Arcs versus Pockets - To d-wave or not to d-wave, that is the question
Blogged by Andrey Chubukov and Aharon Kapitulnik
Arcs vs. Pockets
Shakespearean title: Arcs versus Pockets - To d-wave or not to d-wave, that is the question.
Mike appears, tall, slender, but... with more gray hair than last year.
Cannonical phase diagram of cuprates. Undoped state any AFM insulator.
All theories depend on what is going on in the pseudogap phase. Shows a list of "What is the pseudogap."
Doping a Mott insuator - x vs. 1+x
- Slater approach - AFM causes small pockets around (\pi/2,\pi/2)
- Strong coupling proposal by PWA, uniform RVB. As doping goes to zero, no structure of ordered AFM. - 1987.
However, possibly a stable state is a flux-phase state - PA Lee. Gets a Dirac-like spectrum. At finite filling, pockets.
More recently, YRZ theory, umklapp RVB. GF has zeroes along AFM zone boundary. Pockets are displaced towards \Gamma points. Arc + suppressed intensity in the back side.
Andrey- Mike says that the straightforward
way to track the FS is to analyze quantum oscillations. He discusses early experiments at Los
Alamos which show small FS. But these experiments
were questioned and argued to be possibly a noise effect. He argues that failure of that experiment
forced people to look at ARPES for the information about the FS. He continue with the arc story and its interplay with the pseudogap. Mike discusses the question, first asked by Shen
et al, whether the arc is real or a part of the pocket. Mike shows data by Kanigel it al who found that the length of the arc apparently scales linearly with T. This lead to a suggestion that the arc may a
finite T effect of broadening of the spectrum of a d-wave SC. Mike then discusses recent, higher quality
data from Dessau group. In more
underdoped systems, there is still some evidence for d-wave like gaps.
Need to understand normal state - perform quantum oscillations: specific heat and transport. This probes Periods of extremal orbits. With Fourier Transform of QO, obtain the frequencies - map out Fermi surface.
- Old data on optimally doped, 1992, saw a small Fermi surface - called noise effect - not believed.
- ARPES took over. mapping of Fermi surface (occupied states.) Measure Energy Distribution Curves and Momentum distribution curves.
ARPES observed d-wave like dispersion, Large Fermi surface. Above T*, observe a large Fermi surface with no coherent QP. Between Tc and T*, arcs were observed.
Now Mike discusses: First - Arcs scenario, then Pockets scenario.
- Old data on optimally doped, 1992, saw a small Fermi surface - called noise effect - not believed.
- ARPES took over. mapping of Fermi surface (occupied states.) Measure Energy Distribution Curves and Momentum distribution curves.
ARPES observed d-wave like dispersion, Large Fermi surface. Above T*, observe a large Fermi surface with no coherent QP. Between Tc and T*, arcs were observed.
Now Mike discusses: First - Arcs scenario, then Pockets scenario.
All transport scale as T/T*, and also ARPES arcs scale as T/T*. Maybe the normal phase is similar to the superconducting phase.
- New data by Dan Dessau. He constructed an angle resolved DOS. Arc length as a function of temperature agrees with marginal Fermi liquid. Increase temperature arc length increases.
- Underdoping - still has a d-wave like gap, evidence that d-wave gap persists into the insulating phase.
Pockets in Nd-doped LSCO? Chang et al. paper, evidence for \pi-\pi reconstruction. But, incommensurate.
- Meng et al. Single layer BSCCO - claimed to see the back-side of the pockets. Suspicion that it is structural effects. Indeed, this was subsequently shown experimentally.
- Bilayer BSCCO, see a pocket similar to YRZ ansatz. (Yang et al. - Nature (2008).)
Q (PC) - Can you show how and where flat part appears in the data? Mike explains that in ARPES they need to deconvolve the resolution.
Q (AC) - Any other example? Yang et al. claim arc length is temperature independent. They extract the arc tip. but, since Fermi function is strong function of temperature, conclusion is doubtful.
- Similar data from STM - quasiparticle interference. They do see states terminating at the magnetic zone boundary - it is also a structural zone boundary.
What about quantum oscillations (QO) - also very messy. QO observed using UBC samples. Size of pockets agree with ARPES.
Hall number is negative - either large Hall background, or what they see is electron, not Hall pocket. Unresolved.
LeBoeuf observed hat negative Hall doping appears around 1/8, very narrow, Indicate formation of stripes. Stripes proposed early, origin from segregation of holes.
- For magnetic stripes, electron pockets are stable for range of potentials. Charge-only model - no pockets.
- Kivelson proposed strong nematic order plus charge order - pockets.
- A larger hole Fermi surface from spin-spiral state was proposed. spin spiral instead of spin linear.
Experimental data of Sebastian et al. - three different periods, - but now all think that only one pocket plus bilayer splitting.
Riggs et al. - oscillations appear in specific heat. - there is also a zero-field offset. sqrt(H) persists above irreversibility. Hc2-inferred - 100 T.
Latest from cambridge - checkerboard order of charge, form a pocket centered around point closer to center.
NMR by Marc Julien, NMR agree with charge density wave - charge ordering. Field induced? - no RIX experiments - charge ordering peak - SC sets in charge order persist when superconductivity suppressed. Charge peaks around quantum oscillations. Keimer - edge of detectability. missed before because the wave-vector is not ordinary at \pi/2. they see larger wave-vector. but, ARPES does not see the same.
Q(AK) - but, you compare ARPES on BSCCO and YBCO. Mike replies that indeed this is the case, but indicates that BSCCO is very dirty and hopeless for QO.
Q(AK) - how about use data on LBCO? Mike just compares BSCCO and YBCO.
Q(AC) - charge or spin nematic ? Mike answers that spin nematic. Nematic does not open a gap. Similar problem with Varma model, does not open a big energy gap.
- New data by Dan Dessau. He constructed an angle resolved DOS. Arc length as a function of temperature agrees with marginal Fermi liquid. Increase temperature arc length increases.
- Underdoping - still has a d-wave like gap, evidence that d-wave gap persists into the insulating phase.
Pockets in Nd-doped LSCO? Chang et al. paper, evidence for \pi-\pi reconstruction. But, incommensurate.
- Meng et al. Single layer BSCCO - claimed to see the back-side of the pockets. Suspicion that it is structural effects. Indeed, this was subsequently shown experimentally.
- Bilayer BSCCO, see a pocket similar to YRZ ansatz. (Yang et al. - Nature (2008).)
Q (PC) - Can you show how and where flat part appears in the data? Mike explains that in ARPES they need to deconvolve the resolution.
Q (AC) - Any other example? Yang et al. claim arc length is temperature independent. They extract the arc tip. but, since Fermi function is strong function of temperature, conclusion is doubtful.
- Similar data from STM - quasiparticle interference. They do see states terminating at the magnetic zone boundary - it is also a structural zone boundary.
What about quantum oscillations (QO) - also very messy. QO observed using UBC samples. Size of pockets agree with ARPES.
Hall number is negative - either large Hall background, or what they see is electron, not Hall pocket. Unresolved.
LeBoeuf observed hat negative Hall doping appears around 1/8, very narrow, Indicate formation of stripes. Stripes proposed early, origin from segregation of holes.
- For magnetic stripes, electron pockets are stable for range of potentials. Charge-only model - no pockets.
- Kivelson proposed strong nematic order plus charge order - pockets.
- A larger hole Fermi surface from spin-spiral state was proposed. spin spiral instead of spin linear.
Experimental data of Sebastian et al. - three different periods, - but now all think that only one pocket plus bilayer splitting.
Riggs et al. - oscillations appear in specific heat. - there is also a zero-field offset. sqrt(H) persists above irreversibility. Hc2-inferred - 100 T.
Latest from cambridge - checkerboard order of charge, form a pocket centered around point closer to center.
NMR by Marc Julien, NMR agree with charge density wave - charge ordering. Field induced? - no RIX experiments - charge ordering peak - SC sets in charge order persist when superconductivity suppressed. Charge peaks around quantum oscillations. Keimer - edge of detectability. missed before because the wave-vector is not ordinary at \pi/2. they see larger wave-vector. but, ARPES does not see the same.
Q(AK) - but, you compare ARPES on BSCCO and YBCO. Mike replies that indeed this is the case, but indicates that BSCCO is very dirty and hopeless for QO.
Q(AK) - how about use data on LBCO? Mike just compares BSCCO and YBCO.
Q(AC) - charge or spin nematic ? Mike answers that spin nematic. Nematic does not open a gap. Similar problem with Varma model, does not open a big energy gap.
Andrey: Mike continues with the pocket scenario –
there are data on Nd-doped LSCO which were first interpreted as
evidence for a pocket, but later re-interpreted as a
structural effect. There are data from
P. Johnston group which show consistency with YRZ scenario. Mike suspects that this may again be
structural effect, but stresses that there is no proof
of this. In his view, one issue with the results
from Brookhaven group is that they differ from other groups in the T dependence of the arc –
Dessau and Campuzano groups argue that arcs are T dependent, while Brookhaven
group argues that the length of the arc
is T-independent.
Mike then discusses the revival of quantum oscillation
measurements. The size of the pocket
inferred from quantum oscillations is consistent with “closed arc”, but the Hall number is negative, what implies
that the pocket is likely an electron pocket.
He then discusses the stripe scenario by Millis and Norman and by Kivelson
et al, and the results by
Cambridge group which found that the effective mass extracted from quantum oscillations diverges at the lowest doping at which
oscillations are still seen. Another
scenario for quantum oscillations is checkerboard charge order. Mike discusses NMR evidence for charge order
around 1/8 doping. There is also
evidence for charge order from x-ray data from Keimer’s group. His conclusion is that FS extracted from
pocket scenario is inconsistent with ARPES.
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