton fluid is created when the bias voltage applied between the two electrically isolated TMD layers is tuned to a range that populates bound electron–hole pairs, but not free electrons or holes15–17. Capacitance measurements show that the fluid is exciton-compressible but charge-incompressible—direct thermodynamic evidence of the EI. The fluid is also strongly correlated with a dimensionless exciton coupling constant exceeding 10. We construct an exciton phase diagram that reveals both the Mott transition and interaction-stabilized quasi-condensation. Our experiment paves the path for realizing exotic quantum phases of excitons8, as well as multi-terminal exciton circuitry for applications18–20. So far only signatures of excitonic insulators have been reported, but here direct thermodynamic evidence is provided for a strongly correlated excitonic insulating state in transition metal dichalcogenide semiconductor double layers.

Jiang H., Kivelson S.A.

We have performed density-matrix renormalization group studies of a square lattice $t\text{\ensuremath{-}}J$ model with small hole doping, $\ensuremath{\delta}\ensuremath{\ll}1$, on long four and six-leg cylinders. We include frustration in the form of a second-neighbor exchange coupling, ${J}_{2}={J}_{1}/2$, such that the undoped ($\ensuremath{\delta}=0$) ``parent'' state is a quantum spin liquid. In contrast to the relatively short range superconducting (SC) correlations that have been observed in recent studies of the six-leg cylinder in the absence of frustration, we find power-law SC correlations with a Luttinger exponent, ${K}_{\mathrm{SC}}\ensuremath{\approx}1$, consistent with a strongly diverging SC susceptibility, $\ensuremath{\chi}\ensuremath{\sim}{T}^{\ensuremath{-}(2\ensuremath{-}{K}_{\mathrm{SC}})}$ as the temperature $T\ensuremath{\rightarrow}0$. The spin-spin correlations---as in the undoped state---fall exponentially suggesting that the SC ``pairing'' correlations evolve smoothly from the insulating parent state.

Nakagawa Y., Kasahara Y., Nomoto T., Arita R., Nojima T., Iwasa Y.

Inducing a crossover In conventional superconductors, the electron pairs responsible for superconductivity are large and overlapping. Starting from this so-called Bardeen-Cooper-Schrieffer (BCS) limit, increasing interactions can set the system on a path of crossover to the opposite limit of small, tightly bound electron pairs that undergo Bose-Einstein condensation (BEC). Nakagawa et al. intercalated lithium ions into the insulating material zirconium nitride chloride, varying the carrier density across a large range (see the Perspective by Randeria). This induced superconductivity and enabled the system to enter the crossover regime between the BCS and BEC limits. Science , this issue p. 190 ; see also p. 132

Chen S., Hashimoto M., He Y., Song D., Xu K., He J., Devereaux T.P., Eisaki H., Lu D., Zaanen J., Shen Z.

A sharp boundary in the cuprates Many physicists working on cuprate superconductors believe that the so-called strange metal phase in the cuprate phase diagram is associated with a quantum critical point. Within this picture, the quantum critical point gives rise to a V-shaped region in the doping-temperature phase diagram of the cuprates: the strange metal phase. Chen et al. used angle-resolved photoemission spectroscopy in the cuprate family Bi2212 to challenge this view. By taking comprehensive measurements as a function of doping and temperature—and making sure that the signal was not affected by environmental conditions—they found an incoherent strange metal phase that was sharply separated from a conventional phase by a temperature-independent vertical line in the phase diagram. Science , this issue p. 1099

Zhou P., Chen L., Liu Y., Sochnikov I., Bollinger A.T., Han M., Zhu Y., He X., Boz̆ović I., Natelson D.

In the quest to understand high-temperature superconductivity in copper oxides, debate has been focused on the pseudogap—a partial energy gap that opens over portions of the Fermi surface in the ‘normal’ state above the bulk critical temperature1. The pseudogap has been attributed to precursor superconductivity, to the existence of preformed pairs and to competing orders such as charge-density waves1–4. A direct determination of the charge of carriers as a function of temperature and bias could help resolve among these alternatives. Here we report measurements of the shot noise of tunnelling current in high-quality La2−xSrxCuO4/La2CuO4/La2−xSrxCuO4 (LSCO/LCO/LSCO) heterostructures fabricated using atomic layer-by-layer molecular beam epitaxy at several doping levels. The data delineate three distinct regions in the bias voltage–temperature space. Well outside the superconducting gap region, the shot noise agrees quantitatively with independent tunnelling of individual charge carriers. Deep within the superconducting gap, shot noise is greatly enhanced, reminiscent of multiple Andreev reflections5–7. Above the critical temperature and extending to biases much larger than the superconducting gap, there is a broad region in which the noise substantially exceeds theoretical expectations for single-charge tunnelling, indicating pairing of charge carriers. These pairs are detectable deep into the pseudogap region of temperature and bias. The presence of these pairs constrains current models of the pseudogap and broken symmetry states, while phase fluctuations limit the domain of superconductivity. Shot-noise measurements in copper oxides reveal paired charge carriers existing in the pseudogap above the superconducting critical temperature, shedding light on the properties of high-temperature superconductivity in these materials.

Jurkutat M., Erb A., Haase J.

Nuclear magnetic resonance (NMR) in cuprate research is a prominent bulk local probe of magnetic properties. NMR also, as was shown over the last years, actually provides a quantitative measure of local charges in the CuO 2 plane. This has led to fundamental insights, e.g., that the maximum T c is determined by the sharing of the parent planar hole between Cu and O. Using bonding orbital hole contents on planar Cu and O measured by NMR, instead of the total doping x, the thus defined two-dimensional cuprate phase diagram reveals significant differences between the various cuprate materials. Even more importantly, the reflected differences in material chemistry appear to set a number of electronic properties as we discuss here, for undoped, underdoped and optimally doped cuprates. These relations should advise attempts at a theoretical understanding of cuprate physics as well as inspire material chemists towards new high- T c materials. Probing planar charges, NMR is also sensitive to charge variations or ordering phenomena in the CuO 2 plane. Thereby, local charge order on planar O in optimally doped YBCO could recently be proven. Charge density variations seen by NMR in both planar bonding orbitals with amplitudes between 1% to 5% appear to be omnipresent in the doped CuO 2 plane, i.e., not limited to underdoped cuprates and low temperatures.

Pelc D., Anderson Z., Yu B., Leighton C., Greven M.

A pivotal challenge posed by unconventional superconductors is to unravel how superconductivity emerges upon cooling from the generally complex normal state. Here, we use nonlinear magnetic response, a probe that is uniquely sensitive to the superconducting precursor, to uncover remarkable universal behaviour in three distinct classes of oxide superconductors: strontium titanate, strontium ruthenate, and the cuprate high-Tc materials. We find unusual exponential temperature dependence of the diamagnetic response above the transition temperature Tc, with a characteristic temperature scale that strongly varies with Tc. We correlate this scale with the sensitivity of Tc to local stress and show that it is influenced by intentionally-induced structural disorder. The universal behaviour is therefore caused by intrinsic, self-organized structural inhomogeneity, inherent to the oxides’ perovskite-based structure. The prevalence of such inhomogeneity has far-reaching implications for the interpretation of electronic properties of perovskite-related oxides in general. The understanding of how superconductivity emerges from a complex normal state remains elusive in unconventional superconductors. Here, Pelc et al. report exponential temperature dependence of the diamagnetic response in the normal state with a characteristic temperature scale, universally existing in three classes of oxide superconductors.

Kramer K.P., Horio M., Tsirkin S.S., Sassa Y., Hauser K., Matt C.E., Sutter D., Chikina A., Schröter N.B., Krieger J.A., Schmitt T., Strocov V.N., Plumb N.C., Shi M., Pyon S., et. al.

A comprehensive angle resolved photoemission spectroscopy study of the band structure in single layer cuprates is presented with the aim of uncovering universal trends across different materials. Five different hole- and electron-doped cuprate superconductors (La$_{1.59}$Eu$_{0.2}$Sr$_{0.21}$CuO$_4$, La$_{1.77}$Sr$_{0.23}$CuO$_4$, Bi$_{1.74}$Pb$_{0.38}$Sr$_{1.88}$CuO$_{6+\delta}$, Tl$_{2}$Ba$_{2}$CuO$_{6+\delta}$, and Pr$_{1.15}$La$_{0.7}$Ce$_{0.15}$CuO$_{4}$) have been studied with special focus on the bands with predominately $d$-orbital character. Using light polarization analysis, the $e_g$ and $t_{2g}$ bands are identified across these materials. A clear correlation between the $d_{3z^2-r^2}$ band energy and the apical oxygen distance $d_\mathrm{A}$ is demonstrated. Moreover, the compound dependence of the $d_{x^2-y^2}$ band bottom and the $t_{2g}$ band top is revealed. Direct comparison to density functional theory (DFT) calculations employing hybrid exchange-correlation functionals demonstrates excellent agreement. We thus conclude that the DFT methodology can be used to describe the global band structure of overdoped single layer cuprates on both the hole and electron doped side.

He Y., Hashimoto M., Song D., Chen S.-., He J., Vishik I.M., Moritz B., Lee D.-., Nagaosa N., Zaanen J., Devereaux T.P., Yoshida Y., Eisaki H., Lu D.H., Shen Z.-.

Conspiring interactions in a cuprate More than 30 years after the discovery of high-temperature superconductivity in copper oxides, its mechanism remains a mystery. Electron pairing mediated solely by lattice vibrations—phonons—is thought to be insufficient to account for the high transition temperatures. He et al. found a rapid and correlated increase of the superconducting gap and electron-phonon interactions as the chemical composition of their bismuth-based cuprate samples was varied across a critical doping concentration. The interplay of electron-phonon with electron-electron interactions may lead to enhanced transition temperatures. Science , this issue p. 62

Kovač K., Nocera A., Damascelli A., Bonča J., Berciu M.

Van Loon S., Sá de Melo C.A.

Watanabe H., Ikeda H.

Zheng Y., Wú W.

Homeier L., Lange H., Demler E., Bohrdt A., Grusdt F.

AbstractResonant interactions associated with the emergence of a bound state constitute one of the cornerstones of modern many-body physics. Here we present a Feshbach perspective on the origin of strong pairing in Fermi-Hubbard type models. We perform a theoretical analysis of interactions between spin-polaron charge carriers in doped Mott insulators, modeled by a near-resonant two-channel scattering problem, and report evidence for Feshbach-type interactions in the $${d}_{{x}^{2}-{y}^{2}}$$ d x 2 − y 2 channel, consistent with the established phenomenology of cuprates. Existing experimental and numerical results on hole-doped cuprates lead us to conjecture the existence of a light, long-lived, low-energy excited state of two holes, which enables near-resonant interactions. To put our theory to a test we suggest to use coincidence angle-resolved photoemission spectroscopy (cARPES), pair-tunneling measurements or pump-probe experiments. The emergent Feshbach resonance among spin-polarons could also underlie superconductivity in other doped antiferromagnetic Mott insulators highlighting its potential as a unifying strong-coupling pairing mechanism rooted in quantum magnetism.

Krasavin A.V., Vagov A.V., Vasenk A.S., Stolyarov V.S., Shanenko A.A.

Witt N., Nomura Y., Brener S., Arita R., Lichtenstein A.I., Wehling T.O.

AbstractSuperconductivity emerges from the spatial coherence of a macroscopic condensate of Cooper pairs. Increasingly strong binding and localization of electrons into these pairs compromises the condensate’s phase stiffness, thereby limiting critical temperatures – a phenomenon known as the BCS–BEC crossover in lattice systems. In this study, we demonstrate enhanced superconductivity in a multiorbital model of alkali-doped fullerides (A3C60) that goes beyond the limits of the lattice BCS–BEC crossover. We identify that the interplay of strong correlations and multiorbital effects results in a localized superconducting state characterized by a short coherence length but robust stiffness and a domeless rise in critical temperature with increasing pairing interaction. To derive these insights, we introduce a new theoretical framework allowing us to calculate the fundamental length scales of superconductors, namely the coherence length (ξ0) and the London penetration depth (λL), even in presence of strong electron correlations.

Chen Q., Wang Z., Boyack R., Yang S., Levin K.

Homeier L., Bermes P., Grusdt F.

Modeling the underlying pairing mechanism of charge carriers in strongly correlated electrons, starting from a microscopic theory, is among the central challenges of condensed-matter physics. Hereby, the key task is to understand what causes the appearance of superconductivity at comparatively high temperatures upon hole doping an antiferromagnetic (AFM) Mott insulator. Recently, it has been proposed that at strong coupling and low doping, the fundamental one- and two-hole meson-type constituents---magnetic polarons and bipolaronic pairs---likely realize an emergent Feshbach resonance producing near-resonant ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ interactions between charge carriers. Here, we provide detailed calculations of the proposed scenario by describing the open and closed meson scattering channels in the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model using a truncated basis method. After integrating out the closed channel constituted by bipolaronic pairs, we find ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ attractive interactions between open channel magnetic polarons. The closed form of the derived interactions allows us analyze the resonant pairing interactions and we find enhanced (suppressed) attraction for hole (electron) doping in our model. The formalism we introduce provides a framework to analyze the implications of a possible Feshbach scenario, e.g., in the context of BEC-BCS crossover, and establishes a foundation to test quantitative aspects of the proposed Feshbach pairing mechanisms in doped antiferromagnets.

Chen Q., Wang Z., Boyack R., Levin K.

AbstractIn this paper we address the question of whether high-temperature superconductors have anything in common with BCS-BEC crossover theory. Towards this goal, we present a proposal and related predictions which provide a concrete test for the applicability of this theoretical framework. These predictions characterize the behavior of the Ginzburg-Landau coherence length, $${\xi }_{0}^{{{{\rm{coh}}}}}$$ ξ 0 coh , near the transition temperature Tc, and across the entire superconducting Tc dome in the phase diagram. That we are lacking a systematic characterization of $${\xi }_{0}^{{{{\rm{coh}}}}}$$ ξ 0 coh in the entire class of cuprate superconductors is perhaps surprising, as it is one of the most fundamental properties of any superconductor. This paper is written to motivate further experiments and, thus, address this shortcoming. Here we show how measurements of $${\xi }_{0}^{{{{\rm{coh}}}}}$$ ξ 0 coh contain direct indications for whether or not the cuprates are associated with BCS-BEC crossover and, if so, where within the crossover spectrum a particular superconductor lies.

Sá de Melo C.A., Van Loon S.

We review aspects of the evolution from Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) in two dimensions, which have now become relevant in systems with low densities, such as gated superconductors Li xZrNCl, magic-angle twisted trilayer graphene, FeSe, FeSe1− xS x, and ultracold Fermi superfluids. We emphasize the important role played by chemical potentials in determining crossovers or topological quantum phase transitions during the BCS–BEC evolution in one-band and two-band superfluids and superconductors. We highlight that crossovers from BCS to BEC occur for pairing in nonnodal s-wave channels, whereas topological quantum phase transitions, in which the order parameter symmetry does not change, arise for pairing in any nodal higher angular momentum channels, such as d-wave. We conclude by discussing a few open questions regarding the BCS-to-BEC evolution in 2D, including modulus fluctuations of the order parameter, tighter upper bounds on critical temperatures, and the exploration of lattice effects in two-band superconductors and superfluids.

Krasavin A.V., Vagov A.V., Vasenko A.S., Stolyarov V.A., Shanenko A.A.

The combination of strongly coupled Cooper pairs and weak superconducting fluctuations is an important prerequisite for achieving high-temperature superconductivity. The review is devoted to the implementation of this condition in multiband superconductors, in which strongly coupled pairs in the shallow conduction band (the Fermi level is close to the band edge) coexist with ordinary, weakly fluctuating Cooper pairs formed in the deep band. As a result of the Josephson coupling between condensates in different bands, such a system is characterized by a high critical coherence temperature due to the presence of strongly coupled pairs and the suppression of superconducting fluctuations. This suppression does not require any special preconditions, and is almost total even if the Josephson coupling between the bands is weak.

Imajo S., Kobayashi T., Matsumura Y., Maeda T., Nakazawa Y., Taniguchi H., Kindo K.

The condensation of paired fermions into superfluid states changes progressively depending on the coupling strength. At the midpoint of the crossover between Bardeen-Cooper-Schrieffer (BCS) weak-coupling and Bose-Einstein condensate (BEC) strong-coupling limits, paired fermions condensate most robustly, thereby leading to the emergence of a pseudogap due to enhanced pairing fluctuations. In the case of electrons in solids, excessively strong interactions often induce competing electronic orders instead of strong-coupling superconductivity, and experimental comprehension of the pseudogap remains incomplete. In this study, we provide experimental evidence demonstrating the opening of a pseudogap, marking the incipient stage of the BCS-BEC crossover in the organic system $\ensuremath{\kappa}\text{\ensuremath{-}}(\mathrm{BEDT}\text{\ensuremath{-}}{\mathrm{TTF})}_{2}X$. By controlling electron correlations, we investigate the thermodynamic properties of the BCS-BEC crossover and pseudogap phase. Since the superconductivity of $\ensuremath{\kappa}\text{\ensuremath{-}}{(\text{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}X$ arises from a simple Fermi liquid that does not exhibit any other electronic orders, our study sheds light on the inherent nature of the BCS-BEC crossover.