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.     

Quantum phase transition in a resonant level coupled to interacting leads

A Luttinger liquid is an interacting one-dimensional electronic system, quite distinct from the 'conventional' Fermi liquids formed by interacting electrons in two and three dimensions. Some of the most striking properties of Luttinger liquids are revealed in the process of electron tunnelling. For example, as a function of the applied bias voltage or temperature, the tunnelling current exhibits a non-trivial power-law suppression. (There is no such suppression in a conventional Fermi liquid.) Here, using a carbon nanotube connected to resistive leads, we create a system that emulates tunnelling in a Luttinger liquid, by controlling the interaction of the tunnelling electron with its environment. We further replace a single tunnelling barrier with a double-barrier, resonant-level structure and investigate resonant tunnelling between Luttinger liquids. At low temperatures, we observe perfect transparency of the resonant level embedded in the interacting environment, and the width of the resonance tends to zero. We argue that this behaviour results from many-body physics of interacting electrons, and signals the presence of a quantum phase transition. Given that many parameters, including the interaction strength, can be precisely controlled in our samples, this is an attractive model system for studying quantum critical phenomena in general, with wide-reaching implications for understanding quantum phase transitions in more complex systems, such as cold atoms and strongly correlated bulk materials.     

Evidence for spin-charge separation in quasi-one-dimensional organic conductors

Interacting conduction electrons are usually described within Fermi-liquid theory, which states that, in spite of strong interactions, the low-energy excitations are electron-like quasiparticles with charge and spin. In recent years there has been tremendous interest in conducting systems that are not Fermi liquids, motivated by the observation of highly anomalous metallic states in various materials, most notably the copper oxide superconductors. Non-Fermi-liquid behaviour is generic to one-dimensional interacting electron systems, which are predicted to be Luttinger liquids. One of their key properties is spin-charge separation: instead of quasiparticles, collective excitations of charge (with no spin) and spin (with no charge) are formed, which move independently and at different velocities. However, experimental confirmation of spin-charge separation remains a challenge. Here we report experiments probing the charge and heat current in quasi-one-dimensional conductors--the organic Bechgaard salts. It was found that the charge and spin excitations have distinctly different thermal conductivities, which gives strong evidence for spin-charge separation. The spin excitations have a much larger thermal conductivity than the charge excitations, which indicates that the coupling of the charge excitations to the lattice is important.     

Antiferromagnetic order induced by an applied magnetic field in a high-temperature superconductor.

One view of the high-transition-temperature (high-Tc) copper oxide superconductors is that they are conventional superconductors where the pairing occurs between weakly interacting quasiparticles (corresponding to the electrons in ordinary metals), although the theory has to be pushed to its limit. An alternative view is that the electrons organize into collective textures (for example, charge and spin stripes) which cannot be 'mapped' onto the electrons in ordinary metals. Understanding the properties of the material would then need quantum field theories of objects such as textures and strings, rather than point-like electrons. In an external magnetic field, magnetic flux penetrates type II superconductors via vortices, each carrying one flux quantum. The vortices form lattices of resistive material embedded in the non-resistive superconductor, and can reveal the nature of the ground state-for example, a conventional metal or an ordered, striped phase-which would have appeared had superconductivity not intervened, and which provides the best starting point for a pairing theory. Here we report that for one high-Tc superconductor, the applied field that imposes the vortex lattice also induces 'striped' antiferromagnetic order. Ordinary quasiparticle models can account for neither the strength of the order nor the nearly field-independent antiferromagnetic transition temperature observed in our measurements.     

Direct observation of Tomonaga-Luttinger-liquid state in carbon nanotubes at low temperatures

The electronic transport properties of conventional three-dimensional metals are successfully described by Fermi-liquid theory. But when the dimensionality of such a system is reduced to one, the Fermi-liquid state becomes unstable to Coulomb interactions, and the conduction electrons should instead behave according to Tomonaga-Luttinger-liquid (TLL) theory. Such a state reveals itself through interaction-dependent anomalous exponents in the correlation functions, density of states and momentum distribution of the electrons. Metallic single-walled carbon nanotubes (SWNTs) are considered to be ideal one-dimensional systems for realizing TLL states. Indeed, the results of transport measurements on metal-SWNT and SWNT-SWNT junctions have been attributed to the effects of tunnelling into or between TLLs, although there remains some ambiguity in these interpretations. Direct observations of the electronic states in SWNTs are therefore needed to resolve these uncertainties. Here we report angle-integrated photoemission measurements of SWNTs. Our results reveal an oscillation in the pi-electron density of states owing to one-dimensional van Hove singularities, confirming the one-dimensional nature of the valence band. The spectral function and intensities at the Fermi level both exhibit power-law behaviour (with almost identical exponents) in good agreement with theoretical predictions for the TLL state in SWNTs.     

Hall-effect evolution across a heavy-fermion quantum critical point

A quantum critical point (QCP) develops in a material at absolute zero when a new form of order smoothly emerges in its ground state. QCPs are of great current interest because of their singular ability to influence the finite temperature properties of materials. Recently, heavy-fermion metals have played a key role in the study of antiferromagnetic QCPs. To accommodate the heavy electrons, the Fermi surface of the heavy-fermion paramagnet is larger than that of an antiferromagnet. An important unsolved question is whether the Fermi surface transformation at the QCP develops gradually, as expected if the magnetism is of spin-density-wave (SDW) type, or suddenly, as expected if the heavy electrons are abruptly localized by magnetism. Here we report measurements of the low-temperature Hall coefficient (R(H))--a measure of the Fermi surface volume--in the heavy-fermion metal YbRh2Si2 upon field-tuning it from an antiferromagnetic to a paramagnetic state. R(H) undergoes an increasingly rapid change near the QCP as the temperature is lowered, extrapolating to a sudden jump in the zero temperature limit. We interpret these results in terms of a collapse of the large Fermi surface and of the heavy-fermion state itself precisely at the QCP.     

Dimensional reduction at a quantum critical point

Competition between electronic ground states near a quantum critical point (QCP)--the location of a zero-temperature phase transition driven solely by quantum-mechanical fluctuations--is expected to lead to unconventional behaviour in low-dimensional systems. New electronic phases of matter have been predicted to occur in the vicinity of a QCP by two-dimensional theories, and explanations based on these ideas have been proposed for significant unsolved problems in condensed-matter physics, such as non-Fermi-liquid behaviour and high-temperature superconductivity. But the real materials to which these ideas have been applied are usually rendered three-dimensional by a finite electronic coupling between their component layers; a two-dimensional QCP has not been experimentally observed in any bulk three-dimensional system, and mechanisms for dimensional reduction have remained the subject of theoretical conjecture. Here we show evidence that the Bose-Einstein condensate of spin triplets in the three-dimensional Mott insulator BaCuSi2O6 (refs 12-16) provides an experimentally verifiable example of dimensional reduction at a QCP. The interplay of correlations on a geometrically frustrated lattice causes the individual two-dimensional layers of spin-(1/2) Cu2+ pairs (spin dimers) to become decoupled at the QCP, giving rise to a two-dimensional QCP characterized by linear power law scaling distinctly different from that of its three-dimensional counterpart. Thus the very notion of dimensionality can be said to acquire an 'emergent' nature: although the individual particles move on a three-dimensional lattice, their collective behaviour occurs in lower-dimensional space.     

二维正方格子自由电子气的费米面

在当前的固体物理学教材中，对费米面构造都没有详细阐述，费米面附近的电子对金属的性质有重要影响，了解和掌握费米面的概念以及距布里渊区边界多远的问题是对金属中电子的物理特性获得深刻理解的一个根本问题。针对上述问题，系统地介绍了二维正方格子自由电子气费米面的构图方法以及费米面和布里渊区的关系。     

Observation of a roton collective mode in a two-dimensional Fermi liquid

Understanding the dynamics of correlated many-body quantum systems is a challenge for modern physics. Owing to the simplicity of their Hamiltonians, (4)He (bosons) and (3)He (fermions) have served as model systems for strongly interacting quantum fluids, with substantial efforts devoted to their understanding. An important milestone was the direct observation of the collective phonon-roton mode in liquid (4)He by neutron scattering, verifying Landau's prediction and his fruitful concept of elementary excitations. In a Fermi system, collective density fluctuations (known as 'zero-sound' in (3)He, and 'plasmons' in charged systems) and incoherent particle-hole excitations are observed. At small wavevectors and energies, both types of excitation are described by Landau's theory of Fermi liquids. At higher wavevectors, the collective mode enters the particle-hole band, where it is strongly damped. The dynamics of Fermi liquids at high wavevectors was thus believed to be essentially incoherent. Here we report inelastic neutron scattering measurements of a monolayer of liquid (3)He, observing a roton-like excitation. We find that the collective density mode reappears as a well defined excitation at momentum transfers larger than twice the Fermi momentum. We thus observe unexpected collective behaviour of a Fermi many-body system in the regime beyond the scope of Landau's theory. A satisfactory interpretation of the measured spectra is obtained using a dynamic many-body theory.     

Strong coupling between local moments and superconducting 'heavy' electrons in UPd2Al3

The electronic structure of heavy-fermion compounds arises from the interaction of nearly localized 4f- or 5f-shell electrons (with atomic magnetic moments) with the free-electron-like itinerant conduction-band electrons. In actinide or rare-earth heavy-fermion materials, this interaction yields itinerant electrons having an effective mass about 100 times (or more) the bare electron mass. Moreover, the itinerant electrons in UPd2Al3 are found to be superconducting well below the magnetic ordering temperature of this compound, whereas magnetism generally suppresses superconductivity in conventional metals. Here we report the detection of a dispersive excitation of the ordered f-electron moments, which shows a strong interaction with the heavy superconducting electrons. This 'magnetic exciton' is a localized excitation which moves through the lattice as a result of exchange forces between the magnetic moments. By combining this observation with previous tunnelling measurements on this material, we argue that these magnetic excitons may produce effective interactions between the itinerant electrons, and so be responsible for superconductivity in a manner analogous to the role played by phonons in conventional superconductors.     

High-resolution spectroscopy of two-dimensional electron systems

Spectroscopic methods involving the sudden injection or ejection of electrons in materials are a powerful probe of electronic structure and interactions. These techniques, such as photoemission and tunnelling, yield measurements of the 'single-particle' density of states spectrum of a system. This density of states is proportional to the probability of successfully injecting or ejecting an electron in these experiments. It is equal to the number of electronic states in the system able to accept an injected electron as a function of its energy, and is among the most fundamental and directly calculable quantities in theories of highly interacting systems. However, the two-dimensional electron system (2DES), host to remarkable correlated electron states such as the fractional quantum Hall effect, has proved difficult to probe spectroscopically. Here we present an improved version of time-domain capacitance spectroscopy that allows us to measure the single-particle density of states of a 2DES with unprecedented fidelity and resolution. Using the method, we perform measurements of a cold 2DES, providing direct measurements of interesting correlated electronic effects at energies that are difficult to reach with other techniques; these effects include the single-particle exchange-enhanced spin gap, single-particle lifetimes in the quantum Hall system, and exchange splitting of Landau levels not at the Fermi surface.     

Lanthanide contraction and magnetism in the heavy rare earth elements

The heavy rare earth elements crystallize into hexagonally close packed (h.c.p.) structures and share a common outer electronic configuration, differing only in the number of 4f electrons they have. These chemically inert 4f electrons set up localized magnetic moments, which are coupled via an indirect exchange interaction involving the conduction electrons. This leads to the formation of a wide variety of magnetic structures, the periodicities of which are often incommensurate with the underlying crystal lattice. Such incommensurate ordering is associated with a 'webbed' topology of the momentum space surface separating the occupied and unoccupied electron states (the Fermi surface). The shape of this surface-and hence the magnetic structure-for the heavy rare earth elements is known to depend on the ratio of the interplanar spacing c and the interatomic, intraplanar spacing a of the h.c.p. lattice. A theoretical understanding of this problem is, however, far from complete. Here, using gadolinium as a prototype for all the heavy rare earth elements, we generate a unified magnetic phase diagram, which unequivocally links the magnetic structures of the heavy rare earths to their lattice parameters. In addition to verifying the importance of the c/a ratio, we find that the atomic unit cell volume plays a separate, distinct role in determining the magnetic properties: we show that the trend from ferromagnetism to incommensurate ordering as atomic number increases is connected to the concomitant decrease in unit cell volume. This volume decrease occurs because of the so-called lanthanide contraction, where the addition of electrons to the poorly shielding 4f orbitals leads to an increase in effective nuclear charge and, correspondingly, a decrease in ionic radii.     

Ni-Co固溶体合金价电子结构分析——Co在合金中作用的初步探讨

本文应用经验电子理论,对工业范围内(Co含量<25％)的Ni—Co固溶体合金的价电子结构进行计算,给出了价电子结构分布参数(键共价电子对数、共价电子总数、晶格电子总数)。计算的理论键距、理论磁距与实验值符合得很好。本文还初步探讨了Ni基高温合金中加Co的微观本质。为进一步研究合金的宏观物理、化学性质提供了微观资料。     

Evidence for ubiquitous strong electron-phonon coupling in high-temperature superconductors

Coupling between electrons and phonons (lattice vibrations) drives the formation of the electron pairs responsible for conventional superconductivity. The lack of direct evidence for electron-phonon coupling in the electron dynamics of the high-transition-temperature superconductors has driven an intensive search for an alternative mechanism. A coupling of an electron with a phonon would result in an abrupt change of its velocity and scattering rate near the phonon energy. Here we use angle-resolved photoemission spectroscopy to probe electron dynamics-velocity and scattering rate-for three different families of copper oxide superconductors. We see in all of these materials an abrupt change of electron velocity at 50-80 meV, which we cannot explain by any known process other than to invoke coupling with the phonons associated with the movement of the oxygen atoms. This suggests that electron-phonon coupling strongly influences the electron dynamics in the high-temperature superconductors, and must therefore be included in any microscopic theory of superconductivity.     

大电流弧光放电机理讨论

用电磁学理论结合能带理论讨论了弧光放电机理问题,认为在大电流的条件下,电极上能够产生大量的焦耳热使得阴极上的自由电子在晶格势场中的能态升高;由于大电流可以使得大量载流子参与定向运动,当电极断开时,大量载流子的定向运动动能转化为阴极上自由电子在晶格势场中的电势能,进一步升高阴极上自由电子在晶格势场中的能态;由于大电流使得阴极上聚集的自由电子数量巨大,从而在阳极和阴极间产生强电场,在两极间强电场的作用下,可以产生场致发射。解释了弧光放电过程申的负伏安特性;分析了弧光放电过程,比较了热电子发射和场致发射的联系与区别。     

Emergence of preformed Cooper pairs from the doped Mott insulating state in Bi2Sr2CaCu2O8+delta

Superconductors are characterized by an energy gap that represents the energy needed to break the pairs of electrons (Cooper pairs) apart. At temperatures considerably above those associated with superconductivity, the high-transition-temperature copper oxides have an additional 'pseudogap'. It has been unclear whether this represents preformed pairs of electrons that have not achieved the coherence necessary for superconductivity, or whether it reflects some alternative ground state that competes with superconductivity. Paired electrons should display particle-hole symmetry with respect to the Fermi level (the energy of the highest occupied level in the electronic system), but competing states need not show such symmetry. Here we report a photoemission study of the underdoped copper oxide Bi(2)Sr(2)CaCu(2)O(8+delta) that shows the opening of a symmetric gap only in the anti-nodal region, contrary to the expectation that pairing would take place in the nodal region. It is therefore evident that the pseudogap does reflect the formation of preformed pairs of electrons and that the pairing occurs only in well-defined directions of the underlying lattice.     

Electronic and structural transitions in dense liquid sodium

At ambient conditions, the light alkali metals are free-electron-like crystals with a highly symmetric structure. However, they were found recently to exhibit unexpected complexity under pressure. It was predicted from theory--and later confirmed by experiment--that lithium and sodium undergo a sequence of symmetry-breaking transitions, driven by a Peierls mechanism, at high pressures. Measurements of the sodium melting curve have subsequently revealed an unprecedented (and still unexplained) pressure-induced drop in melting temperature from 1,000 K at 30 GPa down to room temperature at 120 GPa. Here we report results from ab initio calculations that explain the unusual melting behaviour in dense sodium. We show that molten sodium undergoes a series of pressure-induced structural and electronic transitions, analogous to those observed in solid sodium but commencing at much lower pressure in the presence of liquid disorder. As pressure is increased, liquid sodium initially evolves by assuming a more compact local structure. However, a transition to a lower-coordinated liquid takes place at a pressure of around 65 GPa, accompanied by a threefold drop in electrical conductivity. This transition is driven by the opening of a pseudogap, at the Fermi level, in the electronic density of states--an effect that has not hitherto been observed in a liquid metal. The lower-coordinated liquid emerges at high temperatures and above the stability region of a close-packed free-electron-like metal. We predict that similar exotic behaviour is possible in other materials as well.     

Attractive and repulsive Fermi polarons in two dimensions

The dynamics of a single impurity in an environment is a fundamental problem in many-body physics. In the solid state, a well known case is an impurity coupled to a bosonic bath (such as lattice vibrations); the impurity and its accompanying lattice distortion form a new entity, a polaron. This quasiparticle plays an important role in the spectral function of high-transition-temperature superconductors, as well as in colossal magnetoresistance in manganites. For impurities in a fermionic bath, studies have considered heavy or immobile impurities which exhibit Anderson's orthogonality catastrophe and the Kondo effect. More recently, mobile impurities have moved into the focus of research, and they have been found to form new quasiparticles known as Fermi polarons. The Fermi polaron problem constitutes the extreme, but conceptually simple, limit of two important quantum many-body problems: the crossover between a molecular Bose-Einstein condensate and a superfluid with BCS (Bardeen-Cooper-Schrieffer) pairing with spin-imbalance for attractive interactions, and Stoner's itinerant ferromagnetism for repulsive interactions. It has been proposed that such quantum phases (and other elusive exotic states) might become realizable in Fermi gases confined to two dimensions. Their stability and observability are intimately related to the theoretically debated properties of the Fermi polaron in a two-dimensional Fermi gas. Here we create and investigate Fermi polarons in a two-dimensional, spin-imbalanced Fermi gas, measuring their spectral function using momentum-resolved photoemission spectroscopy. For attractive interactions, we find evidence for a disputed pairing transition between polarons and tightly bound dimers, which provides insight into the elementary pairing mechanism of imbalanced, strongly coupled two-dimensional Fermi gases. Additionally, for repulsive interactions, we study novel quasiparticles--repulsive polarons--the lifetime of which determines the possibility of stabilizing repulsively interacting Fermi systems.