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Spin gap effects on the c-axis and in-plane charge dynamics of high-Tc cuprates
PHYSICA ELSEVIER
Physica C 282-287 (1997) 12-18
Spin gap effects on the c-axis and in-plane charge dynamics of high-To cuprates S. Uchida Department of Superconductivity and Department of Applied Physics, University of Tokyo Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan The spin gap in the normal state is a phenomenon characteristic of high-Te cuprates in the underdoped regime. The spin gap is apparently connected to the normal-state pseudogap seen in the c-axis optical conductivity and photoemission spectra, and the fundamental features of the cuprates, two-dimensional charge dynamics and reduced Drude spectral weight, result from the spin gap.
1. I N T R O D U C T I O N It is an anomalous and unique phenomenon of high-To cuprates that a gap opens in the spin excitation spectrum at temperature Ta well above Tc [1,2]. It is also suggested that the decreasing magnetic susceptibility, which starts up at temperature To higher than Ta, might be connected to a spin gap (formation of spin singlets). The spin gap is a universal property of the underdoped high-Tc cuprates, not restricted to bilayer systems. Recently, it has been confirmed by NMR for a single-layer La2_xSr=CuO4 (La214) [3] and a tri-layer Hg-based cuprate [4]. Closely connected to the spin gap, a pseudogap opens below temperature T* in the angleresolved-photoemission (ARPES) [5] and in the c-axis optical conductivity spectrum (at(w)) [6]. The pseudogap deepens with lowering tempera. ture and evolves, without changing its width, into the superconducting (SC) gap below To. The difference between pseudogap and SC gap is that the depressed spectral weight goes to a 6-function at w = 0 in a~(w), giving rise to the so-called Josephson plasma [7], or forms a pile-up peak near the gap edge in ARPES below To, whereas it spreads over a wide energy range in the normal state. It is found that associated with the pseudogap (or spin gap) the in-plane resistivity deviates from the T-linear behavior [8] and the T coefficient of the c-axis resistivity changes sign, showing semiconducting behavior at low temperatures [9]. The 092124534/97/$17.00 © Elsevier Science B.V. All fights reserved PII S0921-4534(97)00195-0
pseudogap and the anomalies in resistivity start at T* which is near To and become substantial at T ,'., Ta. In this paper, I review and summarize the effects of 'spin gap' on the c-axis and in-plane charge dynamics of the underdoped cuprates. It is illustrated based on the Zn-doping experiments that the fundamental features of the electronic state of the high-Te cuprates result from the spin gap in the normal state. 400
300
200
Ts
~B~ )
100
0
0.1
0.2
0.3
X
Figure 1. Doping dependences of various temperature (energy) scales of high-Tc cuprates. TMF is defined by 2Ao -- 4kBTMF with Ao being the maximum of the d-wave SC gap.
S. Uchida/Physica C 282-287 (1997) 12-18
2. S P I N G A P E F F E C T S O N C H A R G E DYNAMICS
The a¢(w) and ARPES experiments so far performed display that the width of the pseudogap and SC gap is almost independent of doping at least in the underdoped regime [10, 11]. The ae(w) results suggest that the gap width is even material independent (2A0 ~ 50-60 meV, A0 is the maximum of the d-wave gap). This is in contrast to the strongly doping dependent characteristic temperatures T* (or To and Ts) and Te (Fig. 1), indicating that T* and Te do not represent any energy scale, and T* is not directly connected to the formation of preformed pairs (or the development of the amplitude of the SC order parameter). 2.1. o-axis dynamics The electroniccontribution to at(w) in the normal state of the underdoped cuprates is nearly coindependent and does not form a Drude peak at co = 0, indicating incoherent nature of charge dynamics along the o-axis [12]. A pseudogap develops below 7"* with ac depressed below ~ 50 m e V with lowering temperature. The semiconducting T dependence of the c-axis resistivityPc is associated with the deepening of the pseudogap (Fig. 2). The connection to the spin gap is discussed in terms of interlayercharge hopping assistedby the spin fluctuations [13]or by spinon-holon recombination [14]. In this regard, the spin gap presents a barrier to c-axis charge transport[15]. A basic question that arises is whether Pc diverges or not if the normal state of the high-To cuprates lasts to T = 0 or whether ac(co) is suppressed to zero without opening an SC gap. This question will be addressed by the Zn doping experiment. 2.2. I n - p l a n e d y n a m i c s It should be emphasized that the pseudogap appears only in at(co), while the in-plane spectrum at(co) is dominated by a Drude peak at w = 0. The effect of spin gap or a change in the in-plane charge dynamics at T* is seen in the change of the T dependence of the in-plane resistivity (Pab). Pab is linear in T above T* and decreases more steeply (following Pab ~" :I~ with
8/
13
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i
el-
,
i
,
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,
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to (cm-') Figure 2. Temperature dependences of the inplane and c-axis resistivity for Y123 with various dopings. In-plane and c-axis optical conductivity spectra of an underdoped cuprate at various temperatures are shown in the lower panels.
S. Uchida/Physica C 282-287 (1997) 12-18
14
N 2.5) below 7"* [8]. This change is universal for any underdoped cuprate and for any doping. As displayed in Fig. 3, all the Pab vs T characteristics for underdoped bilayer YBa~CuaOr_y (Y123) and trilayer HgBaaCa2CuaOs+u [16] fall into a single curve by scaling T / T * and Pab(T)/pab(T*). A single-layer system La214 also shows a good scaling when the residual resistivity component is subtracted from pab(T) [17]. The change in the T dependence of Pab at T* and the scaling shown in Fig. 3 suggest that the effect of the spin gap might be on the carrier scattering for the in-plane charge dynamics. Actually, the development of a pseudogap in ae(w) is correlated with a rapid narrowing of the Drude width in ae(~0) [10] (Fig. 2). A naive interpretation of this would be that the opening of the spin gap below T* leads to a reduction in the scattering rate ( l / r ) between charge carriers and spin fluctuations. It is anomalous that the same physical effect acts on the c-axis and in-plane charge transport in the opposite direction, which points to totally different charge dynamics between two directions. A consequence of the reduction in 1/T is that the Drude component in ae (w) is isolated from the so-called mid-IR band. Its implication is a reduction of the Drude (or coherent) spectral weight which is linked with the low carrier density as will also be illustrated by the Zn doping experiment.
,
!
HgBa2Ca2Cu3Os+y~~
atoms
Zn substituted for Cu sites in the CuO2 planes greatly reduce the SC critical temperature and act as a potential scatterer for the in-plane charge transport. It is shown that a superconductor-insulator (SI) transition takes place in the underdoped regime, when the residual sheet resistance induced by the Zn doping reaches a value near the universal twodimensional resistance h/4e 2 [18]. Reflecting the totally different charge dynamics in the two directions, the Zn doping has distinct effect on the charge dynamics, from which one can get deeper insight into the electronic state of highTe cuprates.
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Tff* Figure 3. The scaling of the T dependence of the in-plane resistivity for various underdoped cuprates.
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Temperature (K) Figure 4. Temperature dependence of Pc for Zndoped YBa~CuaOe.ea. The inset shows the lowtemperature part of Pc and Pab for z = 0.03.
S. Uchida/Physica C 282-287 (1997) 12-18
3.1. o-axis d y n - m i c s The T dependence of Pc is shown in Fig.4 for a typical underdoped cuprate YBva (Cut -z Znz)3 O0.o3 with various Zn contents up to z = 0.03. z -- 0.03 is close to the SI transition with Tc lower than 1K. As shown also in the inset, Pc continues to increase in the normal state when Tc is suppressed by Zn doping. For z = 0.03 the semlconducting Pc persists down to T=0.SK, the lowest temperature of the present experiment, and tends to diverge toward T = 0 whereas P-b remains finite (metallic). Such contrasting behavior has also been observed for BiaSr2CuOs+~ under sufficiently magnetic fields for Tc suppression [19,20]. One may claim that, as the Zn doping has a radical effect on To, it would have seriously altered the c-axis dynamics and the divergent pc might be a consequence of this serious change. Certaintly, Zn or other entities that introduce disorder into the CuO2 planes affect the low-energy 10(~
.
,
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.
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co (cm "1) Figure 5. a t ( w ) spectra with phonons removed for Zn-free and Zn-doped Y123 and La214 crystals.
15
in-plane dynamics [21]. However, from the study of the ae(w)-spectrum it turns out that Zn does not change the basic pseudogap feature in the low-energy region. The Zn doping effect on a t ( w ) is shown in Fig. 5 for underdoped Y123 and La214. The onset temperature 7+" for pseudogap is independent of Zn content [22], and the conductivity in the lowenergy region (below N 20meV) continues to be uniformly suppressed with decreasing temperature in the normal state (and even in the SC state). Zn induced changes in ae(w) are visible only in the high-energy gap region. This result gives a credit to the result that the divergent pc is an intrinsic property, and the contrasting behavior from the in-plane dynamics points toward the charge confinement [23]. In-plane d y n a m i c s A primary effect of Zn doping on the in-plane dynamics is to produce a residual dc resistivity as an elastic potential scatterer. It is found that the residual resistivity P0 is extremely large particularly in the underdoped regime, amounting to 100t~l cm at 1% Zn [18]. This value is the largest among so-far observed residual resistivity in any type of metals. In the case of Zn impurity in the CuO2 planes, the s-wave (l = 0) scattering is expected to dominate P0, since Zn (Zn 2+) has closed shell of the d-orbitals and the relevant conduction band of the CuO2 planes is non-degenerate. Then, the two-dimensional residual resistivity is given as po = 4(h/e2)(n+/n)sin25o, where ni is the impurity concentration, n the carrier density, and 50 is the s-wave phase shift [24]. The extremely large Po observed for underdoped compounds can only be fitted by putting n = x (x ; the doped hole density), the lowest carrier density expected from theories, and 5o -- r / 2 corresponding to the unitariry-limit scattering. It should be noted that, as long as 5o(= r / 2 ) is unchanged with increasing dopant concentration, Po is dependent only on the carrier density n. The experimental fact that Po for overdoped La214 (x : 0.30) is fitted with 50 : 7r/2 and n : 1 - x which is expected in a Fermi liquid state gives evidence that ~o remains to be 7r/2 all over the doping range 3.2.
S. Uchida/Physica C 282-287 (1997) 12-18
16
[18]. Therefore, one can estimate the evolution of the carrier density n with doping from the doping dependence of p0 without ambiguity from the unknown x dependence of the effective mass rn* - - the conductivity or Drude spectral weight is proportional to n/m*. The experimental results for La214 and Y123 show that P0 rapidly decreases as the doping proceeds to the optical and overdoped regions, which is interpreted as a crossover from n = x in the underdoped regime to n = 1 - x in the overdoped regime [18]. In Fig. 6 is also plotted the Drude spectral weight No which is estimated by isolating the Drude component from the mid-IR band in ~rc(co). ND evolves with x just in harmony with the evolution of n in the underdoped regime. Note that ND amounts only 20% or less of the total spectral weight (Neff), Drude + mid-IR, which is transferred from the high-energy charge- transfer excitations upon doping and shows a distinct dependence. From these results it is concluded that the spin gap in the underdoped regime radically suppresses the Drude component (or coherent part) of the in-plane optical conductivity which is linked to the low carrier density n --- z involved in the in-plane charge transport. 4. A D D I T I O N A L
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.
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Figure 6. Variation of the carrier density, estimated from the Zn-induced residual resistivity, with doping. Also plotted the Drude spectral weight separated out from t h e mid-IR band in Gab(CO). I
I
YBa2Cu307_y
600
ISSUES
4.1. Effect o n t h e H a l l coefficient The deviation from the T-linearity in pab(T) correlates with the T dependence of the Hall coefficient (RH) [8]. While RH ,,, lIT for the optimally doped compound, a deviation from the 1/T dependence is seen below T* for the underdoped compounds and RH shows a peak as T is reduced. The T dependent RH in the high-Tc cuprates is not fully understood even at present. Anderson proposed a novel explanation by introducing another scattering time TH [25], assumed to be relevant to the Hall effect and directly connected to the Hall angle by cot0H = 1/cocT/a (coc: cyclotron frequency). The experimental result for the optimally doped Y123 indicates that rH 1 ~,, T 2 [24]. It is found that the T dependence of TH is basically unchanged in the underdoped regime and no significant feature is seen in 7~ (T) at T* (Fig.7). This implies that 7~ ~,, T -~ irrespective of the
1.0
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.'*.
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---6.85\~ z 400
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B=5 Tesla j//ab B//c i
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i
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i
3
=
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6
I
i
9
T 2 (I04K 2) Figure 7. Hall angle plotted a s a function of T 2 for Y123 with various dopings.
S. Uchida/Physica C 282-287 (1997) 12-18
presence or otherwise of the spin gap and that the characteristic change of RH at T* is induced by that in the T dependence of T, since RH N TH/T. However, the implication of the 'transverse' scattering time TH is still an open question. 4.2. C h a r g e t r a n s p o r t in Y B a 2 C u 4 O s YBa2Cu4Os (Y124) is an intrinsically underdoped compound. In fact, the in-plane resistivity (Pa) changes its T dependence at 7"* in a similar manner to that observed for other cuprates [26], and at(w) shows a feature of pseudogap [27]. Recently, it has turned out that the T dependence of Pc is quite exceptional [28,29]. In contrast to other systems the semiconducting behavior of Pc is not seen, but Pc steeply decreases below ~ T*. In this respect, the pseudogap feature observed in a¢(w) does not correlate with pc(T). Moreover, Zn doping into Y124 appears to destroy the pseudogap in ae(w) [30]. These exceptional behaviors may be understood by dominant contribution from the Cu-O chains in Y124. The structure of the double Cu-O chains is almost perfect with negligible oxygen deficiency, and they are highly conductive along the chain direction. It appears that the chains might be also conductive in the c-direction, so that the chain contribution to Pc would have dominated, since the plane contribution should have been suppressed owing to the spin gap. 5. S U M M A R Y One of the most anomalous properties of highTe cuprates is the presence of a gap in the spin excitations with no gap in the charge excitations. In the charge excitation spectrum the corresponding feature appears as a pseudogap only in the c-axis direction, and the pseudogap is responsible for the divergent c-axis dc resistivity toward T=0. On the other hand, the in-plane spectrum is dominated by a Drude term. The spin gap effect is seen by a rapid narrowing of the Drude peak or a rapid enhancement of the Drude peak height below a characteristic temperature T*, in correspondence with the faster decrease in the in-plane resistivity. As a consequence, the Drude weight is
17
isolated from the dominant mid-IR band, and the reduced Drude weight is linked to the low cartier density involved in the in-plane charge transport. These results are generic to the underdoped cuprates and demonstrate that the fundamental features of high-To cuprates, two-dimensionality and low carrier density, result from the spin gap. ACKNOWLEDGEMENTS I thank N. Nagaosa, T. Ito, K. Takenaka, Y. Fukuzumi and K. Tamasaku for discussions. The work was supported by Grants for Priority Area and for COE Research from Mombusho, by a NEDO Grant for International Joint Research, and by Nissan Science Foundation. REFERENCES 1. H. Yasuoka, T. Imal and T. Shimizu, in Strong Correlation and Superconductivity, H. Fukuyama, S. Maekawa and A. P. Malozemoff (eds.) Springer, 1989, p.254. 2. J. Rossat-Mignod et aL, Physica C 185-189 (1991) 86. 3. H. Yasuoka, this conference. 4. M . - H . Julien et aL, Phys. Rev. Lett. 76 (1996) 4238. 5. A.G. Loeser, D. S. Dessau and Z. -X. Shen, Physica C263 (1996) 208. 6. C.C. Homes et aL, Phys. Rev. Lett. 71 (1993) 1645. 7. K. Tamasaku, Y. Nakamura and S. Uchida, Phys. Rev. Lett. 6 9 (1992) 1455. 8. T. Ito, K. Takenaka and S. Uchida, Phys. Rev. Lett. ?0 (1993) 3995. 9. K. Takenaka et aL, Phys. Rev. BS0 (1994) 6534. 10. S. Uchida et aL, J. Low Temp. Phys.105 (1996) 723. 11. H. Ding et aL, Nature 382 (1996) 51. 12. K. Tamasaku et aL, Phys. Rev. Lett. 7'2 (1994) 3088. 13. A. G. Rojo and K. Levin, Phys. Rev. B48 (1993) 16861. 14. N. Nagaosa, Phys. Rev. B52 (1995) 10561. 15. N. P. Ong, Science 273 (1996) 32. 16. A. Carrington et aL, Physica C234 (1994) 1.
S. Uchida/Physica C 282-287 (1997) 12-18
18
17. Y. Nakamura and S. Uchida, Phys. Rev. B47 (1993) 8369. 18. Y. Fukuzumi et aL, Phys. Rev. Lett. 76
(1996) 19. Y. Ando et aL, Phys. Rev. Lett. 77 (1996) 2065. 20. G. S. Boebinger et aL, Phys. Rev. Lett. 77 (1996) 5417, for the underdoped La214 both Pab and Pc are divergent when SC is suppressed by magnetic fields. This exceptional behavior may be understood as fluctuation effect of the stripe order discovered by J. M. Tranquada et aL, Nature 375 (1995) 561. 21. D. N. Basov et aL, Phys. Rev. B49 (1994) 12165. 22. K. Mizuhashi et aL, Phys. Rev. B52 R3884 (1995). 23. P. W. Anderson, Phys. Rev. Lett. 67 (1991) 3844. 24. T. P~ Chien, Z. Z. Wang and N. P. Ong, Phys. Rev. Lett. 67 (1991) 2088. 25. P. W. Anderson, Phys. Rev. Left. 67 (1991) 2092. 26. B. Bucher et aL, Phys. Rev. Lett. 70 (1993) 2012. 27. D. N. Basov et aL, Phys. Rev. B50 (1994) 3511. 28. B. Bucher et aL, a report at theMeeting of the American Physical Society, San Jose, 1995. 29. J. -S. Zhou et aL, Phys. Rev. Lett. 77 (1996) 4253. 30. D. N. Basov et aL, Phys. Rev. Lett. 77' (1996) 4090.
Physica C 282-287 (1997) 12-18
Spin gap effects on the c-axis and in-plane charge dynamics of high-To cuprates S. Uchida Department of Superconductivity and Department of Applied Physics, University of Tokyo Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan The spin gap in the normal state is a phenomenon characteristic of high-Te cuprates in the underdoped regime. The spin gap is apparently connected to the normal-state pseudogap seen in the c-axis optical conductivity and photoemission spectra, and the fundamental features of the cuprates, two-dimensional charge dynamics and reduced Drude spectral weight, result from the spin gap.
1. I N T R O D U C T I O N It is an anomalous and unique phenomenon of high-To cuprates that a gap opens in the spin excitation spectrum at temperature Ta well above Tc [1,2]. It is also suggested that the decreasing magnetic susceptibility, which starts up at temperature To higher than Ta, might be connected to a spin gap (formation of spin singlets). The spin gap is a universal property of the underdoped high-Tc cuprates, not restricted to bilayer systems. Recently, it has been confirmed by NMR for a single-layer La2_xSr=CuO4 (La214) [3] and a tri-layer Hg-based cuprate [4]. Closely connected to the spin gap, a pseudogap opens below temperature T* in the angleresolved-photoemission (ARPES) [5] and in the c-axis optical conductivity spectrum (at(w)) [6]. The pseudogap deepens with lowering tempera. ture and evolves, without changing its width, into the superconducting (SC) gap below To. The difference between pseudogap and SC gap is that the depressed spectral weight goes to a 6-function at w = 0 in a~(w), giving rise to the so-called Josephson plasma [7], or forms a pile-up peak near the gap edge in ARPES below To, whereas it spreads over a wide energy range in the normal state. It is found that associated with the pseudogap (or spin gap) the in-plane resistivity deviates from the T-linear behavior [8] and the T coefficient of the c-axis resistivity changes sign, showing semiconducting behavior at low temperatures [9]. The 092124534/97/$17.00 © Elsevier Science B.V. All fights reserved PII S0921-4534(97)00195-0
pseudogap and the anomalies in resistivity start at T* which is near To and become substantial at T ,'., Ta. In this paper, I review and summarize the effects of 'spin gap' on the c-axis and in-plane charge dynamics of the underdoped cuprates. It is illustrated based on the Zn-doping experiments that the fundamental features of the electronic state of the high-Te cuprates result from the spin gap in the normal state. 400
300
200
Ts
~B~ )
100
0
0.1
0.2
0.3
X
Figure 1. Doping dependences of various temperature (energy) scales of high-Tc cuprates. TMF is defined by 2Ao -- 4kBTMF with Ao being the maximum of the d-wave SC gap.
S. Uchida/Physica C 282-287 (1997) 12-18
2. S P I N G A P E F F E C T S O N C H A R G E DYNAMICS
The a¢(w) and ARPES experiments so far performed display that the width of the pseudogap and SC gap is almost independent of doping at least in the underdoped regime [10, 11]. The ae(w) results suggest that the gap width is even material independent (2A0 ~ 50-60 meV, A0 is the maximum of the d-wave gap). This is in contrast to the strongly doping dependent characteristic temperatures T* (or To and Ts) and Te (Fig. 1), indicating that T* and Te do not represent any energy scale, and T* is not directly connected to the formation of preformed pairs (or the development of the amplitude of the SC order parameter). 2.1. o-axis dynamics The electroniccontribution to at(w) in the normal state of the underdoped cuprates is nearly coindependent and does not form a Drude peak at co = 0, indicating incoherent nature of charge dynamics along the o-axis [12]. A pseudogap develops below 7"* with ac depressed below ~ 50 m e V with lowering temperature. The semiconducting T dependence of the c-axis resistivityPc is associated with the deepening of the pseudogap (Fig. 2). The connection to the spin gap is discussed in terms of interlayercharge hopping assistedby the spin fluctuations [13]or by spinon-holon recombination [14]. In this regard, the spin gap presents a barrier to c-axis charge transport[15]. A basic question that arises is whether Pc diverges or not if the normal state of the high-To cuprates lasts to T = 0 or whether ac(co) is suppressed to zero without opening an SC gap. This question will be addressed by the Zn doping experiment. 2.2. I n - p l a n e d y n a m i c s It should be emphasized that the pseudogap appears only in at(co), while the in-plane spectrum at(co) is dominated by a Drude peak at w = 0. The effect of spin gap or a change in the in-plane charge dynamics at T* is seen in the change of the T dependence of the in-plane resistivity (Pab). Pab is linear in T above T* and decreases more steeply (following Pab ~" :I~ with
8/
13
,
i
el-
,
i
,
6.6a \ 6.75
.S_. T
"-'E° 8 o
• I;
=
o
Olo.
-
. 6.63 !\ 6.75 \ : \6.83 \\
4
0 0[ r
,
(oo)
6
0
i
/ ¢I
100
~ i
I
200 T
T~Tc ~ 2.4T~7 /
,
I
300 (K)
400
_ . ~
. ' 0%
,ooo
to (cm-') Figure 2. Temperature dependences of the inplane and c-axis resistivity for Y123 with various dopings. In-plane and c-axis optical conductivity spectra of an underdoped cuprate at various temperatures are shown in the lower panels.
S. Uchida/Physica C 282-287 (1997) 12-18
14
N 2.5) below 7"* [8]. This change is universal for any underdoped cuprate and for any doping. As displayed in Fig. 3, all the Pab vs T characteristics for underdoped bilayer YBa~CuaOr_y (Y123) and trilayer HgBaaCa2CuaOs+u [16] fall into a single curve by scaling T / T * and Pab(T)/pab(T*). A single-layer system La214 also shows a good scaling when the residual resistivity component is subtracted from pab(T) [17]. The change in the T dependence of Pab at T* and the scaling shown in Fig. 3 suggest that the effect of the spin gap might be on the carrier scattering for the in-plane charge dynamics. Actually, the development of a pseudogap in ae(w) is correlated with a rapid narrowing of the Drude width in ae(~0) [10] (Fig. 2). A naive interpretation of this would be that the opening of the spin gap below T* leads to a reduction in the scattering rate ( l / r ) between charge carriers and spin fluctuations. It is anomalous that the same physical effect acts on the c-axis and in-plane charge transport in the opposite direction, which points to totally different charge dynamics between two directions. A consequence of the reduction in 1/T is that the Drude component in ae (w) is isolated from the so-called mid-IR band. Its implication is a reduction of the Drude (or coherent) spectral weight which is linked with the low carrier density as will also be illustrated by the Zn doping experiment.
,
!
HgBa2Ca2Cu3Os+y~~
atoms
Zn substituted for Cu sites in the CuO2 planes greatly reduce the SC critical temperature and act as a potential scatterer for the in-plane charge transport. It is shown that a superconductor-insulator (SI) transition takes place in the underdoped regime, when the residual sheet resistance induced by the Zn doping reaches a value near the universal twodimensional resistance h/4e 2 [18]. Reflecting the totally different charge dynamics in the two directions, the Zn doping has distinct effect on the charge dynamics, from which one can get deeper insight into the electronic state of highTe cuprates.
)j/
_xSrxCoO,
"0.10~/
x.--.o.12 O.
E 1
///
O.
7-y~6.45
///
i //I ¢ i i
-6.68
...6.78 -6.85
• J J';
,
.,:
i
,
1
Tff* Figure 3. The scaling of the T dependence of the in-plane resistivity for various underdoped cuprates.
0.60
1.0
, ~ z=0 02 ~ /"
"~0.4
. . . . . . . .
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0.8 " ,
°V 3. Z n D O P I N G E F F E C T S
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,
300
Temperature (K) Figure 4. Temperature dependence of Pc for Zndoped YBa~CuaOe.ea. The inset shows the lowtemperature part of Pc and Pab for z = 0.03.
S. Uchida/Physica C 282-287 (1997) 12-18
3.1. o-axis d y n - m i c s The T dependence of Pc is shown in Fig.4 for a typical underdoped cuprate YBva (Cut -z Znz)3 O0.o3 with various Zn contents up to z = 0.03. z -- 0.03 is close to the SI transition with Tc lower than 1K. As shown also in the inset, Pc continues to increase in the normal state when Tc is suppressed by Zn doping. For z = 0.03 the semlconducting Pc persists down to T=0.SK, the lowest temperature of the present experiment, and tends to diverge toward T = 0 whereas P-b remains finite (metallic). Such contrasting behavior has also been observed for BiaSr2CuOs+~ under sufficiently magnetic fields for Tc suppression [19,20]. One may claim that, as the Zn doping has a radical effect on To, it would have seriously altered the c-axis dynamics and the divergent pc might be a consequence of this serious change. Certaintly, Zn or other entities that introduce disorder into the CuO2 planes affect the low-energy 10(~
.
,
. . . .
.
,
YBa (Cut. h0+75
"7'
3 "+' "
I
"
/
.."
,,."f
,~d
~
(r,=+0K)
tv;::+o S
I-
+.£Y
"---"~"~I ~-"
I(
_ I ,
toK ,
I ,
Lal.ssSr0.1s(CUl.]~:)4
0
200
,
+ I ,
z=O.O05
400
"
600
co (cm "1) Figure 5. a t ( w ) spectra with phonons removed for Zn-free and Zn-doped Y123 and La214 crystals.
15
in-plane dynamics [21]. However, from the study of the ae(w)-spectrum it turns out that Zn does not change the basic pseudogap feature in the low-energy region. The Zn doping effect on a t ( w ) is shown in Fig. 5 for underdoped Y123 and La214. The onset temperature 7+" for pseudogap is independent of Zn content [22], and the conductivity in the lowenergy region (below N 20meV) continues to be uniformly suppressed with decreasing temperature in the normal state (and even in the SC state). Zn induced changes in ae(w) are visible only in the high-energy gap region. This result gives a credit to the result that the divergent pc is an intrinsic property, and the contrasting behavior from the in-plane dynamics points toward the charge confinement [23]. In-plane d y n a m i c s A primary effect of Zn doping on the in-plane dynamics is to produce a residual dc resistivity as an elastic potential scatterer. It is found that the residual resistivity P0 is extremely large particularly in the underdoped regime, amounting to 100t~l cm at 1% Zn [18]. This value is the largest among so-far observed residual resistivity in any type of metals. In the case of Zn impurity in the CuO2 planes, the s-wave (l = 0) scattering is expected to dominate P0, since Zn (Zn 2+) has closed shell of the d-orbitals and the relevant conduction band of the CuO2 planes is non-degenerate. Then, the two-dimensional residual resistivity is given as po = 4(h/e2)(n+/n)sin25o, where ni is the impurity concentration, n the carrier density, and 50 is the s-wave phase shift [24]. The extremely large Po observed for underdoped compounds can only be fitted by putting n = x (x ; the doped hole density), the lowest carrier density expected from theories, and 5o -- r / 2 corresponding to the unitariry-limit scattering. It should be noted that, as long as 5o(= r / 2 ) is unchanged with increasing dopant concentration, Po is dependent only on the carrier density n. The experimental fact that Po for overdoped La214 (x : 0.30) is fitted with 50 : 7r/2 and n : 1 - x which is expected in a Fermi liquid state gives evidence that ~o remains to be 7r/2 all over the doping range 3.2.
S. Uchida/Physica C 282-287 (1997) 12-18
16
[18]. Therefore, one can estimate the evolution of the carrier density n with doping from the doping dependence of p0 without ambiguity from the unknown x dependence of the effective mass rn* - - the conductivity or Drude spectral weight is proportional to n/m*. The experimental results for La214 and Y123 show that P0 rapidly decreases as the doping proceeds to the optical and overdoped regions, which is interpreted as a crossover from n = x in the underdoped regime to n = 1 - x in the overdoped regime [18]. In Fig. 6 is also plotted the Drude spectral weight No which is estimated by isolating the Drude component from the mid-IR band in ~rc(co). ND evolves with x just in harmony with the evolution of n in the underdoped regime. Note that ND amounts only 20% or less of the total spectral weight (Neff), Drude + mid-IR, which is transferred from the high-energy charge- transfer excitations upon doping and shows a distinct dependence. From these results it is concluded that the spin gap in the underdoped regime radically suppresses the Drude component (or coherent part) of the in-plane optical conductivity which is linked to the low carrier density n --- z involved in the in-plane charge transport. 4. A D D I T I O N A L
1.0 "'--./1=1-x 0.8
°,=~
0 E}-.. "'Q-
La214
0.6 Y123[-]
0.5
f.= °~
Z
0.4 I'-] + - ~
rC+.--'fi=x
0.2 00
"#
t
,
l
I
.
I
I
I
l
I
t
I
I
I
0
0.1 0.2 0.3 Doped Hole Density x
Figure 6. Variation of the carrier density, estimated from the Zn-induced residual resistivity, with doping. Also plotted the Drude spectral weight separated out from t h e mid-IR band in Gab(CO). I
I
YBa2Cu307_y
600
ISSUES
4.1. Effect o n t h e H a l l coefficient The deviation from the T-linearity in pab(T) correlates with the T dependence of the Hall coefficient (RH) [8]. While RH ,,, lIT for the optimally doped compound, a deviation from the 1/T dependence is seen below T* for the underdoped compounds and RH shows a peak as T is reduced. The T dependent RH in the high-Tc cuprates is not fully understood even at present. Anderson proposed a novel explanation by introducing another scattering time TH [25], assumed to be relevant to the Hall effect and directly connected to the Hall angle by cot0H = 1/cocT/a (coc: cyclotron frequency). The experimental result for the optimally doped Y123 indicates that rH 1 ~,, T 2 [24]. It is found that the T dependence of TH is basically unchanged in the underdoped regime and no significant feature is seen in 7~ (T) at T* (Fig.7). This implies that 7~ ~,, T -~ irrespective of the
1.0
7-y---6.90~
.'*.
•
---6.85\~ z 400
~"6"58 . ~ . . ~" .~,'." ,~i .'" ..""T _
CD
•
O ¢.)
.. I°e
~,.°"
,.-."
,,-
..-......-
200
B=5 Tesla j//ab B//c i
0
i
|
i
3
=
t
6
I
i
9
T 2 (I04K 2) Figure 7. Hall angle plotted a s a function of T 2 for Y123 with various dopings.
S. Uchida/Physica C 282-287 (1997) 12-18
presence or otherwise of the spin gap and that the characteristic change of RH at T* is induced by that in the T dependence of T, since RH N TH/T. However, the implication of the 'transverse' scattering time TH is still an open question. 4.2. C h a r g e t r a n s p o r t in Y B a 2 C u 4 O s YBa2Cu4Os (Y124) is an intrinsically underdoped compound. In fact, the in-plane resistivity (Pa) changes its T dependence at 7"* in a similar manner to that observed for other cuprates [26], and at(w) shows a feature of pseudogap [27]. Recently, it has turned out that the T dependence of Pc is quite exceptional [28,29]. In contrast to other systems the semiconducting behavior of Pc is not seen, but Pc steeply decreases below ~ T*. In this respect, the pseudogap feature observed in a¢(w) does not correlate with pc(T). Moreover, Zn doping into Y124 appears to destroy the pseudogap in ae(w) [30]. These exceptional behaviors may be understood by dominant contribution from the Cu-O chains in Y124. The structure of the double Cu-O chains is almost perfect with negligible oxygen deficiency, and they are highly conductive along the chain direction. It appears that the chains might be also conductive in the c-direction, so that the chain contribution to Pc would have dominated, since the plane contribution should have been suppressed owing to the spin gap. 5. S U M M A R Y One of the most anomalous properties of highTe cuprates is the presence of a gap in the spin excitations with no gap in the charge excitations. In the charge excitation spectrum the corresponding feature appears as a pseudogap only in the c-axis direction, and the pseudogap is responsible for the divergent c-axis dc resistivity toward T=0. On the other hand, the in-plane spectrum is dominated by a Drude term. The spin gap effect is seen by a rapid narrowing of the Drude peak or a rapid enhancement of the Drude peak height below a characteristic temperature T*, in correspondence with the faster decrease in the in-plane resistivity. As a consequence, the Drude weight is
17
isolated from the dominant mid-IR band, and the reduced Drude weight is linked to the low cartier density involved in the in-plane charge transport. These results are generic to the underdoped cuprates and demonstrate that the fundamental features of high-To cuprates, two-dimensionality and low carrier density, result from the spin gap. ACKNOWLEDGEMENTS I thank N. Nagaosa, T. Ito, K. Takenaka, Y. Fukuzumi and K. Tamasaku for discussions. The work was supported by Grants for Priority Area and for COE Research from Mombusho, by a NEDO Grant for International Joint Research, and by Nissan Science Foundation. REFERENCES 1. H. Yasuoka, T. Imal and T. Shimizu, in Strong Correlation and Superconductivity, H. Fukuyama, S. Maekawa and A. P. Malozemoff (eds.) Springer, 1989, p.254. 2. J. Rossat-Mignod et aL, Physica C 185-189 (1991) 86. 3. H. Yasuoka, this conference. 4. M . - H . Julien et aL, Phys. Rev. Lett. 76 (1996) 4238. 5. A.G. Loeser, D. S. Dessau and Z. -X. Shen, Physica C263 (1996) 208. 6. C.C. Homes et aL, Phys. Rev. Lett. 71 (1993) 1645. 7. K. Tamasaku, Y. Nakamura and S. Uchida, Phys. Rev. Lett. 6 9 (1992) 1455. 8. T. Ito, K. Takenaka and S. Uchida, Phys. Rev. Lett. ?0 (1993) 3995. 9. K. Takenaka et aL, Phys. Rev. BS0 (1994) 6534. 10. S. Uchida et aL, J. Low Temp. Phys.105 (1996) 723. 11. H. Ding et aL, Nature 382 (1996) 51. 12. K. Tamasaku et aL, Phys. Rev. Lett. 7'2 (1994) 3088. 13. A. G. Rojo and K. Levin, Phys. Rev. B48 (1993) 16861. 14. N. Nagaosa, Phys. Rev. B52 (1995) 10561. 15. N. P. Ong, Science 273 (1996) 32. 16. A. Carrington et aL, Physica C234 (1994) 1.
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18
17. Y. Nakamura and S. Uchida, Phys. Rev. B47 (1993) 8369. 18. Y. Fukuzumi et aL, Phys. Rev. Lett. 76
(1996) 19. Y. Ando et aL, Phys. Rev. Lett. 77 (1996) 2065. 20. G. S. Boebinger et aL, Phys. Rev. Lett. 77 (1996) 5417, for the underdoped La214 both Pab and Pc are divergent when SC is suppressed by magnetic fields. This exceptional behavior may be understood as fluctuation effect of the stripe order discovered by J. M. Tranquada et aL, Nature 375 (1995) 561. 21. D. N. Basov et aL, Phys. Rev. B49 (1994) 12165. 22. K. Mizuhashi et aL, Phys. Rev. B52 R3884 (1995). 23. P. W. Anderson, Phys. Rev. Lett. 67 (1991) 3844. 24. T. P~ Chien, Z. Z. Wang and N. P. Ong, Phys. Rev. Lett. 67 (1991) 2088. 25. P. W. Anderson, Phys. Rev. Left. 67 (1991) 2092. 26. B. Bucher et aL, Phys. Rev. Lett. 70 (1993) 2012. 27. D. N. Basov et aL, Phys. Rev. B50 (1994) 3511. 28. B. Bucher et aL, a report at theMeeting of the American Physical Society, San Jose, 1995. 29. J. -S. Zhou et aL, Phys. Rev. Lett. 77 (1996) 4253. 30. D. N. Basov et aL, Phys. Rev. Lett. 77' (1996) 4090.