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Cuprate Superconductors

Schematic phase diagram of a hole doped cuprate superconductor and crystal structure of CuO2 planes

High-transition-temperature (Tc) superconductivity in copper oxides (cuprates) is one of the most intriguing emergent phenomena in strongly correlated electron systems. It has attracted great attention since its discovery because Tc can exceed the boiling temperature of liquid nitrogen, which is much higher than the putative limit of Tc ~ 40 K derived from the BCS theory for conventional superconductivity.

The cuprate superconductors have a layered crystal structure consisting of CuO2 planes separated by charge reservoir layers, which may dope electrons or holes into the CuO2 planes. On doping holes, the antiferromagnetic Mott insulating phase of the parent compounds disappears and superconductivity emerges. Tc follows a dome-like shape as a function of doping, with a maximum Tc around 16% doped per CuO2 plaquette. A similar phase diagram is seen on doping electrons, albeit with a more robust antiferromagnetic phase and a lower Tc. On the hole-doped side, there exists an enigmatic state above Tc called the pseudogap, where the electron density of states within certain momentum region is suppressed.

Over the past two decades, angle-resolved photoemission spectroscopy (ARPES) has emerged as a leading experimental tool in the cuprates field due to its ability to directly measure the electronic structure of solids. Utilizing ARPES, Shen group discovered the anisotropic energy gap in the d-wave superconducting state in 1993, and the mysterious pseudogap above Tc in 1996. Past research topics also include nodal-antinodal gap dichotomy [1], itinerant spin in overdoped (OD) LSCO [2], chemical potential puzzle in underdoped (UD) Ca2−xNaxCuO2Cl2 [3], antinodal quasiparticle intensity and superfluid density [4], density wave order/stripes in cuprates [5], and the universality of kink structure [6-7].

Currently we are focused on three cuprate materials: Bi2212, Bi2201, and LSCO. We are interested in studying the physics of nodal gap as well as electron-phonon coupling. We are also interested in characterizing the relationship between the pseudogap and superconductivity so as to gain more insights into the complex phases of cuprates.

Selected Publications

[1] W. S. Lee et al. Abrupt onset of a second energy gap at the superconducting transition of underdoped Bi2212. Nature 450, 81 (2007)

[2] R.-H. He et al. Hidden itinerant-spin phase in heavily overdoped La2−xSrxCuO4 superconductors revealed by dilute Fe doping: a combined neutron scattering and angle-resolved photoemission study. Phys. Rev. Lett. 107, 127002 (2011)

[3] K. M. Shen et al. Missing quasiparticles and the chemical potential puzzle in the doping evolution of the cuprate superconductors. Phys. Rev. Lett. 93, 267002 (2004)

[4] D. L. Feng et al. Signature of superfluid density in the single particle excitation spectrum of Bi2212. Science 289, 277 (2000)

[5] K. M. Shen et al. Nodal quasiparticles and antinodal charge ordering in Ca2-xNaxCuO2Cl2. Science 307, 901 (2005)

[6] A. Lanzara et al. Evidence for ubiquitous strong electron-phonon coupling in high-Tc superconductors. Nature 412, 510 (2001)

[7] X. J. Zhou et al. High-temperature superconductors: Universal nodal Fermi velocity. Nature 423, 398 (2003)

[8] M. Hashimoto et al. Energy gaps in high-transition-temperature cuprate superconductors. Nature Phys. 10, 483 (2014)

[9] R.-H. He, M. Hashimoto et al. From a single band metal to a high-temperature superconductor via two thermal phase transitions. Science 331, 1579 (2011)

[10] I. M. Vishik et al. Phase competition in trisected superconducting dome. PNAS 109, 18332 (2012)

[11] M. Hashimoto et al. Direct spectroscopic evidence for phase competition between the pseudogap and superconductivity in Bi2Sr2CaCu2O8+δ. accepted to Nature Materials

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Contents

· Resources

· The Parent Compound: Mott Insulator

· Energy Gaps and Phase Diagram

· Electron-Phonon Coupling

· Polaron Excitation

Resources

Samples  Our group has a long tradition of collaboration with top material scientists in the world. We also perform our own cuprate crystal growth using the optical floating zone method.

Collaborations Complementary experiments and inter-group collaborations are essential to our research. Leveraging on the research environment at Stanford and SLAC, we have collaborations with top research groups that specialize in theory, numerical simulation, scattering, scanning microscopy, film and interface engineering, and transport measurement.

Doping-dependent evolution of electronic structure from Mott insulator to superconductor

The Parent Compound: Mott Insulator

The cuprate families of high-Tc superconductors evolve from parent, undoped compounds that are antiferromagnetic (AF) insulators. As part of a class of insulators called Mott insulators, these parent compounds have a half-filled electron band, but do not conduct electricity. Instead, due to the high on-site Coulomb repulsion, a single electron occupies each copper atom. The electrons interact with the neighboring electrons only through the AF exchange interaction. These AF fluctuations show up as "hot spots" of depleted intensity along the Fermi surface of a doped compound. The "hot spots" are located where the Fermi surface crosses the Brillouin zone boundary of the AF lattice. One of the proposed mechanisms for high-Tc superconductivity is precisely the AF interaction.

Selected Publications

[1] B. O. Wells et al. E vs. k relations and many body effects in the model insulating copper oxide Sr2CuO2Cl2. Phys. Rev. Lett. 74, 964 (1995)

[2] N. P. Armitage et al. Doping dependence of n-type superconductors investigated by ARPES. Phys. Rev. Lett. 88, 257001 (2002)

Schematic of a d-wave order
parameter on a circular Fermi
surface.

Energy Gaps and Phase Diagram

Superconducting Gap

In conventional BCS superconductors, an energy gap SC opens below Tc with s-wave symmetry and minimal momentum dependence. 2SC is the energy required to break each of the Cooper pairs of electrons, which form the superconducting condensate. In contrast, the superconducting gap in the cuprates is characterized by a strong momentum dependence. Early debates came to the conclusion that the superconducting gap function is consistent with an order parameter having dx2y2 symmetry, with support from ARPES, penetration depth, Raman, and phase-sensitive measurements. The d-wave symmetry of the superconducting gap has become an accepted fact when one constructs theories and interprets experimental results.

Pseudogap

Abrupt onset of the particle-hole asymmetric antinodal gap at T*

The pseudogap refers to the anomalous energy gap observed above Tc that has an enigmatic origin. It was discovered as the 'spin gap', which manifests itself as an anomaly at T* in the spin-lattice relaxation rate of nuclear magnetic resonance (NMR), suggesting the suppression of the density of states around EF below T*. In 1996, the momentum structure of the pseudogap was revealed by ARPES measurements [2-3], showing a similar anisotropy as the superconducting gap. As high-Tc superconductivity emerges from this pseudogap state as the temperature is lowered, the pseudogap has been suggested to be intimately connected to the mechanism of high Tc and should provide clues of how even higher Tc values can be achieved.

There has been intense debate over whether the pseudogap state contains a distinct order from superconductivity. Over the past decade, systematic ARPES measurements of cuprates have suggested that pseudogap and superconductivity gap have different physical origins. One indication is the nodal-antinodal gap dichotomy, where the gaps measured near the node follow a different temperature and doping dependences from the gaps measured near the antinode. Moreover, in optimally doped Bi2201 sample where pseudogap is suggested to coexist with superconductivity, an abrupt onset at T* of a particle-hole asymmetric antinodal gap was observed using three different techniques (ARPES, polar Kerr effect, and time-resolved reflectivity) [7]. In contrast to superconductivity in which the particle-hole symmetry is preserved, this evidence shows that pseudogap may contain a distinct order that breaks the particle-hole symmetry.

Proposed phase diagram for Bi2212, feautring a reentrant behavior of the pseudogap state inside the superconducting dome.

Phase competition in trisected superconducting dome

A detailed phenomenology of the spectral gap is a crucial starting point for understanding how superconductivity and pseudogap interact in momentum space. At low temperature, it was found that the nodal gap velocity (vΔ) shows three distinct doping-dependences in three doping regions, separated by two potential critical points at p = 0.076 and p = 0.19. The latter is interpreted as the T = 0 endpoint of the pseudogap. Considering the observation that pseudogap persists to higher dopings at temperatures slightly above Tc, a phase diagram with a new pseudogap phase boundary inside the superconducting dome is proposed as shown in the diagram [8].

Recently, we have also developed new data analysis method to investigate the temperature and doping dependance of the antinodal spectrum line shape. The results further support the competing behavior between the superconducting phase and the pseudogap phase, and hints at the proposed reentrant behavior in the overdoped side of the phase diagram [9].

Selected Publications

[1] Z.-X. Shen et al. Anomalously large gap anisotropy in the a-b plane of Bi2Sr2CaCu2O8+δ. Phys. Rev. Lett. 70, 1553 (1993)

[2] D. S. Marshall et al. Unconventional electronic structure evolution with hole doping in Bi2Sr2CaCu2O8+δ: Angle-resolved photoemission results. Phys. Rev. Lett. 76, 4841 (1996)

[3] A. G. Loeser et al. Excitation gap in the normal state of underdoped Bi2Sr2CaCu2O8+δ. Science 273, 325 (1996)

[4] K. Tanaka et al. Distinct Fermi-momentum dependent energy gaps in deeply underdoped Bi2212. Science 314, 1910 (1996)

[5] W. S. Lee et al. Abrupt onset of a second energy gap at the superconducting transition of underdoped Bi2212. Nature 450, 81 (2007)

[6] M. Hashimoto et al. Energy gaps in high-transition-temperature cuprate superconductors. Nature Phys. 10, 483 (2014)

[7] R.-H. He, M. Hashimoto et al. From a single band metal to a high-temperature superconductor via two thermal phase transitions. Science 331, 1579 (2011)

[8] I. M. Vishik et al. Phase competition in trisected superconducting dome. PNAS 109, 18332 (2012)

[9] M. Hashimoto et al. Direct spectroscopic evidence for phase competition between the pseudogap and superconductivity in Bi2Sr2CaCu2O8+δ. accepted to Nature Materials

Electron-Phonon Coupling

Low energy 'kink' features below 10 meV (above) and the doping dependences of vF and vmid.

In conventional superconductors, phonon mediated interactions attract the electrons and form Cooper pairs required for bose condensation and zero resistance. In the high-Tc superconductors, the boson that mediates the pairing — termed the 'mechanism' of superconductivity — has been long-debated. In ARPES, we have found that the electrons are strongly coupled to a bosonic mode, as manifested by a kink in the dispersion along the nodal (0,0)-(π,π) direction and evolving into an even stronger renormalization of the dispersion in the anti-nodal (0,π)-(π,π) direction [1-3]. This anisotropy follows that of the d-wave gap, suggesting an intimate connection to the superconductivity. We have, by comparing with other spectroscopies that measure the phonons directly, identified the bosonic mode as a phonon and one in particular that couples anisotropically to the Fermi surface.

With the advent of laser ARPES, which allows for experiments with superior energy and momentum resolution, a number of groups were able to observe a new kink at very low energy (~ 10 meV) at the node. We studied the doping dependence of this kink, finding that the renormalization became stronger with under-doping, giving rise to a doping-dependent nodal Fermi velocity [5], in contrast to earlier conclusions [4]. With this result, we were able to reconciliate the previous discrepancies between the results of ARPES (a surface spectroscopy) and thermal conductivity experiments (a bulk thermodynamic probe). We also looked at the momentum dependence of the low-energy kink away from the node and found that it shifted to higher binding energy parallel with the d-wave superconducting gap [6]. We were able to show that strong coupling between electrons and acoustic phonons is able to reproduce the doping and momentum dependent phenomenology of this low energy kink.

Selected Publications

[1] A. Lanzara et al. Strong electron-phonon coupling in high-Tc superconductors. Nature 412, 510 (2001)

[2] T. Cuk et al. Coupling of the B1g phonon to the antinodal electronic states of Bi2Sr2Ca0.92Y0.08Cu2O8+δ. Phys. Rev. Lett. 93, 117003 (2004)

[3] T. Cuk et al. A review of electron-phonon coupling seen in the high-Tc superconductors by ARPES. Physica Status Solidi (b) 242, 11 (2005)

[4] X. J. Zhou et al. Universal nodal Fermi velocity in high-temperature superconductors. Nature 423, 398 (2003)

[5] I. M. Vishik et al. Doping-dependent nodal Fermi velocity of the high-temperature superconductor Bi2Sr2CaCu2O8+δ revealed using high-resolution ARPES. Phys. Rev. Lett. 104, 207002 (2010)

[6] S. Johnston et al. Evidence for the importance of extended Coulomb interactions and forward scattering in cuprate superconductors. Phys. Rev. Lett. 108, 166404 (2012)

Polaron Excitation

Recent studies have shed some more light on the nature of excitations that make up the broad, gapped spectral feature through detailed studies of Ca2-xNaxCuO2Cl2 as a function of doping. Quasiparticles are coherent electron states that form in metals, while 'polarons' are the exact opposite — incoherent excitations of electrons strongly coupled to a bath of lattice vibrations and commonly found in insulators. We have found that the spectral intensity near the Fermi level in the metallic copper-oxides evolves from a polaron-like distribution of intensity in the pseudo-gaped insulators. Further work shows that these polaronic excitations may be related to a charge order in the pseudogap region of the phase diagram, seen also by scanning tunneling microscopy.

Selected Publications

[1] K. M. Shen et al. Missing quasiparticles and the chemical potential puzzle in the doping evolution of the cuprate superconductors. Phys. Rev. Lett. 93, 267002 (2004)