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Common phase diagram for low-dimensional superconductors
Journal of Magnetism and Magnetic Materials 260 (2003) 336–337
Common phase diagram for low-dimensional superconductors Rudi Michalak* Max-Planck Institute for Chemical Physics of Solids, Noethnitzer Str. 40, 01187 Dresden, Germany
Abstract A phenomenological phase diagram which has been derived for high-temperature superconductors from NMR Knight-shift measurements of the pseudogap is compared to the phase diagram that is obtained for organic superconductors and spin-ladder superconductors, both low-dimensional systems. This is contrasted to the phase diagram of some Heavy Fermion superconductors, i.e. superconductors not constrained to a low dimensionality. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Superconductivity; Low dimensionality; NMR; Pseudogap
Recently, Williams et al. [1] have suggested a phenomenological phase diagram for high-temperature superconductors based on the hole doping dependency of the pseudogap energy. They find that the pseudogap coexists with the superconducting gap up to a hole doping of p ¼ 0:19; which is slightly above p ¼ 0:16; the optimally doped compound. The best fit for their data was found for d-wave symmetry for both gaps. Batlogg et al. [2] arrived at a similar phenomenological phase diagram. We note that there is a characteristic temperature scale for the opening of the pseudogap as a function of carrier concentration, i.e. in the case of the cuprates as a function of hole doping. Furthermore, we see (Fig. 1) that there exists a universal curve for the superconducting transition temperature, which is essentially parabolic as a function of hole concentration. Towards the underdoped side, one finds a region of magnetic order. Several theoretical approaches (see for instance Ref. [3] or [4]) discuss the possible coexistence of the antiferromagnetic order and the superconductivity. Furthermore, Batlogg et al. distinguish possibly independent energy scales: the so-called spin-gap and the pseudogap. In the analysis of Williams et al., no such extra energy scale is necessary to explain their data. Originally, the difference between the two terms ‘pseudogap’ and ‘spin-gap’ was made because the phenomenon was first only being *Tel.: +49-351-4646-3211; fax: +49-351-4646-3232. E-mail address: [email protected] (R. Michalak).
observed by NMR and neutron scattering, two methods that work in the spin channel and it remains to some degree unclear whether the observations of a normal state gap by charge-channel methods actually does discuss the same thing. In comparison, the phase diagrams of low-dimensional organic superconductors look strikingly similar. For instance, for the quasi one-dimensional (TM)2X series with maximum Tc about 1 K one finds on the low charge carrier side of the superconducting regime a rich variety of ground states that include a region of spin density wave and spin-Peierls order [5]. Fig. 2 shows the phase diagram for (TM)2X where log T is plotted against the applied pressure. When comparing Figs. 1 and 2, one has to bare in mind that there is no linear relationship between the hole doping scale and the applied pressure scale. However, qualitatively the comparison shows again magnetic order on the low doping side of superconductivity. Ladder materials like Sr14xCaxCu24O41 are another representative of low-dimensional superconductors. Their maximum Tc is near 10 K. Again, their phase diagram (here the spin-gap as seen by NMR is shown as a function of doping—Fig. 3 [6]) shows a near parabolic dependence of Tc on the charge carrier density and on the low doping side a spin-gap state with the gap energy falling towards the range of superconductivity. In summary, for the known low-dimensional superconductors we find a striking similarity in their respective phase diagrams, with a peculiar dependence
0304-8853/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 1 0 5 2 - 0
R. Michalak / Journal of Magnetism and Magnetic Materials 260 (2003) 336–337
337
600 900 500
300
10
Tc
100
S.C. 0 0.05
0.10
0.15 p
0.20
0.25
0.30
Fig. 1. (a) The dependence of the pseudogap on the hole concentration in high-temperature superconductors determined by NMR Knight shifts (after Ref. [1]), and (b) distinction between a spin-gap and a pseudogap energy scale in hightemperature superconductors (after Ref. [2]).
(TM)2X
100 CL T (K)
20 300
200
0 0.00
600
Tc (K)
Spin Gap (K)
Eg/kB, Tc (K)
400
Conductor
10 SP
SDW
1
2
4
6 X
8
10
0
2 4 6 P (GPa)
0
Fig. 3. Spin gap and superconducting regime in Sr14xCaxCu24O41 ladder compounds by NMR Knight shift and spinlattice relaxation time [6].
conductors. At the present state, this question cannot be answered yet. In fact, although there is the astonishing similarity other examples can be found which follow a similar phase diagram; namely the Heavy Fermion superconductors CePd2Si2 and CeIn3 as has been shown by Mathur et al. [7] exhibit an similar suppression of the ordered antiferromagnetic state with pressure—and hence with increasing doping—towards the superconducting regime. Of course, Heavy Fermions cannot be regarded as ‘low-dimensional’, rather they are pretty much ‘normal’ metals aside from their unusual effective masses (see for instance Ref. [8]).
SC Applied pressure
5 kbar
Fig. 2. Generalized phase diagram for the organic superconductor (TM)2X series indicating spin-Peierls (SP), spin density wave (SDW), charge localization (CL) and superconducting (SC) ground states [5].
of their characteristic energy scale on the doping. It is therefore reasonable to ask whether there may be a common phase diagram for low-dimensional super-
References [1] G.V.M. Williams, J.L. Tallon, et al., Phys. Rev. Lett. 78 (1997) 721. [2] B. Batlogg, Physica C 282–287 (1997) xxiv. [3] D. Pines, Physica C 282–287 (1997) 273. [4] J. Jaklic, P. Prelovsek, Adv. Phys. 49 (2000) 1. [5] D. Jerome, Science 252 (1991) 1501. [6] A. Magishi, et al., Phys. Rev B 57 (1998) 11533. [7] N.D. Mathur, Nature 394 (1998) 39. [8] F. Steglich, P. Gegenwart, et al., Z. Phys. B 103 (1997) 235.
Common phase diagram for low-dimensional superconductors Rudi Michalak* Max-Planck Institute for Chemical Physics of Solids, Noethnitzer Str. 40, 01187 Dresden, Germany
Abstract A phenomenological phase diagram which has been derived for high-temperature superconductors from NMR Knight-shift measurements of the pseudogap is compared to the phase diagram that is obtained for organic superconductors and spin-ladder superconductors, both low-dimensional systems. This is contrasted to the phase diagram of some Heavy Fermion superconductors, i.e. superconductors not constrained to a low dimensionality. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Superconductivity; Low dimensionality; NMR; Pseudogap
Recently, Williams et al. [1] have suggested a phenomenological phase diagram for high-temperature superconductors based on the hole doping dependency of the pseudogap energy. They find that the pseudogap coexists with the superconducting gap up to a hole doping of p ¼ 0:19; which is slightly above p ¼ 0:16; the optimally doped compound. The best fit for their data was found for d-wave symmetry for both gaps. Batlogg et al. [2] arrived at a similar phenomenological phase diagram. We note that there is a characteristic temperature scale for the opening of the pseudogap as a function of carrier concentration, i.e. in the case of the cuprates as a function of hole doping. Furthermore, we see (Fig. 1) that there exists a universal curve for the superconducting transition temperature, which is essentially parabolic as a function of hole concentration. Towards the underdoped side, one finds a region of magnetic order. Several theoretical approaches (see for instance Ref. [3] or [4]) discuss the possible coexistence of the antiferromagnetic order and the superconductivity. Furthermore, Batlogg et al. distinguish possibly independent energy scales: the so-called spin-gap and the pseudogap. In the analysis of Williams et al., no such extra energy scale is necessary to explain their data. Originally, the difference between the two terms ‘pseudogap’ and ‘spin-gap’ was made because the phenomenon was first only being *Tel.: +49-351-4646-3211; fax: +49-351-4646-3232. E-mail address: [email protected] (R. Michalak).
observed by NMR and neutron scattering, two methods that work in the spin channel and it remains to some degree unclear whether the observations of a normal state gap by charge-channel methods actually does discuss the same thing. In comparison, the phase diagrams of low-dimensional organic superconductors look strikingly similar. For instance, for the quasi one-dimensional (TM)2X series with maximum Tc about 1 K one finds on the low charge carrier side of the superconducting regime a rich variety of ground states that include a region of spin density wave and spin-Peierls order [5]. Fig. 2 shows the phase diagram for (TM)2X where log T is plotted against the applied pressure. When comparing Figs. 1 and 2, one has to bare in mind that there is no linear relationship between the hole doping scale and the applied pressure scale. However, qualitatively the comparison shows again magnetic order on the low doping side of superconductivity. Ladder materials like Sr14xCaxCu24O41 are another representative of low-dimensional superconductors. Their maximum Tc is near 10 K. Again, their phase diagram (here the spin-gap as seen by NMR is shown as a function of doping—Fig. 3 [6]) shows a near parabolic dependence of Tc on the charge carrier density and on the low doping side a spin-gap state with the gap energy falling towards the range of superconductivity. In summary, for the known low-dimensional superconductors we find a striking similarity in their respective phase diagrams, with a peculiar dependence
0304-8853/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 1 0 5 2 - 0
R. Michalak / Journal of Magnetism and Magnetic Materials 260 (2003) 336–337
337
600 900 500
300
10
Tc
100
S.C. 0 0.05
0.10
0.15 p
0.20
0.25
0.30
Fig. 1. (a) The dependence of the pseudogap on the hole concentration in high-temperature superconductors determined by NMR Knight shifts (after Ref. [1]), and (b) distinction between a spin-gap and a pseudogap energy scale in hightemperature superconductors (after Ref. [2]).
(TM)2X
100 CL T (K)
20 300
200
0 0.00
600
Tc (K)
Spin Gap (K)
Eg/kB, Tc (K)
400
Conductor
10 SP
SDW
1
2
4
6 X
8
10
0
2 4 6 P (GPa)
0
Fig. 3. Spin gap and superconducting regime in Sr14xCaxCu24O41 ladder compounds by NMR Knight shift and spinlattice relaxation time [6].
conductors. At the present state, this question cannot be answered yet. In fact, although there is the astonishing similarity other examples can be found which follow a similar phase diagram; namely the Heavy Fermion superconductors CePd2Si2 and CeIn3 as has been shown by Mathur et al. [7] exhibit an similar suppression of the ordered antiferromagnetic state with pressure—and hence with increasing doping—towards the superconducting regime. Of course, Heavy Fermions cannot be regarded as ‘low-dimensional’, rather they are pretty much ‘normal’ metals aside from their unusual effective masses (see for instance Ref. [8]).
SC Applied pressure
5 kbar
Fig. 2. Generalized phase diagram for the organic superconductor (TM)2X series indicating spin-Peierls (SP), spin density wave (SDW), charge localization (CL) and superconducting (SC) ground states [5].
of their characteristic energy scale on the doping. It is therefore reasonable to ask whether there may be a common phase diagram for low-dimensional super-
References [1] G.V.M. Williams, J.L. Tallon, et al., Phys. Rev. Lett. 78 (1997) 721. [2] B. Batlogg, Physica C 282–287 (1997) xxiv. [3] D. Pines, Physica C 282–287 (1997) 273. [4] J. Jaklic, P. Prelovsek, Adv. Phys. 49 (2000) 1. [5] D. Jerome, Science 252 (1991) 1501. [6] A. Magishi, et al., Phys. Rev B 57 (1998) 11533. [7] N.D. Mathur, Nature 394 (1998) 39. [8] F. Steglich, P. Gegenwart, et al., Z. Phys. B 103 (1997) 235.