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Two Phase Transitions Make a High-Temperature Superconductor Print

Superconductivity—conceptually remarkable and practically revolutionary—is a quantum phenomenon in which bound electron pairs flow through a material in perfect synchrony, without friction. Conventional superconducting materials reach this state via a single thermal phase transition at a critical temperature (Tc). It was generally believed that such a picture also applied to the copper oxide (cuprate) superconductors—first discovered 25 years ago and the current record holders for highest Tc. However, three groups of researchers who performed measurements on the same cuprate material recently joined forces to prove that this view is inaccurate. Their work showed that another phase transition actually exists at a higher temperature in the cuprate phase diagram, below which electrons, instead of pairing up, organize themselves in a drastically different way.

What is a Pseudogap?

In conventional superconductors, there is a range of energies that the most loosely bound conducting electrons are forbidden to take. In a diagram of electron energies, these forbidden energies appear as a gap. The presence of this gap signals the pairing up of electrons that is necessary for superconductivity; the gap completely disappears as the electron pairs split up above the superconducting critical temperature, Tc. However, in the so-called "high-Tc" cuprate superconductors, a "pseudogap" remains, even above Tc, and does not vanish until a characteristic temperature, T* ("T-star"), is reached.

He and Hashimoto et al. have now shown that the pseudogap represents, not a smooth crossover phenomenon with gradually increasing electron-pairing correlation, but a sharp transition to a separate phase in which electrons do not exist in pairs but in a distinct yet elusive order. This revised picture of the high-Tc phase diagram demands a paradigm shift in attempts to achieve a higher Tc in cuprates and beyond, depending on whether the pseudogap order turns out to be a friend or foe of superconductivity.

Three complementary approaches to probing the phase transition in crystals of the cuprate superconductor, Pb-Bi2201, using (1) angle-resolved photoemission spectroscopy (ARPES) at Beamline 5-4 of the Stanford Synchrotron Radiation Lightsource (SSRL) and  Beamline 10.0.1 of the ALS, (2) high-resolution measurements of the magneto-optical Kerr effect at Stanford, and (3) time-resolved reflectivity at UC Berkeley/Berkeley Lab.

The new phase transition occurs at the so-called "pseudogap" temperature (T*). The pseudogap has been traditionally understood as reflecting the formation of electron pairs that lack the long-range phase coherence required for superconductivity. This traditional view was supported by many early experiments that detected subtle anomalies in various measurable quantities (electron density of states, transport, and thermoelectric and magnetic response properties) broadly around T*. Such a "precursor pairing" interpretation of the pseudogap raised hopes of increasing Tc (perhaps as high as T*—comparable to room temperature) by promoting phase coherence in cuprates.

With the advent of advanced experimental techniques, however, researchers have paid increasing attention to the possibility of a true phase transition at T*. For example, time-resolved reflectivity measurements at different temperatures have shown that a fast-changing, negative signal sets in below T* that is distinct from the slow-changing, positive signal at the onset of Tc, hinting at the different nature of both pseudogap and superconducting phases. Despite the accumulation of similar evidence, however, a more definitive result has been lacking.

High-precision measurements of the magneto-optical Kerr effect, a bulk, thermodynamic probe of magnetization, had also revealed the clear onset of a signal at T*, going from zero above to finite below, a behavior expected in a phase transition. However, although the thermodynamic nature of the probe could permit a strong conclusion on the pseudogap phase transition, the small size of the overall signal previously measured in an yttrium-based cuprate was in strong contrast to the sizeable effect of the pseudogap found in many other measurements, including angle-resolved photoemission spectroscopy (ARPES).

ARPES, a surface, microscopic probe in energy–momentum space, allows the entire thermal evolution of the pseudogap to be monitored in detail. However, largely owing to an exclusive focus on the superconducting transition, such ARPES experiments on the pseudogap had rarely been performed; data recently obtained on a bismuth-based cuprate showed that the pseudogap opens rather abruptly below T* and evolves in a way incompatible with the formation of incoherent electron pairs but consistent with the development of some density-wave-like order. Nevertheless, the extreme surface sensitivity and microscopic nature of ARPES, together with the considerable variation of T* among different cuprate families, have precluded a definitive conclusion about a connection between the pronounced spectral change in ARPES and the small Kerr signal observed in different materials.

Here, in this work, three research groups from Berkeley and Stanford report convincing data on the subject using a combination of the three complementary methods described above, including ARPES at ALS Beamline 10.0.1. Taken together, the results have allowed the Stanford-Berkeley groups to reach a firmer conclusion than would otherwise be possible. The mutually consistent results show that the ordering of electrons persists through the superconducting phase transition and coexists microscopically in the ground state with the electron pairs that first emerge close to Tc. Albeit belated, such a major revision in our understanding of high-Tc superconductivity will undoubtedly transform our thinking about how to make Tc higher.

Left inset: ARPES spectra for Pb-Bi2201 taken at several temperatures around Tc (38 K). Blue circles indicate the binding energies of pseudogap-related states and green circles indicate the binding energies of superconductivity-related states. Center: Experimental energy–momentum relations (dispersions) of both pseudogap (blue) and superconductivity (green) states across Tc. Note that the superconductivity-related states (green) only emerge close to Tc and coexist with the pseudogap-related states (blue) modified from the original (red). Right: Simulated ARPES spectral intensity map that assumes the coexistence of superconductivity with a checkerboard-style electron order. Note that various candidate orders for the pseudogap considered in this work give a qualitative agreement with the experiment in varying degrees.



Research conducted by: R.-H. He, M. Hashimoto, and J.P. Testaud (Stanford University and ALS); H. Karapetyan, V. Nathan, R.G. Moore, D.H. Lu, T.P. Devereaux, S.A. Kivelson, A. Kapitulnik, and Z.-X. Shen (Stanford University); J.D. Koralek, J.P. Hinton, and J. Orenstein (University of California, Berkeley, and Berkeley Lab); Y. Yoshida and H. Eisaki (National Institute of Advanced Industrial Science and Technology, Japan); H. Yao (Stanford University, University of California, Berkeley, and Berkeley Lab); K. Tanaka (Stanford University, ALS, and Osaka University, Japan); W. Meevasana (Stanford University and Suranaree University of Technology, Thailand); S.-K. Mo and Z. Hussain (ALS); and M. Ishikado (Japan Atomic Energy Agency).

Research funding: U.S. Department of Energy (DOE), Office of Basic Energy Sciences (BES); Stanford Graduate Fellowship. Operation of SSRL and ALS are supported by DOE BES.

Publication about this research: R.-H. He, M. Hashimoto, H. Karapetyan, J.D. Koralek, J.P. Hinton, J.P. Testaud, V. Nathan, Y. Yoshida, H. Yao, K. Tanaka, W. Meevasana, R.G. Moore, D.H. Lu, S.-K. Mo, M. Ishikado, H. Eisaki, Z. Hussain, T.P. Devereaux, S.A. Kivelson, J. Orenstein, A. Kapitulnik, and Z.-X. Shen, "From a single-band metal to a high-temperature superconductor via two thermal phase transitions," Science 331, 1579 (2011).

ALS Science Highlight #239


ALSNews Vol. 326