Abstract
A number of spectacular experimental anomalies have been discovered recently in certain cuprates, notably La2−xBaxCuO4 and La1.6−xNd0.4SrxCuO4, which show unidirectional spin and charge order (known as stripe order). We have recently proposed to interpret these observations as evidence for a new ‘striped’ superconducting state, in which the superconducting order parameter is modulated in space, such that its average is precisely zero. Here, we show that thermal melting of the striped superconducting state can lead to a number of unusual phases, of which the most novel is a charge-4e superconducting state, with a corresponding fractional flux quantum h c=4e. These are never-before-observed states of matter, which, moreover, cannot arise from the conventional Bardeen–Cooper–Schrieffer mechanism. Thus, direct confirmation of their existence, even in a small subset of the cuprates, could have much broader implications for our understanding of high-temperature superconductivity. We propose experiments to observe fractional flux quantization, which could confirm the existence of these states.
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References
Li, Q., Hücker, M., Gu, G. D., Tsvelik, A. M. & Tranquada, J. M. Two-dimensional superconducting fluctuations in stripe-ordered La1.875Ba0.125CuO4 . Phys. Rev. Lett. 99, 067001–067004 (2007).
Ding, J. F., Xiang, X. Q., Zhang, Y. Q., Liu, H. & Li, X. G. Two-dimensional superconductivity in stripe-ordered La1.6−xNd0.4SrxCuO4 single crystals. Phys. Rev. B 77, 214524–214528 (2008).
Berg, E. et al. Dynamical layer decoupling in a stripe-ordered high Tc superconductor. Phys. Rev. Lett. 99, 127003–127006 (2007).
Berg, E., Fradkin, E. & Kivelson, S. A. Theory of the striped superconductor. Phys. Rev. B 79, 064515–064529 (2009).
Berg, E., Fradkin, E., Kivelson, S. A. & Tranquada, J. M. Striped superconductors: How the cuprates intertwine spin, charge and superconducting orders. Preprint at <http://arxiv.org/abs/0901.4826> (2009).
Tranquada, J. M. et al. Evidence for unusual superconducting correlations coexisting with stripe order in La1.875Ba0.125CuO4 . Phys. Rev. B 78, 174529–174541 (2008).
Kivelson, S. A., Emery, V. J. & Lin, H. Q. Doped antiferromagnets in the weak-hopping limit. Phys. Rev. B 42, 6523–6530 (1990).
Wu, C. Competing orders in one-dimensional spin-3/2 Fermionic systems. Phys. Rev. Lett. 95, 266404–266407 (2005).
Agterberg, D. F. & Tsunetsugu, H. Dislocations and vortices in pair-density-wave superconductors. Nature Phys. 4, 639–642 (2008).
Agterberg, D. F., Sigrist, M. & Tsunetsugu, H. Order parameter and vortices in the superconducting Q-phase of CeCoIn5. Preprint at <http://arxiv.org/abs/0902.0843> (2009).
Radzihovsky, L. & Vishwanath, A. Quantum liquid crystals in imbalanced Fermi gas: Fluctuations and fractional vortices in Larkin–Ovchinnikov states. Phys. Rev. Lett. 103, 010404–010407 (2009).
Larkin, A. I. & Ovchinnikov, Y. N. Nonuniform state of superconductors. Sov. Phys. JETP 20, 762–769 (1965).
Babaev, E. Phase diagram of planar U(1)×U(1) superconductor condensation of vortices with fractional flux and a superfluid state. Nucl. Phys. B 686, 397–412 (2004).
Kosterlitz, J. M. & Thouless, D. J. Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C 6, 1181–1203 (1973).
Nelson, D. R. & Halperin, B. I. Dislocation-mediated melting in two dimensions. Phys. Rev. B 19, 2457–2484 (1979).
Young, A. P. Melting and the vector coulomb gas in two dimensions. Phys. Rev. B 19, 1855–1866 (1979).
Nienhuis, B. in Phase Transitions and Critical Phenomena Vol. 11 (eds Domb, C. & Lebowitz, J.) 1–51 (Academic, 1987).
Krüger, F. & Scheidl, S. Nonuniversal ordering of spin and charge in stripe phases. Phys. Rev. Lett. 89, 095701–095704 (2002).
Podolsky, D., Chandrasekharan, S. & Vishwanath, A. Phase transitions of S=1 spinor condensates in an optical lattice. Preprint at <http://arxiv.org/abs/0707.0695v2> (2007).
Kondev, J. & Henley, C. L. Kac–Moody symmetries of critical ground states. Nucl. Phys. B 464, 540–575 (1996).
Baruch, S. & Orgad, D. Spectral signatures of modulated d-wave superconducting phases. Phys. Rev. B. 77, 174502–174510 (2008).
Nussinov, Z. & Zaanen, J. Stripe fractionalization I: The generation of Ising local symmetry. J. Phys. IV 12, 245–250 (2002).
Schneider, C. W. et al. Half-h/2e critical current oscillations of SQUIDs. Europhys. Lett. 68, 86–92 (2004).
Acknowledgements
We thank D. Basov, T. Leggett, D. Podolsky, L. Radzihovsky, D. Scalapino, J. Tranquada and D. Van Harlingen for discussions. This work was supported in part by the National Science Foundation, under grants DMR 0758462 (E.F.) and DMR 0531196 (S.A.K.) and by the Office of Science, US Department of Energy, under Contracts DE-FG02-91ER45439 through the Frederick Seitz Materials Research Laboratory at the University of Illinois (E.F.) and DE-FG02-06ER46287 through the Geballe Laboratory of Advanced Materials at Stanford University (S.A.K. and E.B.).
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Berg, E., Fradkin, E. & Kivelson, S. Charge-4e superconductivity from pair-density-wave order in certain high-temperature superconductors. Nature Phys 5, 830–833 (2009). https://doi.org/10.1038/nphys1389
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DOI: https://doi.org/10.1038/nphys1389
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