ARPES studies of cuprate fermiology: Superconductivity, pseudogap and quasiparticle dynamics Yoon Tiem Leong Talk given at theory group weekly seminar, School of Physics, Universiti Sains Malaysia Tuesday, 7 June 2011
ABSTRACT In this presentation, I will briefly review the paper by M Vishik, W S Lee, R-H He, M Hashimoto, Z Hussain, T P Devereaux and Z-X Shen (2010 New J. Phys. 12 105008). In this paper, the authors provide a review of the experimental status on cuprates using angle-resolved photoemission specstrocopy (ARPES). This is a very powerful experimental tool used to study cuprate high-temperature superconductors (HTCS). These studies elucidate the relations between superconductivity and the pseudogap and highlight low-energy quasiparticle dynamics in superconducting state. The implications of the experimental findings in constraining the explanation of pseudogap and superconductivity in cuptrates will be briefly discussed.
Two general approaches to study HTCS ◮ Study the state that exists at temperature higher than T c in order to posit how it may become unstable to SC. ◮ Search for bosonic excitations which might bind electron into Cooper pairs. ◮ Examination of the quasiparticle properties: Fermiology of the charge carriers.
Angle-resolved Photoemission Spectoscopy ◮ Ideal tool for studying Fermiology – directly measures the occupied part of the single-particle spectral function in momentum space. ◮ Most obvious spectral features: pseudogap, nodal, antinodal (AN) kinks. ◮ Origins of these features are still debatable. ◮ Normal state (i.e., T > T c ) of conventional (low T c ) superconductor (SC) can be charactersised by Fermi liquid theory. ◮ But ‘normal state’ HTSC of underdoped cuprates remains contraversial.
STS data on temperature dependence of the gap ◮ Scanning tunnelling spectroscopy (STS) vs. Andreev reflection. See Fig. 1. ◮ In STS data (Fig.1a), gap is defined as peak-to-peak separation in tunnelling conductance below T c or by a depletion of DOS near zero bias in the normal state. ◮ STS data shows the gap is largely unchaged across T c and persists to temperature much higher than T c . ◮ Support ‘One-gap scanario’: the onset of the pseudogap (PG) ( T ∗ ) marks the onset of Cooper-pair formation, whereas T c marks the onset of phase coherence. ◮ Also supported by Nernst effect measurements.
Figure: 1. (a) STS measurements of Bi 2 Sr 2 CaCu 2 O 8+ δ (Bi-2212, T c = 83) from [1]. (b) Andreev reection measurements of Bi 2 Sr 2 Ca 2 Cu 3 O 10+ δ (Bi-2223, T c = 113) from [2]. The two experiments imply different temperature dependences of the gap.
Andreev reflection experiments ◮ Indicate a gap with a BCS-like temperature dependence that vanishes near T c - no pseudogap. ◮ A temperature-dependent gap closing near T c . ◮ Raman scattering experiments also supported this picture. ◮ The temperature dependence from AR is incompatible with that obtained from STS. ◮ Motivation for Vishik et al. conduct the ARPES experiments to resolve the descrepency.
Figure: 2. Symmetrized EDC near the antinode for underdoped Bi-2212 with a T c of 50 K. Two features are seen in the spectrum: a low-energy peak associated with superconductivity and a broader feature at higher energy associated with the pseudogap. For such a deeply underdoped system, the intensity and energy position of the superconducting feature are strongly inuenced by the underlying pseudogap.
ARPES data of two distinct gaps below T c ◮ T c marks the realm of SC. ◮ But in sufficiently underdoped cuprates, two distinct gaps can be distinguished below T c . ◮ Energy distribution curve (EDC) - intensity as a function of energy at fixed momentum. ◮ See Figure 2 - data taken near the antinodal k F (i.e., k F ∼ (0 , π ), momenta near the Brillouin zone axis). ◮ Sharp peak at lower binding energy ( | E − E F | ∼ 0) is associated with superconductivity. ◮ Broader features at higher binding energy ( | E − E F | ∼ 0 . 1 − 0 . 2 eV) is associated with pseudogap. ◮ The SC gap is strongly influenced by the pseudogap.
The broadly peaked features in the EDC data are due to pseudogap ◮ Many other factors may contribute to the broadly peaked features, but pseudogap stands out to be the most reasonable one. ◮ Reasons: Increased influence of the PG in the underdoped regime; doping dependence of the feature at higher energy; the proximity of this larger energy scale to the pseudogap energy scale above T c . ◮ Momentum-dependence study of the SC gap in experiments (to discuss later) also support this assertion.
Deviation of d -wave in the SC state ◮ d -wave SC gap is a hallmark of cuprate HTCS. ◮ ∆ k = | cos( k x ) − cos( k y ) | / 2. ◮ But deviation from simple d -wave form has been observed in underdoped systems near the antinode. ◮ See Fig. 3 and the caption there. ◮ Fig. 4 shows experimental evidence for such increasing deviation from d -wave form with increasing underdoping. ◮ It is well known that PG energy scale increases with underdoping, so it is natural to associate the increasing deviation with the increading influence of PG physics in the SC state of underdoped cuprates. ◮ Near the near-nodal region lacks this strong doping dependence in this doping regime. ◮ Conclusion: Fermi surface (FS) can be divided into two general regions with distinct momentum dependences of the gap.
Figure: 3. Leading edge gap function for LBCO x = 0.11 (T c = 23 K) and LSCO x = 0.11 (T c = 26 K) measured at 19 ± 2 K and 21 ± 2 K, respectively, plotted as a function of the simple d-wave form; the gure is adopted from [3]. As in other underdoped cuprates, the gap function has a simple d-wave form near the node, and deviates from this behavior at the antinode. This deviation increases as the hole concentration is reduced.
Figure: 4. Gap function for underdoped Bi-2212, measured at 10 K [4], [5]. Underdoped samples with Tc ¡ 92 K show a deviation from a simple d-wave form (dashed line) near the antinode.
Figure: 5. (ad) EDCs at k F (T = 10 K) for four dopings. The top curve is near the node and the bottom curve is near the antinode. The insets sketch where the cuts intersect the Fermi surface. The sharp peaks in all
Competition between two distinct states ◮ Fig. 5 shows quasiparticles (sharp peaks at low binding energy) are ubiquitous all around the FS, well into the near-nodal and near-antinodal regions, for all the dopings in Bi-2212. ◮ This experimental evidence is used to argue against the claim that the deviation from d -wave symmetry is an artifact from the loss of sharp quasiparticles in the antinodal region [8]. ◮ As doping decreases, the antinodal PG becomes stronger, and the features at higher binding energy becomes less strong as compared to the peak near the antinode (AN). ◮ This suggess SC becomes weaker as the gap near AN becomes stronger ◮ Competition between two distinct states.
The message ◮ Two features seen in momentum space by ARPES: a simple d -wave gap near the node and a larger gap near the antinode. ◮ The PG state is present even below T c and it resides in the AN region of momentum space ◮ SC dominates near the node. ◮ Any reasonable theoretical model for HTCS has to address these behaviour.
STS data in the light of the ARPES findings ◮ STS data of Fig.1a measures the local DOS averaged over all momentum. ◮ Hece they are interpreted as momentum-space average of ARPES data. ◮ Low bias voltage (low engery) in STS data correspondes to near-nodal region; AN region is completely gapped (more hardly be ’seen’ at low energy). ◮ The peaks at higher bias voltage (higher energy) corresponds to features of AN states. ◮ The STS data is consistent with the features seen in ARPES.
Figure: 6. (a) Locus of quasiparticles observed by ARPES and QPI [6] [7] for samples of similar Tc . ARPES observes sharp quasiparticles all around the FS, whereas QPI implies quasiparticle termination at the AF zone boundary (dashed line). (b, c) The gap and scattering rate around the Fermi surface for UD92 and UD75, demonstrating that all the peaks in gures 5(c) and (d) are quasiparticle- like with a smoothly evolving scattering rate.
Fourier transform STS (FT-STS) ◮ Exploit Quasiparticle interference phenomena (QPI) to learn momentum-space properties of cuprates. ◮ The QPI represents a two-particle process. ◮ Interference of QP scattering from impurities in a SC produce standing wave patter in local DOS, which is then studied via Fourier transform. ◮ Dispersion of the peaks in the FT of the DOS yield information about the FS and momentum dependence of the SC gap. ◮ FT-STS confirms d -wave dispersion at low bias voltage (interpreted as the SC-dominated regime) - consistent with ARPES. ◮ However, FT-STS results (see Fig.6) suggest SC QP extincts at the Antiferroelectric (AF) boundary ◮ But the ARPES data refure such extinction claim, as the QP peaks extent beyond the AF boundary. ◮ The momentum dependence of the QP is inconsistent with that of ARPES.
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