Hidden order in the cuprates

Chakravarty, Sudip; Laughlin, R. B.; Morr, Dirk K.; Nayak, Chetan

doi:10.1103/physrevb.63.094503

Cited by 1,180 publications

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“…As suggested by its different momentum dependence from its nodal counterpart, the antinodal pseudogap may have a different origin, which has been the subject for intense discussions in the literature [2][3][4][5][6][7][8][9] . Generally, as inferred from Supplementary Information, Fig.…”

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confidence: 99%

Energy gaps in the failed high-Tc superconductor La1.875Ba0.125CuO4

Tanaka

et al. 2008

Nature Phys

104

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A central issue in high-T c superconductivity is the nature of the normal-state gap (pseudogap) 1 in the underdoped regime and its relationship with superconductivity. Despite persistent efforts, theoretical ideas for the pseudogap evolve around fluctuating superconductivity 2 , competing order 3-8 and spectral weight suppression due to many-body effects 9 . Recently, although some experiments in the superconducting state indicate a distinction between the superconducting gap and pseudogap 10-14 , others in the normal state, either by extrapolation from high-temperature data 15 The first high-T c superconductor discovered, La 2−x Ba x CuO 4 (LBCO), holds a unique position in the field because of an anomalously strong bulk T c suppression near x = 1/8. Right around this 'magic' doping level, scattering experiments by neutrons 18,19 and X-rays 20 find a static spin and charge (stripe) order. By itself, this observation raises a series of intriguing questions: whether the stripe order is a competing order that suppresses the superconductivity in LBCO-1/8; if the answer is positive, which aspect, the pairing strength or the phase coherence, is involved in the T c suppression and how this mechanism applies to other dopings or families. For our investigation of the 'ground-state' pseudogap, as defined in ref. 16, which ignores the residual superconductivity, its sufficiently high doping yet extremely low bulk T c (∼4 K) makes LBCO-1/8 an ideal system: especially for the small-gap measurement near the node, difficulties due to either the unscreened disorder potential, a problem for extremely low doping, or trivial thermal broadening, a problem above T c for higher doping, are circumvented.Whereas thermal effects require an extrapolation from high-temperature data to obtain the ground-state physics 15 , a direct measurement on LBCO-1/8 at low temperature has been made 16 . With experimental resolutions compromised to obtain sufficient signal to noise, a simple d-wave gap function is reported with no discernible nodal quasi-particles found. Given the importance of this issue, we have carried out an angle-resolved photoemission 21 study of LBCO-1/8 at T > T c with much improved resolutions in a measurement geometry favourable for the detection of nodal quasi-particles (see Fig. 1 and Supplementary Information, Section SI). Our data provide two important new insights. First, there is a well-defined nodal quasi-particle peak, suggesting nodal quasi-particles can exist in the stripe-ordered state. Second, there is a rich gap structure, suggesting the pseudogap physics is more elaborate than the simple d-wave version. In particular, a new kind of pseudogap, which is not smoothly connected to the usual one tied to the antinodal region, can exist in the nodal region when superconductivity is suppressed owing to the loss of phase coherence.As shown in Fig. 1, there exists a well-defined quasi-particle peak in the energy distribution curves (EDCs) at the Fermi crossing points (k F ) around the node. On dispersion towards the ant...

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Energy gaps in the failed high-Tc superconductor La1.875Ba0.125CuO4

Tanaka

et al. 2008

Nature Phys

104

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“…The spectrum [see Fig. 2(b), (e), and (f)] is nodally gapped at the Fermi level and the gap maxima at (0, ±π) and (±π, 0) [7,12,8,9,10,11] manifest themselves as the van Hove singularity peaks in the DOS. Local DOS shows that the mid-band has a great part composed of states localized along the stripes (see Fig.…”

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Phases and density of states in a generalized Su–Schrieffer–Heeger model

Voo

Mou

2004

Physica B: Condensed Matter

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Self-consistent solutions to a generalized Su-Schrieffer-Heeger model on a 2-dimensional square lattice are investigated. Away from half-filling, spatially inhomogeneous phases are found. Those phases may have topological structures on the flux order, large unit cell bond order, localized bipolarons, or they are simply short-range ordered and glassy. They have an universal feature of always possessing a gap at the Fermi level.

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“…Any difference in the impurity modified LDOS between the DSC and DDW states may reveal the hidden DDW order and distinguish between the scenario of preformed pairs versus staggered orbital currents as the origin for the pseudo-gap state [15]. Recently, there has been several other proposals to probe the DDW order in the cuprates [14,16].In attempting to make better contact to the experiments we include the tunneling through excited states from the CuO 2 planes to the BiO layer probed by the STM tip [8]. This effect modifies the LDOS, ρ(r, ω) = n |ψ n (r)| 2 δ(ω − n ), by including the four nearest Cu…”

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“…Our main results are the following: 1) investigation of the LDOS around two impurities can pose strong constraints on the potential scattering model, 2) quantum interference can be utilized as an alternative method to detect small subdominant superconducting order parameters, and 3) quantum interference between two nonmagnetic impurities may easily distinguish between the d-wave superconducting (DSC) and d-density wave (DDW) states. The DDW state was recently proposed as a model for the pseudogap state of the cuprates [14]. Any difference in the impurity modified LDOS between the DSC and DDW states may reveal the hidden DDW order and distinguish between the scenario of preformed pairs versus staggered orbital currents as the origin for the pseudo-gap state [15].…”

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Impurity resonances and the origin of the pseudo-gap

Andersen¹

2003

Braz. J. Phys.

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We study the structure of resonance states localized around nonmagnetic impurities in the CuO 2 planes of the cuprate superconductors within a potential scattering formalism. In particular we show that strong quantum interference effects arise between several impurities. This interference can be utilized to distinguish the dwave superconducting state from the phase with d-density wave order. This is important if the origin of the pseudo-gap state in the underdoped regime of the High Tc superconductors is caused by preformed Cooper pairs or staggered orbital currents. Furthermore impurity interference can be utilized to reveal subdominant superconducting order parameters and to pose further constraints on the potential scattering scenario.For conventional superconductors Yu and Shiba[1] first showed that as a result of the interaction between a magnetic impurity and the spin density of the conduction electrons, a bound state located around the magnetic impurity is formed inside the gap in the strong-scattering (unitary) limit. For anisotropic superconductors a number of authors generalized the Yu-Shiba approach to study the effects of single impurities [2].Many important questions concerning the electronic structure of the High T c materials still need to be answered. The study of single impurity effects provide a promising path to yield some answers. This is mainly due to the large experimental progress in low temperature scanning tunneling microscopy (STM). In particular, STM measurements have provided detailed local density of states (LDOS) images around single nonmagnetic [3,4] (Zn) and magnetic [5] (Ni) impurities on the surface of the high temperature superconductor Bi 2 Sr 2 CaCuO 4+δ (BSCCO). More recently the energy dependence of the Fourier transformed LDOS images was measured in the superconducting state of optimally doped BSCCO[6]. The dispersive features were explained by elastic quasi-particle interference resulting from a single weak, nonmagnetic impurity [7]. This gives credence that a scattering potential picture can yield valuable predictions in the superconducting state of these materials. Furthermore, it was recently shown by Martin et al. [8] that both the energetics of the resonance state and its spatial dependence around a strong potential scatterer (e.g. Zn) can be accounted for by including the tunnelling (the filter) through excited states from the CuO 2 planes to the top BiO layer probed by the STM tip. In order to obtain agreement with the measured LDOS one needs to attribute a large negative potential to the Zn site in agreement with the filled d shell of this atom; the potential will strongly repel holes, i.e. attract the electrons.Experimentally there is also evidence from NMR measurements that magnetic moments are induced around nonmagnetic impurities [9]. In this paper we assume, however, that the large potential scattering off the impurity site itself is dominating the final LDOS.Future experimental ability to control the position of the impurities on the surface of a superconduc...

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Hidden order in the cuprates

Cited by 1,180 publications

References 72 publications

Energy gaps in the failed high-Tc superconductor La1.875Ba0.125CuO4

Energy gaps in the failed high-Tc superconductor La1.875Ba0.125CuO4

Phases and density of states in a generalized Su–Schrieffer–Heeger model

Impurity resonances and the origin of the pseudo-gap

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