ARPES studies of cuprate fermiology: Superconductivity, pseudogap - - PowerPoint PPT Presentation

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 Tc in

• rder 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

• ccupied 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 > Tc) of conventional (low Tc)

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 Tc or by a depletion of DOS near zero bias in the normal state.

◮ STS data shows the gap is largely unchaged across Tc and

persists to temperature much higher than Tc.

◮ Support ‘One-gap scanario’: the onset of the pseudogap (PG)

(T ∗) marks the onset of Cooper-pair formation, whereas Tc marks the onset of phase coherence.

◮ Also supported by Nernst effect measurements.

Figure: 1. (a) STS measurements of Bi2Sr2CaCu2O8+δ(Bi-2212, Tc = 83) from [1]. (b) Andreev reection measurements of Bi2Sr2Ca2Cu3O10+δ (Bi-2223, Tc = 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 Tc - no pseudogap.

◮ A temperature-dependent gap closing near Tc. ◮ 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 Tc 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 Tc

◮ Tc marks the realm of SC. ◮ But in sufficiently underdoped cuprates, two distinct gaps can

be distinguished below Tc.

◮ Energy distribution curve (EDC) - intensity as a function of

energy at fixed momentum.

◮ See Figure 2 - data taken near the antinodal kF (i.e.,

kF ∼ (0, π), momenta near the Brillouin zone axis).

◮ Sharp peak at lower binding energy (|E − EF| ∼ 0) is

associated with superconductivity.

◮ Broader features at higher binding energy

(|E − EF| ∼ 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

• ne.

◮ 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 Tc.

◮ 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(kx) − cos(ky)|/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 (Tc = 23 K) and LSCO x = 0.11 (Tc = 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 kF (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 Tc 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.

Figure: 7. (a) From [4]. Underdoped Bi-2212, Tc = 92 K: EDCs near Tc for point A, marked in the Fermi surface schematic. At elevated temperature, the upper Bogoliubov branch, a signature of superconductivity, is thermally populated, and its energy position is marked by a short vertical line. The upper Bogoliubov peak moves closer to EF as it approaches Tc . (b) EDCs at the antinode (point B) for the three temperatures. Although the position of the EDC maximum remains unchanged, the sharp peak disappears across Tc . (c) Gap function at

Temperature dependence of the upper Bogoliubov branch near nodal region

◮ When a SC gap opens on the Fermi surface, the band

dispersion splits into the upper and lower Bogoliubov branches.

◮ At low temperature, only the lower branch is measured by

ARPES.

◮ At higher temperatures, the upper branch can also be partially

seen by ARPES due to thermal excitation near the Fermi surface.

◮ The upper branch is a signature of SC. ◮ Fig.7a shows the temperature evolution of the upper

Bogoliubov branch near the nodal region.

◮ The upper Bogoliubov branch appears as a peak above EF. ◮ As temperature raises towards Tc the position of the peak

move close to EF

Temperature dependence of the upper Bogoliubov branch near antinodal region

◮ Fig.7b shows the temperature evolution of the upper

Bogoliubov branch near the antinodal region.

◮ The position of the peak is largely temperature independent. ◮ However, lineshape is profoundly changed across Tc = 92 K:

Sharp peak present below Tc, but only broadly peakead features seen above Tc.

Momentum dependence of gap function at different temperatures

◮ Fig.7c shows momentum dependence of the gap in Bi-2212

UD92 (Tc = 92 K) at T = 8 K, T = 82 K, T = 102K.

◮ At 8 K, simple d-wave form. ◮ At 102 K, a charecteristically PG feature above Tc is

measured: an ungapped arc near the node and a gap at the antinode whose energy is comparable to AN gap below Tc.

◮ Gap in the antinodal region does not evolve subtantially

across Tc.

◮ At intervening temperatures, the gap evolves more rapidly in

near-nodal region, giving rise to a deviation from a simple d-wave form at 82 K.

Temperature dependence of gap function at nodal and antinodal regions

◮ Fig.7d details the temperature dependence in the near-nodal

and near antinodal regions.

◮ In near antinodal region, the gap in unchanged across Tc. ◮ Gap near nodal region changes drastically near Tc. ◮ Implication: near-nodal region and antinodal region unlikely

be associated with a single order parameter.

◮ Possibility: near-nodal region is dominated by SC, and the

antinodal region by PG physics.

◮ Presence of the QP all around the FS suggests subtle

interaction between these two states in momentum space, but detail still unclear.

ARPES conflict resolution for Andreev reflection vs. STS data

◮ In the light of the ARPES data in Fig.7, the descrepency

between STS and Andreev results can be resolved:

◮ STS and Andreev reflection are likely sensitive to different

portions of the FS in the cuprates.

◮ The Andreev data corresponds to that measured in ARPES

near nodal region where SC dominates.

◮ The STS data corresponds to that measured in ARPES near

antinodal region (where PG dominates), which is largely temperature independent.

Density wave order

◮ The authors of the paper argues that the ARPES studies of

the SC and PG in Bi-2201 supports a fluctuating density-wave

• rder.

◮ We note that this is a possibility, but needs more experimental

support to strengthen the claim.

Summary

Figure 8

Summary of temperature and doping dependence ARPES studies. In the overdoped regime and above T ∗ , the behavior is conventional, with a simple d-wave form of the superconducting gap in the former and a simple metallic Fermi surface in the latter. In the underdoped regime, the low-temperature gap function deviates from a simple d-wave form, showing the strong inuence of the underlying pseudogap on the energy positions of the near-antinodal quasiparticle peaks. In Bi-2201, the pseudogap state was found to be compatible with a density-wave order. Experiments on slightly underdoped Bi-2212 have found that the antinodal gap shows minimal temperature dependence across Tc, but in the near-nodal region the gap collapses near Tc, leading to the mysterious pseudogap state where the near-nodal region is metallic and the near-antinodal region is gapped.

Conclusion

◮ Low-energy excitations in the cuprates was reviewed. ◮ Evidence for the distinct nature ofthe PG and SC ◮ Increasing deviation of SC gap function from a simple d-wave

form in underdoped regime

◮ Different temperature dependence of the gap in the nodal and

antinodal region.

◮ A ‘two-gap’ scenario is established. ◮ The ‘normal’ state (PG) of the cuprates is distinct from SC.

But more detail studies have to be carried out to unveil the details of the ‘normal’ states, and the interplay between the two states.

◮ How the PG promotes HTCS?

References

Renner C, Revaz B, Genoud J-Y, Kadowaki K and Fischer 1998 Phys. Rev. Lett. 80 149. Svistunov V M, Tarenkov V Y, Dyachenko A I and Hatta E 2000 JETP Lett. 71 289. He R-H et al. 2009 Nat. Phys. 5 119. Lee W S, Vishik I M, Tanaka K, Lu D H, Sasagawa T, Nagaosa N, Devereaux T P, Hussain Z and Shen Z-X 2007 Nature 450 81. Tanaka K et al 2006 Science 314 1910. Kohsaka Y et al. 2008 Nature 454 1072. Vishik I M, Nowadnick E A, Lee W S, Shen Z-X, Moritz B, Devereaux T P, Tanaka K, Sasagawa T and Fujii T 2009 Nat.

• Phys. 5 718.

Wei J et al 2008 Phys. Rev. Lett. 01 097005.