- Email: [email protected]
Temperature dependence in threshold photoemission from high-TC-superconductors
Solid State Communications. Vol. 91, No. 8, pp. 655-659. 1994 Ekevier Science Ltd Printed in Great Britain 0038.-1098/94 $7.00 + .OO
Pergamon
00~1098(94) 00361-O
TEMPERATURE
DEPENDENCE IN THRESHOLD PHOTOEMISSION HIGH-Tc-SUPERCONDUCTORS
FROM
W.G. Park, S.A. Nepijko’, A. Fanelsa and E. Kisker Institut fur Angewandte Physik, Universitat Dusseldorf, 40225 Dusseldorf, Germany and L. Winkeler and G. Giintherodt 2. Physikalisches Institut, RWTH Aachen, Templergraben
55, 52056 Aachen, Germany
(Received 6 May 1994 by P.H. Dederichs) In threshold photoemission from single-crystalline BizSrzCal CuzOs+6 high-T= superconducting material we observe that for photon energy some 100meV larger than the work function (- 4.8 eV) the total photoyield changes strongly with temperature, similar as the susceptibility, suggesting that broken Cooper pairs do not contribute to the photocurrent. For photon energy slightly smaller than the work function we observe a BCS-like temperature dependence for the number of quasi-particles above the Fermi energy. Keywords: scopies.
A: high-T= superconductors,
1. INTRODUCTION IN RECENT YEARS considerable progress has been achieved in studying the valence band electronic structure of high-Tc-superconductors by angle-resolved vacuum-ultraviolet photoelectron spectroscopy (ARUPS). Not only the electronic band structure has been determined but also the superconducting energy gap and its temperature dependence have been studied. Especially, evidence for the BCS-like singularity in the density of states (DOS) below EF has been obtained [l]. We exploit a somewhat different access to the temperature dependent electronic structure by using the threshold photoemission technique with high optical resolution (1OmeV for hv = 4eV). The photon energy is chosen to be in the vicinity of the photothreshold (Ethr). One of the advantages of this energy regime is that the electron scattering cross sections are small, and consequently the probing depths are much larger than in VUV photoelectron spectroscopy. This * Permanent address: Institute of Physics, Academy of Sciences of the Ukraine, Prospect Nauki 46, 252650 Kiev-22, C.I.S./Ukraine.
E: photoelectron
spectro-
should be very important in the case of high-T& materials because of their large unit cell. We have measured the total photoelectron yield as a function of photon energy for energies some 0.1 eV below and above threshold. The most prominent observation is a critical dependence of photocurrent on the sample temperature, changing its character when the photon energy is tuned through the photothreshold. We interpret these observations as first evidence for the dynamics of the quasi-particle singularity above EF and for the influence of Cooper pairing on the excitation or transport process of the photoelectrons. The photothreshold Ethr is the minimum photon energy (hvmin) at which photoemission occurs. In metals, Ethr equals the work function (4) which is of the order of a few eV. The threshold energy is only sharply determined at T = 0 K. At finite temperatures, weak photocurrent is observed resulting from electronic states above EF due to the Boltzmann tail of the Fermi-Dirac distribution. At threshold, the emission is confined to a very narrow cone directed perpendicular to the surface since electrons with energy of just 4 travelling with some velocity component parallel to the surface will not be able to overcome the vacuum barrier. With photon energy
655
656
THRESHOLD
PHOTOEMISSION
FROM HIGH-Tc-SUPERCONDUCTORS
exceeding 4, electrons originating from the Fermi level can be emitted despite a small velocity component perpendicular to the surface and the photoelectron escape cone opens, leading to the well-known quadratic dependence of photocurrent on photon energy [2]. In semiconductors, power laws with higher exponents have been predicted and observed. For the high-Tc superconductors (HTSC) the photothresholds have not yet been discussed in the literature. Also, the question of the influence of entering the superconducting state below Tc on the threshold behaviour has not been discussed yet. Very small changes (< 1 meV) of the work function near Tc have been observed in YBa2Cus07_6 with the Kelvin-method by van der Mare1 et al. [3, 41. The total photoyield measured in our experiment as a function of photon energy is E, Z(hu) cc
J J (1 E,. - hv
_f(E)WE)
Vol. 91, No. 8
1 K. However, there might be a temperature gradient of some K between the sample and the Ptl 0 0 temperature sensor. During bake-out of the vacuum chamber the sample temperature was kept below 350 K to avoid the change of oxygen concentration in the chemical composition. The light source was a high-pressure xenon arc lamp in a Suprasil bulb. The light was monochromatized by means of a grating monochromator with band width of 15 meV near photothreshold. Total photoyield was measured by means of a channeltron located nearby to the sample, biased by 150 V with respect to the sample. The total yield measurements were performed as a function of photon energy in the range from 3.5 to 5.5eV for temperatures between 30 and 120 K. The spectra have been normalised to the photon flux which was measured simultaneously by means of a beamsplitter and a photodiode.
dE da,
where a is the angle of the escape cone and E, is the vacuum energy [see inset in Fig. l(a)]. Accordingly, the first derivative dZ/dE is proportional to the function of the density of state D(E) multiplied by the particle statistics f(E), i.e. to the energy distribution curve. The total photoyield as a function of energy might be modulated by structures of the DOS. In case of metallic behaviour, the first derivative should extrapolate to 4. The opening of the superconducting energy gap should manifest itself in a change of the Z(hv) curve. Due to the constraint of emission angle to the surface normal, some change in the angular distribution caused by different conditions (for instance, temperature change) should result in a corresponding strong change in photoyield.
3. RESULTS AND DISCUSSION Total photoyield [Z(hu)] curves have been measured as a function of temperature with about 3 K steps. Figure l(a) shows two curves from this series for temperatures of 119K (open circles) and 50K (filled circles). An inset in Fig. l(a) shows an enlarged view of the photothreshold region. The first derivative curves dZ/dE (not shown) exhibit a quasi-
-__
r
2. EXPERIMENTAL The system investigated in this work is Bi(2 2 12). The single crystalline samples of dimension 3 x 2.5 x 0.5mm3 were grown by the conventional self-flux-method [5] and had the chemical composition B&i Sri,sCaCuzOs +6 according to EDX analysis. The critical temperature T, determined by d.c. susceptibility measurement was about 86K. All experiments were carried out at pressures in the lower lo-” Torr range. The sample was cleaved in-situ at 30K parallel to the a-6 plane immediately before starting the measurements. The sample could be cooled down to about 10K. Sample temperature could be measured with nominal accuracy of about
t
& Photon
energy
leV1
Fig. l(a). Total photoyield at T = 119K (0) and T = 50 K (0) as a function of photon energy. The inset (il) shows the threshold region enlarged. Inset (i2) shows a model for total yield threshold photoelectron spectroscopy.
Vol. 91, No. 8
THRESHOLD
PHOTOEMISSION
FROM HIGH-C-SUPERCONDUCTORS
657
1lOK 99 97 95 93 91 89 87 85 83 81 79 75 73 70 59 50 33
4.00
4.25
4.50
Photon
4.75
5.00
energy
5.25
[eVl 40
Fig. l(b). Difference curves of the total photoyield for different temperatures as obtained by subtracting a reference curve taken just above Tc from the curves taken at the lower temperatures. linear region which extrapolates to a threshold energy of 4.76 f O.O5eV, to first order independent of temperature. This value is in the range of work functions determined by other methods [6-81. The linear increase of the dZ/dE curve suggests metallic behaviour. The origin of emission intensity for energies which becomes visible at about 4eV is not clear (another Bi(2 2 12)-sample showed an even larger intensity in this region). We attribute this intensity to the presence of cleavage surfaces with different chemical composition or to the presence of more than one crystallographic phases. For photon energy below Ethr the intensity exhibits a maximum value near 70 K which is borne out more clearly when subtracting a total yield curve taken above Tc as a reference curve from the data taken below Tc. Figure l(b) shows this difference data. We notice a building up of an intensity hump of about 200meV width at photon energies smaller than q!~,extending towards lower energies when the temperature decreases, but vanishing at the lowest temperature at which we have measured (33 K). Figures 2(a-c) show the dependence of total photoyield on temperature [Z(T)lhv :urves] with photon energies ranging from 4 - 0.1 eV to 4 + 0.5eV. The most remarkable observation in
60
60
100 120
T rK1 Fig. 2. Temperature dependence of the total photoyield at different photon energies (dots): hv = 4.75 eV (a), 4.85 eV (b) and 4.95 eV (c). The intensity scale is the same for the three figures. The line in (c) is the temperature dependence of the susceptibility, measured for the same sample, but the temperature scaled to have the sharp drop observed in the photoyield at 95K to coincide with the drop in susceptibility (86 K).
0
Photon
energy
teV1
Fig. 3. Energy dependence of the absolute temperature-induced change of total photoyield [AZ(hv) = hWK&)
-
z33K(hd1*
658
THRESHOLD
PHOTOEMISSION
FROM HIGH-Tc-SUPERCONDUCTORS
Vol. 91, No. 8
interpreted in this way. The amplitude of the hump in the vicinity of about 200meV above EF increases 3 I upon cooling below Tc before it vanishes at the lowest 2 measured temperature (33 K). Its width is larger than kBTc. This might be expected since the I(hv) curves h 5 are integrated intensities between E, and E, - hv. e” Furthermore, the peak shifts towards lower energy x0 E upon cooling as to be expected from the model. Figure 2(c) suggests to assume that the drop in photoyield is related to superconductivity since the Fig. 4. Schematic description of the density of states shapes of the drop in photoyield and of the at different temperatures (T > T, > q > 5 > q) for susceptibility curve are very similar. In order to a superconductor. The intensity of the total yield is explain the changes in photocurrent with temperaproportional to the area under the curve between E,, ture, we consider not only the existence of the and E,, - hv, corresponding to the proper temperature. singularities but also the momenta (+k, -k) of paired electrons. Since many physical properties of data taken at different temperatures is the strong high-Tc-superconductors show a behaviour characdecrease in intensity upon cooling below Tc for teristic to two-dimensionality within the CuOs planes hv = 4.95 eV [Fig. 2(c)]. Similar curves are obtained we expect that the paired electrons should move for photon energies in the range 4.87 < hv < 5SeV, largely confined to these planes. They are aligned but the total change depends on photon energy as perpendicular to the emission direction of the shown in Fig. 3. The absolute amplitude of the photoelectrons in our and other author’s photoemission experiments. Indeed, in VUV angle-resolved change in photoyield increases sharply and quasilinearly above threshold before reaching a plateau at photoemission data, the singularity below Tc is not about 5.2 < hv < 5.4eV, decreasing at higher photon observed in P-Y-direction for normal emission, but energies. The position of the steep decrease in curve for emission angle of 27” (max. at 30”) with respect to I(T) [see Fig. 2(c)] occurs at 97K. The solid line in the normal to the cleavage surface [9]. If the energy of Fig. 2(c) is the sample’s susceptibility curve with the the electrons in the surface normal direction is temperature axis scaled to align the drop in smaller than 4 (or hv cos Q < 4, where Q is the susceptibility (observed at N 86K) with the drop in internal angle with respect to the surface normal), photocurrent. they are not able to escape into the vacuum. The For photon energies smaller than the work calculated minimum photon energy for electrons to function, the photocurrent first decreases with escape into vacuum with internal angle o = 27” is temperature at high temperatures, followed by a 5.4eV for 4 = 4.8eV. This compares well with the peak near 70K [hv N 4.75eV, Fig. 2(a)]. The photon energy at which the total change in phototransition between these two regimes is gradual [see yield decreases (cf. Fig. 3) since at this energy broken Fig. 2(b)]. At hv N 4+<, where 0 < < < O.leV, the Cooper-pair electrons would fall into the photoelectron escape cone. We expect that the drop in current temperature dependence is more or less linear. should be of the order 2A/[E, - (hv - 4)] N 30%, We interpret the observations shown in Figs. l2(b) on the basis of the BCS model, which is shown which, considering the crudeness of the model DOS, schematically in Fig. 4. The measured photoyield is compares well with the maximum value of 50% proportional to the integral of the product of the observed at hv = 4.95 eV. These observations all give electron energy distribution and the DOS between E,, support to the assumption that the strong decrease of and E, - hv. Above T,, the Fermi-Dirac statistics photoyield which we observe for photon energies governs the energy distribution curve. Below Tc, the above 4 occurs because broken Cooper pairs do not electrons formed to Cooper pairs are causing the contribute to the photoyield at photon energies up to 0.5 eV above threshold. Since the susceptibility singularity of quasiparticles below EF which becomes broader with decreasing temperature since it has to diminishes in proportion to the number of Cooper accumulate more particles. The singularity above EF pairs, the temperature dependence of the photoyield is caused by unpaired electrons. Qualitatively, it is should follow the susceptibility curve in our model. clear that upon cooling below T, the quasi-particle The above-mentioned difference between Tc and the density above EF first increases, before it vanishes at temperature at which the drop in photoyield sets in might arise from the fact that the susceptibility very low temperatures because of the Fermi-Dirac statistics. Our data shown in Fig. l(b) can be measurement is a bulk method, whereas the informaT, >Tc>T, >T, >T,
u)
%
THRESHOLD
Vol. 91, No. 8
PHOTOEMISSION
FROM HIGH-Tc-SUPERCONDUCTORS
659
i.e. it reflects qualitatively the temperature dependence of the width of the energy gap A(T)/A(O). -z
4. CONCLUSIONS
2
5
e, m_ F:
-5
!
a ,a
Fig. 5. Contribution of uncorrelated electrons nl(T) (curve 1) and of electrons in Cooper pairs Q(T) (curve 2). Curve 3, (dashed) shows the derived temperature dependence of the energy gap A(T)/A(O). tion depth in our photoemission measurement is only 20-30 monolayers, corresponding to only 2-3 unit cells. Also, a temperature gradient between the Ptl 0 0 temperature sensor and the sample cannot be excluded. The changes with temperature of the maximum value of the hump above EF in Fig. l(b) corresponds approximately to the temperature dependence of the area under the singularity above EF, i.e. to that part of electrons [rri(T)] transferred from the region of the energy gap to energies above EF + A (which do not build the Cooper pairs) (Fig. 5, curve 1). The electron pairs (bosons) from the singularity below EF are apparently not contributing to the photocurrent for photon energy slightly larger than the work function. The changes of the minimum value in Fig. l(b) also give information about the number of electrons [nz( T), cf. Fig. 5, curve 21 escaped from the region of the energy gap which are coupled to Cooper pairs. Our data show - in agreement with what is to be expected - that nl( T) is much smaller than Q(T). Figure 5 shows q(T), nz(T), and q(T) +nz(T) (curve 3). If we assume that the Fermi surface has spherical symmetry, the number of electrons leaving the energy gap region can be calculated as q(T)
+n2(T)
In summary, we observe that the total photoyield in threshold photoemission for energies some 0.1 eV larger than the photothreshold decreases by up to 50% upon cooling below TC similar as the zero-field cooled susceptibility. It is therefore suggested that the decrease occurs in proportion to the concentration of Cooper pairs which, when broken-up by the photon, apparently do not contribute to the photocurrent because of their large momentum in the Cu02 planes. Accordingly, this method is besides the MeiDner effect a new tool for determining the superconducting state. Furthermore, we obtain for the first time evidence in photoemission for the existence of the quasiparticle peak above EF and for its temperature dependence. The data demonstrate that the relatively simple technique of threshold photoemission is a powerful tool for studying HTC superconductivity. Acknowledgements - We thank F.U. Hillebrecht for his help in the initial stages of the experiment and the technical staff members of the Institut fur Angewandte Physik, Heinrich-Heine-Universitat Dusseldorf, for their excellent assistance. We thank H. Frank, 2. Phys. Inst. RWTH Aachen, for performing the susceptibility measurements. REFERENCES 1.
6.
= 0
0
7.
E,+A
&?dE exp [(E - EF)/~T] + 1
X
8.
EF-A ,312~v2 =
8fin
h3F
A(T),
9.
R.P. Huebener, C.C. Tsuei & D.M. Newns, Phys. Bl.50, 163 (1994), C.G. Olson et al., Science 245, 731 (1989); J.M. Imer et al., Phys. Rev. Lett. 62, 336 (1989); R. Manzke et al., Europhys. Left. 9, 477 (1989); D.S. Dessau et al., Phys. Rev. B45, No. 9, 5095 (1992). R.H. Fowler, Phys. Rev. 38, 45 (1931). D. van der Mare1 & G. Rietveld, Phys. Rev. Lett. 69, 2575 (1992). G. Rietveld, N.Y. Chen & D. van der Marel, Phys. Rev. Left. 69, 2578 (1992). K. Shigematsu, H. Takei, J. Higashi, K. Hoshino & H. Aono, J. Cryst. Growth 100, 661 (1990). F. Minami, T. Kimura & S. Takekawa, Phys. Rev. B39, 4788 (1989). R. Claessen, R. Manzke, H. Carstensen, B. Burandt, T. Buslaps, M. Skibowski & J. Fink, Phys. Rev. B39, 73 16 (1989). R. Biittner, N. Schroeder, E. Dietz, U. Gerhart, W. Assmus & J. Kowalewski, Phys. Rev. B41, 8679 (1990). M. Metzner, Dissertation, Heinrich-HeineUniversitat Dusseldorf, Germany (1993).
Pergamon
00~1098(94) 00361-O
TEMPERATURE
DEPENDENCE IN THRESHOLD PHOTOEMISSION HIGH-Tc-SUPERCONDUCTORS
FROM
W.G. Park, S.A. Nepijko’, A. Fanelsa and E. Kisker Institut fur Angewandte Physik, Universitat Dusseldorf, 40225 Dusseldorf, Germany and L. Winkeler and G. Giintherodt 2. Physikalisches Institut, RWTH Aachen, Templergraben
55, 52056 Aachen, Germany
(Received 6 May 1994 by P.H. Dederichs) In threshold photoemission from single-crystalline BizSrzCal CuzOs+6 high-T= superconducting material we observe that for photon energy some 100meV larger than the work function (- 4.8 eV) the total photoyield changes strongly with temperature, similar as the susceptibility, suggesting that broken Cooper pairs do not contribute to the photocurrent. For photon energy slightly smaller than the work function we observe a BCS-like temperature dependence for the number of quasi-particles above the Fermi energy. Keywords: scopies.
A: high-T= superconductors,
1. INTRODUCTION IN RECENT YEARS considerable progress has been achieved in studying the valence band electronic structure of high-Tc-superconductors by angle-resolved vacuum-ultraviolet photoelectron spectroscopy (ARUPS). Not only the electronic band structure has been determined but also the superconducting energy gap and its temperature dependence have been studied. Especially, evidence for the BCS-like singularity in the density of states (DOS) below EF has been obtained [l]. We exploit a somewhat different access to the temperature dependent electronic structure by using the threshold photoemission technique with high optical resolution (1OmeV for hv = 4eV). The photon energy is chosen to be in the vicinity of the photothreshold (Ethr). One of the advantages of this energy regime is that the electron scattering cross sections are small, and consequently the probing depths are much larger than in VUV photoelectron spectroscopy. This * Permanent address: Institute of Physics, Academy of Sciences of the Ukraine, Prospect Nauki 46, 252650 Kiev-22, C.I.S./Ukraine.
E: photoelectron
spectro-
should be very important in the case of high-T& materials because of their large unit cell. We have measured the total photoelectron yield as a function of photon energy for energies some 0.1 eV below and above threshold. The most prominent observation is a critical dependence of photocurrent on the sample temperature, changing its character when the photon energy is tuned through the photothreshold. We interpret these observations as first evidence for the dynamics of the quasi-particle singularity above EF and for the influence of Cooper pairing on the excitation or transport process of the photoelectrons. The photothreshold Ethr is the minimum photon energy (hvmin) at which photoemission occurs. In metals, Ethr equals the work function (4) which is of the order of a few eV. The threshold energy is only sharply determined at T = 0 K. At finite temperatures, weak photocurrent is observed resulting from electronic states above EF due to the Boltzmann tail of the Fermi-Dirac distribution. At threshold, the emission is confined to a very narrow cone directed perpendicular to the surface since electrons with energy of just 4 travelling with some velocity component parallel to the surface will not be able to overcome the vacuum barrier. With photon energy
655
656
THRESHOLD
PHOTOEMISSION
FROM HIGH-Tc-SUPERCONDUCTORS
exceeding 4, electrons originating from the Fermi level can be emitted despite a small velocity component perpendicular to the surface and the photoelectron escape cone opens, leading to the well-known quadratic dependence of photocurrent on photon energy [2]. In semiconductors, power laws with higher exponents have been predicted and observed. For the high-Tc superconductors (HTSC) the photothresholds have not yet been discussed in the literature. Also, the question of the influence of entering the superconducting state below Tc on the threshold behaviour has not been discussed yet. Very small changes (< 1 meV) of the work function near Tc have been observed in YBa2Cus07_6 with the Kelvin-method by van der Mare1 et al. [3, 41. The total photoyield measured in our experiment as a function of photon energy is E, Z(hu) cc
J J (1 E,. - hv
_f(E)WE)
Vol. 91, No. 8
1 K. However, there might be a temperature gradient of some K between the sample and the Ptl 0 0 temperature sensor. During bake-out of the vacuum chamber the sample temperature was kept below 350 K to avoid the change of oxygen concentration in the chemical composition. The light source was a high-pressure xenon arc lamp in a Suprasil bulb. The light was monochromatized by means of a grating monochromator with band width of 15 meV near photothreshold. Total photoyield was measured by means of a channeltron located nearby to the sample, biased by 150 V with respect to the sample. The total yield measurements were performed as a function of photon energy in the range from 3.5 to 5.5eV for temperatures between 30 and 120 K. The spectra have been normalised to the photon flux which was measured simultaneously by means of a beamsplitter and a photodiode.
dE da,
where a is the angle of the escape cone and E, is the vacuum energy [see inset in Fig. l(a)]. Accordingly, the first derivative dZ/dE is proportional to the function of the density of state D(E) multiplied by the particle statistics f(E), i.e. to the energy distribution curve. The total photoyield as a function of energy might be modulated by structures of the DOS. In case of metallic behaviour, the first derivative should extrapolate to 4. The opening of the superconducting energy gap should manifest itself in a change of the Z(hv) curve. Due to the constraint of emission angle to the surface normal, some change in the angular distribution caused by different conditions (for instance, temperature change) should result in a corresponding strong change in photoyield.
3. RESULTS AND DISCUSSION Total photoyield [Z(hu)] curves have been measured as a function of temperature with about 3 K steps. Figure l(a) shows two curves from this series for temperatures of 119K (open circles) and 50K (filled circles). An inset in Fig. l(a) shows an enlarged view of the photothreshold region. The first derivative curves dZ/dE (not shown) exhibit a quasi-
-__
r
2. EXPERIMENTAL The system investigated in this work is Bi(2 2 12). The single crystalline samples of dimension 3 x 2.5 x 0.5mm3 were grown by the conventional self-flux-method [5] and had the chemical composition B&i Sri,sCaCuzOs +6 according to EDX analysis. The critical temperature T, determined by d.c. susceptibility measurement was about 86K. All experiments were carried out at pressures in the lower lo-” Torr range. The sample was cleaved in-situ at 30K parallel to the a-6 plane immediately before starting the measurements. The sample could be cooled down to about 10K. Sample temperature could be measured with nominal accuracy of about
t
& Photon
energy
leV1
Fig. l(a). Total photoyield at T = 119K (0) and T = 50 K (0) as a function of photon energy. The inset (il) shows the threshold region enlarged. Inset (i2) shows a model for total yield threshold photoelectron spectroscopy.
Vol. 91, No. 8
THRESHOLD
PHOTOEMISSION
FROM HIGH-C-SUPERCONDUCTORS
657
1lOK 99 97 95 93 91 89 87 85 83 81 79 75 73 70 59 50 33
4.00
4.25
4.50
Photon
4.75
5.00
energy
5.25
[eVl 40
Fig. l(b). Difference curves of the total photoyield for different temperatures as obtained by subtracting a reference curve taken just above Tc from the curves taken at the lower temperatures. linear region which extrapolates to a threshold energy of 4.76 f O.O5eV, to first order independent of temperature. This value is in the range of work functions determined by other methods [6-81. The linear increase of the dZ/dE curve suggests metallic behaviour. The origin of emission intensity for energies which becomes visible at about 4eV is not clear (another Bi(2 2 12)-sample showed an even larger intensity in this region). We attribute this intensity to the presence of cleavage surfaces with different chemical composition or to the presence of more than one crystallographic phases. For photon energy below Ethr the intensity exhibits a maximum value near 70 K which is borne out more clearly when subtracting a total yield curve taken above Tc as a reference curve from the data taken below Tc. Figure l(b) shows this difference data. We notice a building up of an intensity hump of about 200meV width at photon energies smaller than q!~,extending towards lower energies when the temperature decreases, but vanishing at the lowest temperature at which we have measured (33 K). Figures 2(a-c) show the dependence of total photoyield on temperature [Z(T)lhv :urves] with photon energies ranging from 4 - 0.1 eV to 4 + 0.5eV. The most remarkable observation in
60
60
100 120
T rK1 Fig. 2. Temperature dependence of the total photoyield at different photon energies (dots): hv = 4.75 eV (a), 4.85 eV (b) and 4.95 eV (c). The intensity scale is the same for the three figures. The line in (c) is the temperature dependence of the susceptibility, measured for the same sample, but the temperature scaled to have the sharp drop observed in the photoyield at 95K to coincide with the drop in susceptibility (86 K).
0
Photon
energy
teV1
Fig. 3. Energy dependence of the absolute temperature-induced change of total photoyield [AZ(hv) = hWK&)
-
z33K(hd1*
658
THRESHOLD
PHOTOEMISSION
FROM HIGH-Tc-SUPERCONDUCTORS
Vol. 91, No. 8
interpreted in this way. The amplitude of the hump in the vicinity of about 200meV above EF increases 3 I upon cooling below Tc before it vanishes at the lowest 2 measured temperature (33 K). Its width is larger than kBTc. This might be expected since the I(hv) curves h 5 are integrated intensities between E, and E, - hv. e” Furthermore, the peak shifts towards lower energy x0 E upon cooling as to be expected from the model. Figure 2(c) suggests to assume that the drop in photoyield is related to superconductivity since the Fig. 4. Schematic description of the density of states shapes of the drop in photoyield and of the at different temperatures (T > T, > q > 5 > q) for susceptibility curve are very similar. In order to a superconductor. The intensity of the total yield is explain the changes in photocurrent with temperaproportional to the area under the curve between E,, ture, we consider not only the existence of the and E,, - hv, corresponding to the proper temperature. singularities but also the momenta (+k, -k) of paired electrons. Since many physical properties of data taken at different temperatures is the strong high-Tc-superconductors show a behaviour characdecrease in intensity upon cooling below Tc for teristic to two-dimensionality within the CuOs planes hv = 4.95 eV [Fig. 2(c)]. Similar curves are obtained we expect that the paired electrons should move for photon energies in the range 4.87 < hv < 5SeV, largely confined to these planes. They are aligned but the total change depends on photon energy as perpendicular to the emission direction of the shown in Fig. 3. The absolute amplitude of the photoelectrons in our and other author’s photoemission experiments. Indeed, in VUV angle-resolved change in photoyield increases sharply and quasilinearly above threshold before reaching a plateau at photoemission data, the singularity below Tc is not about 5.2 < hv < 5.4eV, decreasing at higher photon observed in P-Y-direction for normal emission, but energies. The position of the steep decrease in curve for emission angle of 27” (max. at 30”) with respect to I(T) [see Fig. 2(c)] occurs at 97K. The solid line in the normal to the cleavage surface [9]. If the energy of Fig. 2(c) is the sample’s susceptibility curve with the the electrons in the surface normal direction is temperature axis scaled to align the drop in smaller than 4 (or hv cos Q < 4, where Q is the susceptibility (observed at N 86K) with the drop in internal angle with respect to the surface normal), photocurrent. they are not able to escape into the vacuum. The For photon energies smaller than the work calculated minimum photon energy for electrons to function, the photocurrent first decreases with escape into vacuum with internal angle o = 27” is temperature at high temperatures, followed by a 5.4eV for 4 = 4.8eV. This compares well with the peak near 70K [hv N 4.75eV, Fig. 2(a)]. The photon energy at which the total change in phototransition between these two regimes is gradual [see yield decreases (cf. Fig. 3) since at this energy broken Fig. 2(b)]. At hv N 4+<, where 0 < < < O.leV, the Cooper-pair electrons would fall into the photoelectron escape cone. We expect that the drop in current temperature dependence is more or less linear. should be of the order 2A/[E, - (hv - 4)] N 30%, We interpret the observations shown in Figs. l2(b) on the basis of the BCS model, which is shown which, considering the crudeness of the model DOS, schematically in Fig. 4. The measured photoyield is compares well with the maximum value of 50% proportional to the integral of the product of the observed at hv = 4.95 eV. These observations all give electron energy distribution and the DOS between E,, support to the assumption that the strong decrease of and E, - hv. Above T,, the Fermi-Dirac statistics photoyield which we observe for photon energies governs the energy distribution curve. Below Tc, the above 4 occurs because broken Cooper pairs do not electrons formed to Cooper pairs are causing the contribute to the photoyield at photon energies up to 0.5 eV above threshold. Since the susceptibility singularity of quasiparticles below EF which becomes broader with decreasing temperature since it has to diminishes in proportion to the number of Cooper accumulate more particles. The singularity above EF pairs, the temperature dependence of the photoyield is caused by unpaired electrons. Qualitatively, it is should follow the susceptibility curve in our model. clear that upon cooling below T, the quasi-particle The above-mentioned difference between Tc and the density above EF first increases, before it vanishes at temperature at which the drop in photoyield sets in might arise from the fact that the susceptibility very low temperatures because of the Fermi-Dirac statistics. Our data shown in Fig. l(b) can be measurement is a bulk method, whereas the informaT, >Tc>T, >T, >T,
u)
%
THRESHOLD
Vol. 91, No. 8
PHOTOEMISSION
FROM HIGH-Tc-SUPERCONDUCTORS
659
i.e. it reflects qualitatively the temperature dependence of the width of the energy gap A(T)/A(O). -z
4. CONCLUSIONS
2
5
e, m_ F:
-5
!
a ,a
Fig. 5. Contribution of uncorrelated electrons nl(T) (curve 1) and of electrons in Cooper pairs Q(T) (curve 2). Curve 3, (dashed) shows the derived temperature dependence of the energy gap A(T)/A(O). tion depth in our photoemission measurement is only 20-30 monolayers, corresponding to only 2-3 unit cells. Also, a temperature gradient between the Ptl 0 0 temperature sensor and the sample cannot be excluded. The changes with temperature of the maximum value of the hump above EF in Fig. l(b) corresponds approximately to the temperature dependence of the area under the singularity above EF, i.e. to that part of electrons [rri(T)] transferred from the region of the energy gap to energies above EF + A (which do not build the Cooper pairs) (Fig. 5, curve 1). The electron pairs (bosons) from the singularity below EF are apparently not contributing to the photocurrent for photon energy slightly larger than the work function. The changes of the minimum value in Fig. l(b) also give information about the number of electrons [nz( T), cf. Fig. 5, curve 21 escaped from the region of the energy gap which are coupled to Cooper pairs. Our data show - in agreement with what is to be expected - that nl( T) is much smaller than Q(T). Figure 5 shows q(T), nz(T), and q(T) +nz(T) (curve 3). If we assume that the Fermi surface has spherical symmetry, the number of electrons leaving the energy gap region can be calculated as q(T)
+n2(T)
In summary, we observe that the total photoyield in threshold photoemission for energies some 0.1 eV larger than the photothreshold decreases by up to 50% upon cooling below TC similar as the zero-field cooled susceptibility. It is therefore suggested that the decrease occurs in proportion to the concentration of Cooper pairs which, when broken-up by the photon, apparently do not contribute to the photocurrent because of their large momentum in the Cu02 planes. Accordingly, this method is besides the MeiDner effect a new tool for determining the superconducting state. Furthermore, we obtain for the first time evidence in photoemission for the existence of the quasiparticle peak above EF and for its temperature dependence. The data demonstrate that the relatively simple technique of threshold photoemission is a powerful tool for studying HTC superconductivity. Acknowledgements - We thank F.U. Hillebrecht for his help in the initial stages of the experiment and the technical staff members of the Institut fur Angewandte Physik, Heinrich-Heine-Universitat Dusseldorf, for their excellent assistance. We thank H. Frank, 2. Phys. Inst. RWTH Aachen, for performing the susceptibility measurements. REFERENCES 1.
6.
= 0
0
7.
E,+A
&?dE exp [(E - EF)/~T] + 1
X
8.
EF-A ,312~v2 =
8fin
h3F
A(T),
9.
R.P. Huebener, C.C. Tsuei & D.M. Newns, Phys. Bl.50, 163 (1994), C.G. Olson et al., Science 245, 731 (1989); J.M. Imer et al., Phys. Rev. Lett. 62, 336 (1989); R. Manzke et al., Europhys. Left. 9, 477 (1989); D.S. Dessau et al., Phys. Rev. B45, No. 9, 5095 (1992). R.H. Fowler, Phys. Rev. 38, 45 (1931). D. van der Mare1 & G. Rietveld, Phys. Rev. Lett. 69, 2575 (1992). G. Rietveld, N.Y. Chen & D. van der Marel, Phys. Rev. Left. 69, 2578 (1992). K. Shigematsu, H. Takei, J. Higashi, K. Hoshino & H. Aono, J. Cryst. Growth 100, 661 (1990). F. Minami, T. Kimura & S. Takekawa, Phys. Rev. B39, 4788 (1989). R. Claessen, R. Manzke, H. Carstensen, B. Burandt, T. Buslaps, M. Skibowski & J. Fink, Phys. Rev. B39, 73 16 (1989). R. Biittner, N. Schroeder, E. Dietz, U. Gerhart, W. Assmus & J. Kowalewski, Phys. Rev. B41, 8679 (1990). M. Metzner, Dissertation, Heinrich-HeineUniversitat Dusseldorf, Germany (1993).