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Nernst effect in underdoped cuprates
Physica C 408–410 (2004) 326–327 www.elsevier.com/locate/physc
Nernst effect in underdoped cuprates K. Behnia *, C. Capan, R. Bel Laboratoire de Physique Quantique (CNRS), Ecole Superieure de Physique et Chimie Industrielles, ESPCI, 10 Rue Vauquelin, 75231 Paris, France
Abstract We performed a comparative study of Nernst effect and resistivity in underdoped cuprates. A finite Nernst signal coexists with a field-induced non-metallic resistivity and persists up to temperatures well above Tc . On the other hand, a similar study detects a finite Nernst signal in the normal-state of the conventional superconductor NbSe2 . However, the superconducting fluctuations remain the most plausible source of the anomalous Nernst signal in the underdoped cuprates. Ó 2004 Elsevier B.V. All rights reserved. PACS: 72.15.Jf; 74.25.Fy; 74.40.+k; 74.60.Ge
In the vortex-liquid state of a type II superconductor, movement of vortices induced by a thermal gradient leads to a transverse electric field and a finite Nernst coefficient appears in the mixed state [1]. In metals, on the other hand, the Nernst coefficient is believed to be small due to a fundamental reason put forward in a seminal work by Sondheimer in 1948 [2]. Recently, however, Xu [3] reported that in underdoped La2x Srx CuO4 a large residual signal persists in the normal-state and well above Tc . This observation has been confirmed in other families of cuprate superconductors [4,5]. Moreover, the normal-state Nernst signal is found to persist in presence of high magnetic fields for both overdoped [5] and underdoped [6] limits. Fig. 1 shows Nernst effect and resistivity as a function of temperature in a Bi2 Sr2 CuO6þd thin films. At zero field, the sample presents a broad resistive transition centered around 9 K. This transition is superposed on a slightly non-metallic behavior. The application of a moderate magnetic field (12 T) leads to a reduction of Tc and the emergence of a more pronounced ‘‘insulating’’ behavior. In presence of this magnetic field, the Nernst
*
Corresponding author. Tel.: +33-1-40-79-46-26; fax: +33-140-79-47-44. E-mail address: [email protected] (K. Behnia).
coefficient displays an unusual temperature dependence. First of all, a broad peak in the temperature dependence of Nernst signal commonly associated with the vortex movement still persists. A detailed study on this sample as well other underdoped samples [7] found that the amplitude of this peak increases initially with increasing magnetic field before starting to decrease at 10 T. But the peak does not shift to lower temperatures as the field is increased [7]. This is in sharp contrast with the behavior observed in optimally-doped cuprates, where the Nernst peak follows the field-induced shift in resistive transition [1]. Note that the peak occurs at a temperature interval where resistivity is increasing with decreasing temperature. A second unusual aspect of this figure is the persistence of a residual Nernst signal up to the highest temperatures explored (100 K). This is a confirmation of the original observation reported by Xu [3]. It indicates the presence of strong superconducting fluctuations in a very broad temperature window in the normal-state. It is puzzling, however, that these strong fluctuations are not detected in charge transport. Indeed, as seen in the figure, there is no detectable magnetoresistance in the same temperature window. A recent study of Nernst effect NbSe2 provides fresh input for the ongoing debate on the origin of this anomalous Nernst signal [8]. As seen in Fig. 2, Nernst coefficient displays a sharp maximum close to the superconducting transition. However, this vortex-related
0921-4534/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.02.114
K. Behnia et al. / Physica C 408–410 (2004) 326–327
4.5 (H=12T) 4.0 3.5
(H=0)
N (µV / K)
3.0 2.5 2.0
N (H=12T)
1.5 Bi2Sr 2CuO6+δ
1.0 0.5 0.0 0
20
40
60
80
100
T (K) Fig. 1. Temperature dependence of resistivity and Nernst effect in an underdoped sample of Bi2 Sr2 CuO6þd . A residual Nernst effect persists in temperatures well above Tc . 0.06 8
0.08 (H=1T)
0.04
4
0.00
0
N(µV/K)
0.00
signal is superposed on a large negative signal which peaks at 21 K. As seen in the inset, the positive peak occurs in a temperature window closely related to the superconducting transition. The large negative signal is undoubtedly due to quasi-particles and indicates that a large Nernst signal may arise in the absence of superconducting fluctuations. Measurements of the Hall effect in the same temperature range leads to a compelling picture for the origin of this signal in NbSe2 [8]. This compound undergoes a charge density wave transition at TCDW 32 K, leading to a sign change of the Hall coefficient. The Hall coefficient becomes zero at T 21 K which is the temperature of the Nernst maximum. As argued in Ref. [8] this is an important clue for concluding that the ambipolar flow of electrons and holes in presence of a thermal gradient leads to a spectacular enhancement of the Nernst signal in this metal. The study gives an example of the variety of possible origins for a large Nernst signal in a metal. One should be cautious in regarding vortex-like excitations as the only possible source of the anomalous Nernst signal observed in hole-doped cuprates. We note, however, that no obvious correlation between the Hall and Nernst coefficients has been detected in the holedoped cuprates [6]. Therefore, superconducting fluctuations remain the most plausible explanation of the anomalous normal-state Nersnt signal in the holedoped cuprates. In the electron-doped cuprates, on the other hand, the large quasi-particle contribution to the Nernst signal can be easily distinguished from the vortex contribution and appears to point to a two-band Fermi surface [9,10].
(µ cm)
0.03
(H=0)
327
-0.03
References 5
6
7
8
-0.06 -0.09
NbSe2 H=1T
-0.12 5
6
7 8 9
20
30
40
50 60
T(K)
Fig. 2. Temperature dependence of resistivity and Nernst effect in NbSe2 . A sharp positive signal associated with vortices is superposed on a large negative quasi-particle signal. The inset is a zoom on the region centered around the superconducting transition.
[1] H.C. Ri et al., Phys. Rev. B 50 (1994) 3312. [2] E.H. Sondheimer, Proc. R. Soc., London 193 (1948) 484. [3] Z.A. Xu et al., Nature 406 (2000) 486. [4] Y. Wang et al., Phys. Rev. B 64 (2001) 224519. [5] Y. Wang et al., Phys. Rev. Lett. 88 (2002) 257003. [6] C. Capan et al., Phys. Rev. Lett. 88 (2002) 056601. [7] C. Capan et al., Phys. Rev. B 67 (2003) 100507(R). [8] R. Bel, K. Behnia, H. Berger, Phys. Rev. Lett. 91 (2003) 066602. [9] P. Fournier et al., Phys. Rev. B 56 (1997) 14149. [10] F. Gollnik, M. Naito, Phys. Rev. B 58 (1998) 11734.
Nernst effect in underdoped cuprates K. Behnia *, C. Capan, R. Bel Laboratoire de Physique Quantique (CNRS), Ecole Superieure de Physique et Chimie Industrielles, ESPCI, 10 Rue Vauquelin, 75231 Paris, France
Abstract We performed a comparative study of Nernst effect and resistivity in underdoped cuprates. A finite Nernst signal coexists with a field-induced non-metallic resistivity and persists up to temperatures well above Tc . On the other hand, a similar study detects a finite Nernst signal in the normal-state of the conventional superconductor NbSe2 . However, the superconducting fluctuations remain the most plausible source of the anomalous Nernst signal in the underdoped cuprates. Ó 2004 Elsevier B.V. All rights reserved. PACS: 72.15.Jf; 74.25.Fy; 74.40.+k; 74.60.Ge
In the vortex-liquid state of a type II superconductor, movement of vortices induced by a thermal gradient leads to a transverse electric field and a finite Nernst coefficient appears in the mixed state [1]. In metals, on the other hand, the Nernst coefficient is believed to be small due to a fundamental reason put forward in a seminal work by Sondheimer in 1948 [2]. Recently, however, Xu [3] reported that in underdoped La2x Srx CuO4 a large residual signal persists in the normal-state and well above Tc . This observation has been confirmed in other families of cuprate superconductors [4,5]. Moreover, the normal-state Nernst signal is found to persist in presence of high magnetic fields for both overdoped [5] and underdoped [6] limits. Fig. 1 shows Nernst effect and resistivity as a function of temperature in a Bi2 Sr2 CuO6þd thin films. At zero field, the sample presents a broad resistive transition centered around 9 K. This transition is superposed on a slightly non-metallic behavior. The application of a moderate magnetic field (12 T) leads to a reduction of Tc and the emergence of a more pronounced ‘‘insulating’’ behavior. In presence of this magnetic field, the Nernst
*
Corresponding author. Tel.: +33-1-40-79-46-26; fax: +33-140-79-47-44. E-mail address: [email protected] (K. Behnia).
coefficient displays an unusual temperature dependence. First of all, a broad peak in the temperature dependence of Nernst signal commonly associated with the vortex movement still persists. A detailed study on this sample as well other underdoped samples [7] found that the amplitude of this peak increases initially with increasing magnetic field before starting to decrease at 10 T. But the peak does not shift to lower temperatures as the field is increased [7]. This is in sharp contrast with the behavior observed in optimally-doped cuprates, where the Nernst peak follows the field-induced shift in resistive transition [1]. Note that the peak occurs at a temperature interval where resistivity is increasing with decreasing temperature. A second unusual aspect of this figure is the persistence of a residual Nernst signal up to the highest temperatures explored (100 K). This is a confirmation of the original observation reported by Xu [3]. It indicates the presence of strong superconducting fluctuations in a very broad temperature window in the normal-state. It is puzzling, however, that these strong fluctuations are not detected in charge transport. Indeed, as seen in the figure, there is no detectable magnetoresistance in the same temperature window. A recent study of Nernst effect NbSe2 provides fresh input for the ongoing debate on the origin of this anomalous Nernst signal [8]. As seen in Fig. 2, Nernst coefficient displays a sharp maximum close to the superconducting transition. However, this vortex-related
0921-4534/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.02.114
K. Behnia et al. / Physica C 408–410 (2004) 326–327
4.5 (H=12T) 4.0 3.5
(H=0)
N (µV / K)
3.0 2.5 2.0
N (H=12T)
1.5 Bi2Sr 2CuO6+δ
1.0 0.5 0.0 0
20
40
60
80
100
T (K) Fig. 1. Temperature dependence of resistivity and Nernst effect in an underdoped sample of Bi2 Sr2 CuO6þd . A residual Nernst effect persists in temperatures well above Tc . 0.06 8
0.08 (H=1T)
0.04
4
0.00
0
N(µV/K)
0.00
signal is superposed on a large negative signal which peaks at 21 K. As seen in the inset, the positive peak occurs in a temperature window closely related to the superconducting transition. The large negative signal is undoubtedly due to quasi-particles and indicates that a large Nernst signal may arise in the absence of superconducting fluctuations. Measurements of the Hall effect in the same temperature range leads to a compelling picture for the origin of this signal in NbSe2 [8]. This compound undergoes a charge density wave transition at TCDW 32 K, leading to a sign change of the Hall coefficient. The Hall coefficient becomes zero at T 21 K which is the temperature of the Nernst maximum. As argued in Ref. [8] this is an important clue for concluding that the ambipolar flow of electrons and holes in presence of a thermal gradient leads to a spectacular enhancement of the Nernst signal in this metal. The study gives an example of the variety of possible origins for a large Nernst signal in a metal. One should be cautious in regarding vortex-like excitations as the only possible source of the anomalous Nernst signal observed in hole-doped cuprates. We note, however, that no obvious correlation between the Hall and Nernst coefficients has been detected in the holedoped cuprates [6]. Therefore, superconducting fluctuations remain the most plausible explanation of the anomalous normal-state Nersnt signal in the holedoped cuprates. In the electron-doped cuprates, on the other hand, the large quasi-particle contribution to the Nernst signal can be easily distinguished from the vortex contribution and appears to point to a two-band Fermi surface [9,10].
(µ cm)
0.03
(H=0)
327
-0.03
References 5
6
7
8
-0.06 -0.09
NbSe2 H=1T
-0.12 5
6
7 8 9
20
30
40
50 60
T(K)
Fig. 2. Temperature dependence of resistivity and Nernst effect in NbSe2 . A sharp positive signal associated with vortices is superposed on a large negative quasi-particle signal. The inset is a zoom on the region centered around the superconducting transition.
[1] H.C. Ri et al., Phys. Rev. B 50 (1994) 3312. [2] E.H. Sondheimer, Proc. R. Soc., London 193 (1948) 484. [3] Z.A. Xu et al., Nature 406 (2000) 486. [4] Y. Wang et al., Phys. Rev. B 64 (2001) 224519. [5] Y. Wang et al., Phys. Rev. Lett. 88 (2002) 257003. [6] C. Capan et al., Phys. Rev. Lett. 88 (2002) 056601. [7] C. Capan et al., Phys. Rev. B 67 (2003) 100507(R). [8] R. Bel, K. Behnia, H. Berger, Phys. Rev. Lett. 91 (2003) 066602. [9] P. Fournier et al., Phys. Rev. B 56 (1997) 14149. [10] F. Gollnik, M. Naito, Phys. Rev. B 58 (1998) 11734.