Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor

Despite twenty years of research, the phase diagram of high-transition-temperature superconductors remains enigmatic. A central issue is the origin of the differences in the physical properties of these copper oxides doped to opposite sides of the superconducting region. In the overdoped regime, the material behaves as a reasonably conventional metal, with a large Fermi surface. The underdoped regime, however, is highly anomalous and appears to have no coherent Fermi surface, but only disconnected 'Fermi arcs'. The fundamental question, then, is whether underdoped copper oxides have a Fermi surface, and if so, whether it is topologically different from that seen in the overdoped regime. Here we report the observation of quantum oscillations in the electrical resistance of the oxygen-ordered copper oxide YBa2Cu3O6.5, establishing the existence of a well-defined Fermi surface in the ground state of underdoped copper oxides, once superconductivity is suppressed by a magnetic field. The low oscillation frequency reveals a Fermi surface made of small pockets, in contrast to the large cylinder characteristic of the overdoped regime. Two possible interpretations are discussed: either a small pocket is part of the band structure specific to YBa2Cu3O6.5 or small pockets arise from a topological change at a critical point in the phase diagram. Our understanding of high-transition-temperature (high-T(c)) superconductors will depend critically on which of these two interpretations proves to be correct.     

Electron pockets in the Fermi surface of hole-doped high-Tc superconductors

High-temperature superconductivity in copper oxides occurs when the materials are chemically tuned to have a carrier concentration intermediate between their metallic state at high doping and their insulating state at zero doping. The underlying evolution of the electron system in the absence of superconductivity is still unclear, and a question of central importance is whether it involves any intermediate phase with broken symmetry. The Fermi surface of the electronic states in the underdoped 'YBCO' materials YBa2Cu3O(y) and YBa2Cu4O8 was recently shown to include small pockets, in contrast with the large cylinder that characterizes the overdoped regime, pointing to a topological change in the Fermi surface. Here we report the observation of a negative Hall resistance in the magnetic-field-induced normal state of YBa2Cu3O(y) and YBa2Cu4O8, which reveals that these pockets are electron-like rather than hole-like. We propose that these electron pockets most probably arise from a reconstruction of the Fermi surface caused by the onset of a density-wave phase, as is thought to occur in the electron-doped copper oxides near the onset of antiferromagnetic order. Comparison with materials of the La2CuO4 family that exhibit spin/charge density-wave order suggests that a Fermi surface reconstruction also occurs in those materials, pointing to a generic property of high-transition-temperature (T(c)) superconductors.     

Magnetic-field-induced charge-stripe order in the high-temperature superconductor YBa2Cu3Oy

Electronic charges introduced in copper-oxide (CuO(2)) planes generate high-transition-temperature (T(c)) superconductivity but, under special circumstances, they can also order into filaments called stripes. Whether an underlying tendency towards charge order is present in all copper oxides and whether this has any relationship with superconductivity are, however, two highly controversial issues. To uncover underlying electronic order, magnetic fields strong enough to destabilize superconductivity can be used. Such experiments, including quantum oscillations in YBa(2)Cu(3)O(y) (an extremely clean copper oxide in which charge order has not until now been observed) have suggested that superconductivity competes with spin, rather than charge, order. Here we report nuclear magnetic resonance measurements showing that high magnetic fields actually induce charge order, without spin order, in the CuO(2) planes of YBa(2)Cu(3)O(y). The observed static, unidirectional, modulation of the charge density breaks translational symmetry, thus explaining quantum oscillation results, and we argue that it is most probably the same 4a-periodic modulation as in stripe-ordered copper oxides. That it develops only when superconductivity fades away and near the same 1/8 hole doping as in La(2-x)Ba(x)CuO(4) (ref.?1) suggests that charge order, although visibly pinned by CuO chains in YBa(2)Cu(3)O(y), is an intrinsic propensity of the superconducting planes of high-T(c) copper oxides.     

A hidden pseudogap under the 'dome' of superconductivity in electron-doped high-temperature superconductors

The ground state of superconductors is characterized by the long-range order of condensed Cooper pairs: this is the only order present in conventional superconductors. The high-transition-temperature (high-T(c)) superconductors, in contrast, exhibit more complex phase behaviour, which might indicate the presence of other competing ground states. For example, the pseudogap--a suppression of the accessible electronic states at the Fermi level in the normal state of high-T(c) superconductors-has been interpreted as either a precursor to superconductivity or as tracer of a nearby ground state that can be separated from the superconducting state by a quantum critical point. Here we report the existence of a second order parameter hidden within the superconducting phase of the underdoped (electron-doped) high-T(c) superconductor Pr2-xCe(x)CuO4-y and the newly synthesized electron-doped material La2-xCe(x)CuO4-y (ref. 8). The existence of a pseudogap when superconductivity is suppressed excludes precursor superconductivity as its origin. Our observation is consistent with the presence of a (quantum) phase transition at T = 0, which may be a key to understanding high-T(c) superconductivity. This supports the picture that the physics of high-T(c) superconductors is determined by the interplay between competing and coexisting ground states.     

Signature of optimal doping in Hall-effect measurements on a high-temperature superconductor

High-temperature superconductivity is achieved by doping copper oxide insulators with charge carriers. The density of carriers in conducting materials can be determined from measurements of the Hall voltage--the voltage transverse to the flow of the electrical current that is proportional to an applied magnetic field. In common metals, this proportionality (the Hall coefficient) is robustly temperature independent. This is in marked contrast to the behaviour seen in high-temperature superconductors when in the 'normal' (resistive) state; the departure from expected behaviour is a key signature of the unconventional nature of the normal state, the origin of which remains a central controversy in condensed matter physics. Here we report the evolution of the low-temperature Hall coefficient in the normal state as the carrier density is increased, from the onset of superconductivity and beyond (where superconductivity has been suppressed by a magnetic field). Surprisingly, the Hall coefficient does not vary monotonically with doping but rather exhibits a sharp change at the optimal doping level for superconductivity. This observation supports the idea that two competing ground states underlie the high-temperature superconducting phase.     

离子液体调控超导研究

载流子在超导材料中扮演关键角色,其浓度调控对研究超导特性及相关量子器件至关重要.然而载流子浓度通常与其他自由度相互耦合,难以做到单一物理量变化,例如,化学掺杂同时会导致晶格等发生变化.最近迅速发展的离子液体调控技术,兼具了传统的化学掺杂和场效应晶体管优点——大范围、原位、可逆地调节载流子浓度.随着这项技术的发展,逐渐演变出两类调控思路:静电场效应和电化学调控.本文从这两个方面,回顾了离子液体调控在诱导新奇超导态和调控高温超导薄膜物性上的应用:静电场效应对绝缘或半导体体系十分有效,而对于本身载流子浓度较高的材料(如高温超导体等),电化学调控则发挥了重要作用.离子液体因其强大的原位调控能力和易于与其他手段结合的特点,正逐渐成为超导研究中不可或缺的手段,在构建精确相图、突破高温超导机理等方面发挥不可替代的作用.     

Hidden magnetism and quantum criticality in the heavy fermion superconductor CeRhIn5

With only a few exceptions that are well understood, conventional superconductivity does not coexist with long-range magnetic order (for example, ref. 1). Unconventional superconductivity, on the other hand, develops near a phase boundary separating magnetically ordered and magnetically disordered phases. A maximum in the superconducting transition temperature T(c) develops where this boundary extrapolates to zero Kelvin, suggesting that fluctuations associated with this magnetic quantum-critical point are essential for unconventional superconductivity. Invariably, though, unconventional superconductivity masks the magnetic phase boundary when T < T(c), preventing proof of a magnetic quantum-critical point. Here we report specific-heat measurements of the pressure-tuned unconventional superconductor CeRhIn5 in which we find a line of quantum-phase transitions induced inside the superconducting state by an applied magnetic field. This quantum-critical line separates a phase of coexisting antiferromagnetism and superconductivity from a purely unconventional superconducting phase, and terminates at a quantum tetracritical point where the magnetic field completely suppresses superconductivity. The T --> 0 K magnetic field-pressure phase diagram of CeRhIn5 is well described with a theoretical model developed to explain field-induced magnetism in the high-T(c) copper oxides, but in which a clear delineation of quantum-phase boundaries has not been possible. These experiments establish a common relationship among hidden magnetism, quantum criticality and unconventional superconductivity in copper oxides and heavy-electron systems such as CeRhIn5.     

Diamagnetic activity above Tc as a precursor to superconductivity in La2-xSrxCuO4 thin films

Superconductors show zero resistance to electric current, and expel magnetic flux (the Meissner effect) below the transition temperature (Tc). In conventional superconductors, the 'Cooper pairs' of electrons that are responsible for superconductivity form only below Tc. In the unconventional high-Tc superconductors, however, a strong electron correlation is essential for pair formation: there is evidence that some pairs are formed above Tc in samples that have less than the optimal density of charge carriers (underdoped) and an energy gap-the 'pseudogap'-appears to be present. Moreover, excitations that look like the vortices that carry magnetic flux inside the superconducting state have been reported above Tc (refs 6, 7). Although the origin of the pseudogap remains controversial, phase fluctuations above Tc, leading to some form of local superconductivity or local pairing, seem essential. Here we report magnetic imaging (scanning SQUID microscopy) of La2-xSrxCuO4 thin films. Clear quantized vortex patterns are visible below Tc (18-19 K), and we observe inhomogeneous magnetic domains that persist up to 80 K. We interpret the data as suggesting the existence of diamagnetic regions that are precursors to the Meissner state.     

Interplay of magnetism and high-Tc superconductivity at individual Ni impurity atoms in Bi2Sr2CaCu2O8+delta.

Magnetic interactions and magnetic impurities are destructive to superconductivity in conventional superconductors. By contrast, in some unconventional macroscopic quantum systems (such as superfluid 3He and superconducting UGe2), the superconductivity (or superfluidity) is actually mediated by magnetic interactions. A magnetic mechanism has also been proposed for high-temperature superconductivity. Within this context, the fact that magnetic Ni impurity atoms have a weaker effect on superconductivity than non-magnetic Zn atoms in the high-Tc superconductors has been put forward as evidence supporting a magnetic mechanism. Here we use scanning tunnelling microscopy to determine directly the influence of individual Ni atoms on the local electronic structure of Bi2Sr2CaCu2O8+delta. At each Ni site we observe two d-wave impurity states of apparently opposite spin polarization, whose existence indicates that Ni retains a magnetic moment in the superconducting state. However, analysis of the impurity-state energies shows that quasiparticle scattering at Ni is predominantly non-magnetic. Furthermore, we show that the superconducting energy gap and correlations are unimpaired at Ni. This is in strong contrast to the effects of non-magnetic Zn impurities, which locally destroy superconductivity. These results are consistent with predictions for impurity atom phenomena derived from a magnetic mechanism.     

Crystallization of charge holes in the spin ladder of Sr14Cu24O41

Determining the nature of the electronic phases that compete with superconductivity in high-transition-temperature (high-T(c)) superconductors is one of the deepest problems in condensed matter physics. One candidate is the 'stripe' phase, in which the charge carriers (holes) condense into rivers of charge that separate regions of antiferromagnetism. A related but lesser known system is the 'spin ladder', which consists of two coupled chains of magnetic ions forming an array of rungs. A doped ladder can be thought of as a high-T(c) material with lower dimensionality, and has been predicted to exhibit both superconductivity and an insulating 'hole crystal' phase in which the carriers are localized through many-body interactions. The competition between the two resembles that believed to operate between stripes and superconductivity in high-T(c) materials. Here we report the existence of a hole crystal in the doped spin ladder of Sr14Cu24O41 using a resonant X-ray scattering technique. This phase exists without a detectable distortion in the structural lattice, indicating that it arises from many-body electronic effects. Our measurements confirm theoretical predictions, and support the picture that proximity to charge ordered states is a general property of superconductivity in copper oxides.     

Scaling the Kondo lattice

The origin of magnetic order in metals has two extremes: an instability in a liquid of local magnetic moments interacting through conduction electrons, and a spin-density wave instability in a Fermi liquid of itinerant electrons. This dichotomy between 'local-moment' magnetism and 'itinerant-electron' magnetism is reminiscent of the valence bond/molecular orbital dichotomy present in studies of chemical bonding. The class of heavy-electron intermetallic compounds of cerium, ytterbium and various 5f elements bridges the extremes, with itinerant-electron magnetic characteristics at low temperatures that grow out of a high-temperature local-moment state. Describing this transition quantitatively has proved difficult, and one of the main unsolved problems is finding what determines the temperature scale for the evolution of this behaviour. Here we present a simple, semi-quantitative solution to this problem that provides a basic framework for interpreting the physics of heavy-electron materials and offers the prospect of a quantitative determination of the physical origin of their magnetic ordering and superconductivity. It also reveals the difference between the temperature scales that distinguish the conduction electrons' response to a single magnetic impurity and their response to a lattice of local moments, and provides an updated version of the well-known Doniach diagram.     

A coherent three-dimensional Fermi surface in a high-transition-temperature superconductor

All conventional metals are known to possess a three-dimensional Fermi surface, which is the locus in reciprocal space of the long-lived electronic excitations that govern their electronic properties at low temperatures. These excitations should have well-defined momenta with components in all three dimensions. The high-transition-temperature (high-T(c)) copper oxide superconductors have unusual, highly two-dimensional properties above the superconducting transition. This, coupled with a lack of unambiguous evidence for a three-dimensional Fermi surface, has led to many new and exotic models for the underlying electronic ground state. Here we report the observation of polar angular magnetoresistance oscillations in the overdoped superconductor Tl2Ba2CuO6+delta in high magnetic fields, which firmly establishes the existence of a coherent three-dimensional Fermi surface. Analysis of the oscillations reveals that at certain symmetry points, however, this surface is strictly two-dimensional. This striking form of the Fermi surface topography, long-predicted by electronic band structure calculations, provides a natural explanation for a wide range of anisotropic properties both in the normal and superconducting states. Our data reveal that, despite their extreme electrical anisotropy, the high-T(c) materials at high doping levels can be understood within a framework of conventional three-dimensional metal physics.     

Zero-resistance states induced by electromagnetic-wave excitation in GaAs/AlGaAs heterostructures

The observation of vanishing electrical resistance in condensed matter has led to the discovery of new phenomena such as, for example, superconductivity, where a zero-resistance state can be detected in a metal below a transition temperature T(c) (ref. 1). More recently, quantum Hall effects were discovered from investigations of zero-resistance states at low temperatures and high magnetic fields in two-dimensional electron systems (2DESs). In quantum Hall systems and superconductors, zero-resistance states often coincide with the appearance of a gap in the energy spectrum. Here we report the observation of zero-resistance states and energy gaps in a surprising setting: ultrahigh-mobility GaAs/AlGaAs heterostructures that contain a 2DES exhibit vanishing diagonal resistance without Hall resistance quantization at low temperatures and low magnetic fields when the specimen is subjected to electromagnetic wave excitation. Zero-resistance-states occur about magnetic fields B = 4/5 Bf and B = 4/9 Bf, where Bf = 2pifm*/e,m* is the electron mass, e is the electron charge, and f is the electromagnetic-wave frequency. Activated transport measurements on the resistance minima also indicate an energy gap at the Fermi level. The results suggest an unexpected radiation-induced, electronic-state-transition in the GaAs/AlGaAs 2DES.     

A topological Dirac insulator in a quantum spin Hall phase

When electrons are subject to a large external magnetic field, the conventional charge quantum Hall effect dictates that an electronic excitation gap is generated in the sample bulk, but metallic conduction is permitted at the boundary. Recent theoretical models suggest that certain bulk insulators with large spin-orbit interactions may also naturally support conducting topological boundary states in the quantum limit, which opens up the possibility for studying unusual quantum Hall-like phenomena in zero external magnetic fields. Bulk Bi(1-x)Sb(x) single crystals are predicted to be prime candidates for one such unusual Hall phase of matter known as the topological insulator. The hallmark of a topological insulator is the existence of metallic surface states that are higher-dimensional analogues of the edge states that characterize a quantum spin Hall insulator. In addition to its interesting boundary states, the bulk of Bi(1-x)Sb(x) is predicted to exhibit three-dimensional Dirac particles, another topic of heightened current interest following the new findings in two-dimensional graphene and charge quantum Hall fractionalization observed in pure bismuth. However, despite numerous transport and magnetic measurements on the Bi(1-x)Sb(x) family since the 1960s, no direct evidence of either topological Hall states or bulk Dirac particles has been found. Here, using incident-photon-energy-modulated angle-resolved photoemission spectroscopy (IPEM-ARPES), we report the direct observation of massive Dirac particles in the bulk of Bi(0.9)Sb(0.1), locate the Kramers points at the sample's boundary and provide a comprehensive mapping of the Dirac insulator's gapless surface electron bands. These findings taken together suggest that the observed surface state on the boundary of the bulk insulator is a realization of the 'topological metal'. They also suggest that this material has potential application in developing next-generation quantum computing devices that may incorporate 'light-like' bulk carriers and spin-textured surface currents.     

Antiferromagnetic order as the competing ground state in electron-doped Nd1.85Ce0.15CuO4

Superconductivity in the high-transition-temperature (high-T(c)) copper oxides competes with other possible ground states. The physical explanation for superconductivity can be constrained by determining the nature of the closest competing ground state, and establishing if that state is universal among the high-T(c) materials. Antiferromagnetism has been theoretically predicted to be the competing ground state. A competing ground state is revealed when superconductivity is destroyed by the application of a magnetic field, and antiferromagnetism has been observed in hole-doped materials under the influence of modest fields. None of the previous experiments have revealed the quantum phase transition from the superconducting state to the antiferromagnetic state, because they failed to reach the upper critical field B(c2). Here we report the results of transport and neutron-scattering experiments on electron-doped Nd1.85Ce0.15CuO4 (refs 13, 14), where B(c2) can be reached. The applied field reveals a static, commensurate, anomalously conducting long-range ordered antiferromagnetic state, in which the induced moment scales approximately linearly with the field strength until it saturates at B(c2). This and previous experiments on the hole-doped materials therefore establishes antiferromagnetic order as a competing ground state in the high-T(c) copper oxide materials, irrespective of electron or hole doping.     

Spin correlations in the electron-doped high-transition-temperature superconductor Nd2-xCexCuO4+/-delta

High-transition-temperature (high-T(c)) superconductivity develops near antiferromagnetic phases, and it is possible that magnetic excitations contribute to the superconducting pairing mechanism. To assess the role of antiferromagnetism, it is essential to understand the doping and temperature dependence of the two-dimensional antiferromagnetic spin correlations. The phase diagram is asymmetric with respect to electron and hole doping, and for the comparatively less-studied electron-doped materials, the antiferromagnetic phase extends much further with doping and appears to overlap with the superconducting phase. The archetypal electron-doped compound Nd2-xCexCuO4+/-delta (NCCO) shows bulk superconductivity above x approximately 0.13 (refs 3, 4), while evidence for antiferromagnetic order has been found up to x approximately 0.17 (refs 2, 5, 6). Here we report inelastic magnetic neutron-scattering measurements that point to the distinct possibility that genuine long-range antiferromagnetism and superconductivity do not coexist. The data reveal a magnetic quantum critical point where superconductivity first appears, consistent with an exotic quantum phase transition between the two phases. We also demonstrate that the pseudogap phenomenon in the electron-doped materials, which is associated with pronounced charge anomalies, arises from a build-up of spin correlations, in agreement with recent theoretical proposals.     

Designer Dirac fermions and topological phases in molecular graphene

The observation of massless Dirac fermions in monolayer graphene has generated a new area of science and technology seeking to harness charge carriers that behave relativistically within solid-state materials. Both massless and massive Dirac fermions have been studied and proposed in a growing class of Dirac materials that includes bilayer graphene, surface states of topological insulators and iron-based high-temperature superconductors. Because the accessibility of this physics is predicated on the synthesis of new materials, the quest for Dirac quasi-particles has expanded to artificial systems such as lattices comprising ultracold atoms. Here we report the emergence of Dirac fermions in a fully tunable condensed-matter system-molecular graphene-assembled by atomic manipulation of carbon monoxide molecules over a conventional two-dimensional electron system at a copper surface. Using low-temperature scanning tunnelling microscopy and spectroscopy, we embed the symmetries underlying the two-dimensional Dirac equation into electron lattices, and then visualize and shape the resulting ground states. These experiments show the existence within the system of linearly dispersing, massless quasi-particles accompanied by a density of states characteristic of graphene. We then tune the quantum tunnelling between lattice sites locally to adjust the phase accrual of propagating electrons. Spatial texturing of lattice distortions produces atomically sharp p-n and p-n-p junction devices with two-dimensional control of Dirac fermion density and the power to endow Dirac particles with mass. Moreover, we apply scalar and vector potentials locally and globally to engender topologically distinct ground states and, ultimately, embedded gauge fields, wherein Dirac electrons react to 'pseudo' electric and magnetic fields present in their reference frame but absent from the laboratory frame. We demonstrate that Landau levels created by these gauge fields can be taken to the relativistic magnetic quantum limit, which has so far been inaccessible in natural graphene. Molecular graphene provides a versatile means of synthesizing exotic topological electronic phases in condensed matter using tailored nanostructures.     

Probing carrier dynamics in nanostructures by picosecond cathodoluminescence

Picosecond and femtosecond spectroscopy allow the detailed study of carrier dynamics in nanostructured materials. In such experiments, a laser pulse normally excites several nanostructures at once. However, spectroscopic information may also be acquired using pulses from an electron beam in a modern electron microscope, exploiting a phenomenon called cathodoluminescence. This approach offers several advantages. The multimode imaging capabilities of the electron microscope enable the correlation of optical properties (via cathodoluminescence) with surface morphology (secondary electron mode) at the nanometre scale. The broad energy range of the electrons can excite wide-bandgap materials, such as diamond- or gallium-nitride-based structures that are not easily excited by conventional optical means. But perhaps most intriguingly, the small beam can probe a single selected nanostructure. Here we apply an original time-resolved cathodoluminescence set-up to describe carrier dynamics within single gallium-arsenide-based pyramidal nanostructures with a time resolution of 10 picoseconds and a spatial resolution of 50 nanometres. The behaviour of such charge carriers could be useful for evaluating elementary components in quantum computers, optical quantum gates or single photon sources for quantum cryptography.     

Scanning-tunnelling spectra of cuprates

The study of bosonic modes that couple to the charge carriers is a key element in understanding superconductivity. Using atomic-resolution scanning-tunnelling microscopy (STM) to extract the spectrum of these modes in the high-temperature superconductor Bi2Sr2CaCu2O(8+delta), Lee et al. find a mode whose frequency does not depend on doping but that changes on isotopic substitution of 16O with 18O. From this, they infer a role for lattice modes (phonons). However, examination of their data reveals a weaker, but distinct, feature that has all the characteristics of the magnetic excitation identified as the bosonic mode in other competing experiments. We therefore suggest that the lattice mode seen by Lee et al. is not relevant to superconductivity and is due to inelastic tunnelling through the insulating oxide layer.