Energy scale in ARPES data suggesting Bogoliubov quasiparticles as excitations

by phonons of ~68 meV

Qiang Li

Jinheng Law Firm, Beijing, China

Posted on Slideshare on 10 March 2012

Abstract:

A dip is identified in existing ARPES spectra of Bi2223. The energy separation

between the dip and Bogoliubov (BQP) peak is well-defined at a value of about 68

meV. More remarkably, it is shown that, with a lattice-mode-specific modification

detailed below, the strength of the dip is in well qualitative agreement with that of the

BQP peak. These results strongly suggest an origin of BQPs as excitations by phonons

of a very small number of lattice modes, which could be a direct clue to understanding

the interactions leading to nodal and antinodal energy gap features and even high-

temperature superconductivity itself.

In the study of superconducting cuprates, identification of an energy scale (ES) is of

crucial importance. But ES revealing important physical process is not easy to be

recognized. For example, a peak of Bogoliubov quasiparticles (BQP) was found in

ARPES spectra of Bi2223[1] or Bi2212[2], and if the peak is due to thermal or optical

population as suggested in Ref. 1, it might be possible that the weight transfer leading

to the weight pileup of the peak also results in an ES in the form of a local weight

reduction (most likely a dip). But so far no such an ES, which needless to say would

be valuable to the understanding of superconductivity in cuprates along with its

energy and intensity relationships with respect to the BQP peak, has been clearly

recognized. Here I report identification of such an ES, a dip in Bi2223 ARPES

spectra. The energy separation between the dip and the BQP peak is well-defined at a

value of about 68 meV. More remarkably, it is shown that, with a lattice-mode-

specific modification detailed below, the strength of the dip is in well qualitative

agreement with that of the BQP peak. These results strongly suggest an origin of

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BQPs as excitations by phonons of a very small number of lattice modes, which could

be a direct clue to understanding the interactions leading to nodal and antinodal

energy gap features and even high-temperature superconductivity itself.

As shown in panel (b) of Fig. 1 taken from Fig. 3 of Ref. 1, a small dip can be seen in

the spectra at points B and C in panel (a) respectively at the energy of about 50 meV,

and trace of a dip is also seen at about the same energy in the spectrum at point A.

While the BQP peak, located at about -18 meV, shifts slightly towards smaller energy

from point C to A (see inset of Fig. 1(b)), the dip shifts in the same direction and by

approximately the same amount as the BQP peak, effectively keeping the energy

separation between the dip and BQP peak at about 68 meV at each of points A, B and

C.

The strength of the dip at point B seems to match that of the corresponding BQP peak

well, but obvious mismatch exists between the dip and BQP peak at point C. We

propose, however, that the mismatch is due to experimental setup as shown in inset of

Fig. 2, taken from Ref. 1, provided that the BQP peak and the dip are caused by

phonon excitations in (0,0)-(,) direction.

As shown in the schematic illustration of Fig. 3, made in view of the inset of Fig. 2,

line 101 represents the central line of the Fermi arc in the detection area, which can be

represented by a horizontal stripe schematically shown at 102. The (0,0)-(,)

direction is shown by the arrow, and points A, B, and C in Fig. 1 are schematically

shown here as corresponding to points 1, 2, and 3 on line 101 respectively. Thus, the

BQP peak at points A, B and C would be formed by quasiparticles measured at

around points 1, 2 and 3 respectively. As far as the BQPs are excitations by phonons

in the direction of (,)→(0,0), BQPs at point C should be excited from an area

schematically shown at 103C, and so are BQPs at points B and A with respect to areas

103B and 103A respectively. While points 1, 2 and 3 on the Fermi arc are well

covered by stripe 102, part of area 103C might have been left out of stripe 102,

leading to a weakened dip in the spectrum at point C.

A dip like this, however, can hardly be identified in Ref. 2 or a related report [3]. We

would propose that, due to experimental setup similarly to that discussed above with

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respect to the weakened dip, the weight from the main band part at around 50-70 meV

might have not been included in the data of Refs. 2 and 3, as can be seen from Figs. 4

and 5 of Ref. 3, where the main band part at about 50-70 meV is clearly excluded

from the data-collecting (shade) area. It is also to be noted that a dip as discussed

above might not be seen in a fitting curve, as illustrated in Fig. 1(b).

We have identified a dip in ARPES spectra of a Bi2223 sample. The dip and its

corresponding BQP peak have a well-defined energy separation of about 68 meV.

With a phonon-related modification, the strength of the dip is in good qualitative

agreement with that of the BQP peak, strongly suggesting that the BQPs are

excitations from such a dip by phonons of a very small number of lattice modes. With

such a phonon origin, many questions can arise, such as: 1) how can such a 68 meV

lattice mode(s) be so intense as to excite so many BQPs? 2) How to explain the

seemingly k-deviation the BQPs’ distribution has with respect to the band structure

below the Fermi level? [1] [3] and, 3) why BQPs are measured near the node in Bi2212[2]

[3] while they are measured near the antinode in Bi2223?[1]? Hopefully, questions like

these will stimulate our understanding of superconductivity in cuprates.

[1] Matsui, H. et al. BCS-like Bogoliubov Quasiparticles in High-Tc Superconductors

Observed by Angle-Resolved Photoemission Spectroscopy. Phys. Rev. Lett. 90,

217002 (2003).

[2] Lee, W.S. et al. Abrupt onset of a second energy gap at the superconducting

transition of underdoped Bi2212. Nature 450, 81-84 (1 November 2007).

[3] Balatsky, A. V., Lee, W. S. & Shen, Z. X. Bogoliubov angle, particle-hole mixture,

and angle-resolved photoemission spectroscopy in superconductors. Phys. Rev. B 79,

020505(R) (2009).

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Figure 1 Spectra of Bi2223 taken from Matsui et al. (a) BQP spectra of Bi2223 at

the location shown in the inset in Fig. 2. (b) EDCs at the three points A, B, and C. The

small dip at about 50 meV shows a position shift matching that of the BPQ peak at

about -18 meV. The seemingly mismatch between intensity of dip at C and that of the

corresponding BQP peak can be explained by experimental setup.

Figure 2 The same spectra as Fig. 1, taken from Matsui et al.

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Figure 3 Schematic illustration of experimental setup relating to the results

shown in Fig. 1(b). As far as the BQPs are excitations by phonons in (,)→(0,0)

direction, BQPs at point C come from the area generally represented by square 103C,

which might have been partly left out, as schematically indicated by partial coverage

of square 103C by stripe shown at 102.

103A

103B

103C

1

2

3

A B C

101(π, π)

(0, 0)

102

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