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.     

Cyclotron resonance of composite fermions.

It is occasionally possible to interpret strongly interacting many-body systems within a single-particle framework by introducing suitable fictitious entities, or 'quasi-particles'. A notable recent example of the successful application of such an approach is for a two-dimensional electron system that is exposed to a strong perpendicular magnetic field. The conduction properties of the system are governed by electron-electron interactions, which cause the fractional quantum Hall effect. Composite fermions, electrons that are dressed with magnetic flux quanta pointing opposite to the applied magnetic field, were identified as apposite quasi-particles that simplify our understanding of the fractional quantum Hall effect. They precess, like electrons, along circular cyclotron orbits, but with a diameter determined by a reduced effective magnetic field. The frequency of their cyclotron motion has hitherto remained enigmatic, as the effective mass is no longer related to the band mass of the original electrons and is entirely generated from electron-electron interactions. Here we demonstrate enhanced absorption of a microwave field in the composite fermion regime, and interpret it as a resonance with the frequency of their circular motion. From this inferred cyclotron resonance, we derive a composite fermion effective mass that varies from 0.7 to 1.2 times that of the electron mass in vacuum as their density is tuned from 0.6 x 10(11) cm(-2) to 1.2 x 10(11) cm(-2).     

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.     

Emerging local Kondo screening and spatial coherence in the heavy-fermion metal YbRh2Si2

The entanglement of quantum states is both a central concept in fundamental physics and a potential tool for realizing advanced materials and applications. The quantum superpositions underlying entanglement are at the heart of the intricate interplay of localized spin states and itinerant electronic states that gives rise to the Kondo effect in certain dilute magnetic alloys. In systems where the density of localized spin states is sufficiently high, they can no longer be treated as non-interacting; if they form a dense periodic array, a Kondo lattice may be established. Such a Kondo lattice gives rise to the emergence of charge carriers with enhanced effective masses, but the precise nature of the coherent Kondo state responsible for the generation of these heavy fermions remains highly debated. Here we use atomic-resolution tunnelling spectroscopy to investigate the low-energy excitations of a generic Kondo lattice system, YbRh(2)Si(2). We find that the hybridization of the conduction electrons with the localized 4f electrons results in a decrease in the tunnelling conductance at the Fermi energy. In addition, we observe unambiguously the crystal-field excitations of the Yb(3+) ions. A strongly temperature-dependent peak in the tunnelling conductance is attributed to the Fano resonance resulting from tunnelling into the coherent heavy-fermion states that emerge at low temperature. Taken together, these features reveal how quantum coherence develops in heavy 4f-electron Kondo lattices. Our results demonstrate the efficiency of real-space electronic structure imaging for the investigation of strong electronic correlations, specifically with respect to coherence phenomena, phase coexistence and quantum criticality.     

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.     

拓扑绝缘体量子点中的磁交换相互作用

从理论上研究了拓扑绝缘体量子点中的磁交换相互作用.在拓扑绝缘体量子点中,边缘态电子数可以通过量子点的尺寸和外加电场进行调控.当量子点中掺入单个磁离子并且边缘态填充奇数电子时,电子与单个磁离子之间的交换相互作用达到最大值;而边缘态填充偶数电子时,电子与单个磁离子之间的交换相互作用消失.当量子点中掺入2个磁离子时,电子与Mn离子的sp-d相互作用会出现奇偶振荡行为,Mn离子间的相互作用取决于Mn离子间距和量子点壳层中的电子数,表现出典型的Ruderman-Kittel-Kasuya-Yosida型间接交换机制.工作澄清了拓扑绝缘体量子点壳层结构对其磁性的影响,有助于人们设计基于拓扑绝缘体量子点的自旋电子学或量子信息器件.     

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.     

An electronic Mach-Zehnder interferometer

Double-slit electron interferometers fabricated in high mobility two-dimensional electron gases are powerful tools for studying coherent wave-like phenomena in mesoscopic systems. However, they suffer from low visibility of the interference patterns due to the many channels present in each slit, and from poor sensitivity to small currents due to their open geometry. Moreover, these interferometers do not function in high magnetic fields--such as those required to enter the quantum Hall effect regime--as the field destroys the symmetry between left and right slits. Here we report the fabrication and operation of a single-channel, two-path electron interferometer that functions in a high magnetic field. This device is the first electronic analogue of the optical Mach-Zehnder interferometer, and opens the way to measuring interference of quasiparticles with fractional charges. On the basis of measurements of single edge state and closed geometry transport in the quantum Hall effect regime, we find that the interferometer is highly sensitive and exhibits very high visibility (62%). However, the interference pattern decays precipitously with increasing electron temperature or energy. Although the origin of this dephasing is unclear, we show, via shot-noise measurements, that it is not a decoherence process that results from inelastic scattering events.     

Experimental observation of the quantum Hall effect and Berry's phase in graphene

When electrons are confined in two-dimensional materials, quantum-mechanically enhanced transport phenomena such as the quantum Hall effect can be observed. Graphene, consisting of an isolated single atomic layer of graphite, is an ideal realization of such a two-dimensional system. However, its behaviour is expected to differ markedly from the well-studied case of quantum wells in conventional semiconductor interfaces. This difference arises from the unique electronic properties of graphene, which exhibits electron-hole degeneracy and vanishing carrier mass near the point of charge neutrality. Indeed, a distinctive half-integer quantum Hall effect has been predicted theoretically, as has the existence of a non-zero Berry's phase (a geometric quantum phase) of the electron wavefunction--a consequence of the exceptional topology of the graphene band structure. Recent advances in micromechanical extraction and fabrication techniques for graphite structures now permit such exotic two-dimensional electron systems to be probed experimentally. Here we report an experimental investigation of magneto-transport in a high-mobility single layer of graphene. Adjusting the chemical potential with the use of the electric field effect, we observe an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene. The relevance of Berry's phase to these experiments is confirmed by magneto-oscillations. In addition to their purely scientific interest, these unusual quantum transport phenomena may lead to new applications in carbon-based electronic and magneto-electronic devices.     

Electron dynamics in collisionless magnetic reconnection

Magnetic reconnection provides a physical mechanism for fast energy conversion from magnetic energy to plasma kinetic energy. It is closely associated with many explosive phenomena in space plasma, usually collisionless in character. For this reason, researchers have become more interested in collisionless magnetic reconnection. In this paper, the various roles of electron dynamics in collisionless magnetic reconnection are reviewed. First, at the ion inertial length scale, ions and electrons are decoupled. The resulting Hall effect determines the reconnection electric field. Moreover, electron motions determine the current system inside the reconnection plane and the electron density cavity along the separatrices. The current system in this plane produces an out-of-plane magnetic field. Second, at the electron inertial length scale, the anisotropy of electron pressure determines the magnitude of the reconnection electric field in this region. The production of energetic electrons, which is an important characteristic during magnetic reconnection, is accelerated by the reconnection electric field. In addition, the different topologies, temporal evolution and spatial distribution of the magnetic field affect the accelerating process of electrons and determine the final energy of the accelerated electrons. Third, we discuss results from simulations and spacecraft observations on the secondary magnetic islands produced due to secondary instabilities around the X point, and the associated energetic electrons. Furthermore, progress in laboratory plasma studies is also discussed in regard to electron dynamics during magnetic reconnection. Finally, some unresolved problems are presented.     

The microscopic nature of localization in the quantum Hall effect

The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the electronic transport properties owing to particle localization. In the conventional theory of the quantum Hall effect, strong-field localization is associated with a single-particle drift motion of electrons along contours of constant disorder potential. Transport experiments that probe the extended states in the transition regions between quantum Hall phases have been used to test both the theory and its implications for quantum Hall phase transitions. Although several experiments on highly disordered samples have affirmed the validity of the single-particle picture, other experiments and some recent theories have found deviations from the predicted universal behaviour. Here we use a scanning single-electron transistor to probe the individual localized states, which we find to be strikingly different from the predictions of single-particle theory. The states are mainly determined by Coulomb interactions, and appear only when quantization of kinetic energy limits the screening ability of electrons. We conclude that the quantum Hall effect has a greater diversity of regimes and phase transitions than predicted by the single-particle framework. Our experiments suggest a unified picture of localization in which the single-particle model is valid only in the limit of strong disorder.     

Imaging of localized electronic states in the quantum Hall regime

The concept of electron localization has long been accepted to be essential to the physics of the quantum Hall effect in a two-dimensional electron gas. The exact quantization of the Hall resistance and the zero of the diagonal resistance over a range of filling factors close to integral are attributed to the localization of electronic states at the Fermi level in the interior of the gas. As the electron density is changed, charging of the individual localized states may occur by single-electron jumps, causing associated oscillations in the local electrostatic potential. Here we search for such a manifestation of localized states in the quantum Hall regime, using a scanning electrometer probe. We observe localized potential signals, at numerous locations, that oscillate with changing electron density. In general, the corresponding spatial patterns are complex, but well-defined objects are often seen which evidently arise from individual localized states. These objects interact, and at times form a lattice-like arrangement.     

Electrons surfing on a sound wave as a platform for quantum optics with flying electrons

Electrons in a metal are indistinguishable particles that interact strongly with other electrons and their environment. Isolating and detecting a single flying electron after propagation, in a similar manner to quantum optics experiments with single photons, is therefore a challenging task. So far only a few experiments have been performed in a high-mobility two-dimensional electron gas in which the electron propagates almost ballistically. In these previous works, flying electrons were detected by means of the current generated by an ensemble of electrons, and electron correlations were encrypted in the current noise. Here we demonstrate the experimental realization of high-efficiency single-electron source and detector for a single electron propagating isolated from the other electrons through a one-dimensional channel. The moving potential is excited by a surface acoustic wave, which carries the single electron along the one-dimensional channel at a speed of 3 μm ns(-1). When this quantum channel is placed between two quantum dots several micrometres apart, a single electron can be transported from one quantum dot to the other with quantum efficiencies of emission and detection of 96% and 92%, respectively. Furthermore, the transfer of the electron can be triggered on a timescale shorter than the coherence time T(2)* of GaAs spin qubits. Our work opens new avenues with which to study the teleportation of a single electron spin and the distant interaction between spatially separated qubits in a condensed-matter system.     

Direct electronic measurement of the spin Hall effect

The generation, manipulation and detection of spin-polarized electrons in nanostructures define the main challenges of spin-based electronics. Among the different approaches for spin generation and manipulation, spin-orbit coupling--which couples the spin of an electron to its momentum--is attracting considerable interest. In a spin-orbit-coupled system, a non-zero spin current is predicted in a direction perpendicular to the applied electric field, giving rise to a spin Hall effect. Consistent with this effect, electrically induced spin polarization was recently detected by optical techniques at the edges of a semiconductor channel and in two-dimensional electron gases in semiconductor heterostructures. Here we report electrical measurements of the spin Hall effect in a diffusive metallic conductor, using a ferromagnetic electrode in combination with a tunnel barrier to inject a spin-polarized current. In our devices, we observe an induced voltage that results exclusively from the conversion of the injected spin current into charge imbalance through the spin Hall effect. Such a voltage is proportional to the component of the injected spins that is perpendicular to the plane defined by the spin current direction and the voltage probes. These experiments reveal opportunities for efficient spin detection without the need for magnetic materials, which could lead to useful spintronics devices that integrate information processing and data storage.     

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.     

Measurement of the quantum of thermal conductance

The physics of mesoscopic electronic systems has been explored for more than 15 years. Mesoscopic phenomena in transport processes occur when the wavelength or the coherence length of the carriers becomes comparable to, or larger than, the sample dimensions. One striking result in this domain is the quantization of electrical conduction, observed in a quasi-one-dimensional constriction formed between reservoirs of two-dimensional electron gas. The conductance of this system is determined by the number of participating quantum states or 'channels' within the constriction; in the ideal case, each spin-degenerate channel contributes a quantized unit of 2e(2)/h to the electrical conductance. It has been speculated that similar behaviour should be observable for thermal transport in mesoscopic phonon systems. But experiments attempted in this regime have so far yielded inconclusive results. Here we report the observation of a quantized limiting value for the thermal conductance, Gth, in suspended insulating nanostructures at very low temperatures. The behaviour we observe is consistent with predictions for phonon transport in a ballistic, one-dimensional channel: at low temperatures, Gth approaches a maximum value of g0 = pi2kB2T/3h, the universal quantum of thermal conductance.     

无序杂质、磁场对“三明治”式二维系统电导的影响

为研究二维电子系统中电子输运的问题及在磁场作用下二维无序杂质系统电导的物理性质,通过运用格林函数以及散射矩阵理论的方法,在格点模型的基础上,对"三明治"式二维电子系统电导的量子化现象进行了分析。导线与散射体的接触减小了系统的电导,削减了电导量子台阶现象,使得系统的电导随着导线与介质间耦合的变小而降低;当系统受到外磁场作用时,系统电导的变化随着磁场的变化表现出周期性震荡行为,这种震荡变化的剧烈程度与电子的能量有关;受杂质散射的影响,系统电导随无序杂质浓度的增大而减小,在某些特殊掺杂的浓度下,对于一些特殊的电子能量,系统的电导可以达到理想情况下的阶梯值。研究成果对于"三明治"式二维电子系统电导的进一步研究具有借鉴意义。     

Crossover from 'mesoscopic' to 'universal' phase for electron transmission in quantum dots

The measurement of phase in coherent electron systems--that is, 'mesoscopic' systems such as quantum dots--can yield information about fundamental transport properties that is not readily apparent from conductance measurements. Phase measurements on relatively large quantum dots recently revealed that the phase evolution for electrons traversing the dots exhibits a 'universal' behaviour, independent of dot size, shape, and electron occupancy. Specifically, for quantum dots in the Coulomb blockade regime, the transmission phase increases monotonically by pi throughout each conductance peak; in the conductance valleys, the phase returns sharply to its starting value. The expected mesoscopic features in the phase evolution--related to the dot's shape, spin degeneracy or to exchange effects--have not been observed, and there is at present no satisfactory explanation for the observed universality in phase behaviour. Here we report the results of phase measurements on a series of small quantum dots, having occupancies of between only 1-20 electrons, where the phase behaviour for electron transmission should in principle be easier to interpret. In contrast to the universal behaviour observed thus far only in the larger dots, we see clear mesoscopic features in the phase measurements when the dot occupancy is less than approximately 10 electrons. As the occupancy increases, the manner of phase evolution changes and universal behaviour is recovered for some 14 electrons or more. The identification of a transition from the expected mesoscopic behaviour to universal phase evolution should help to direct and constrain theoretical models for the latter.     

Direct observation of second-order atom tunnelling

Tunnelling of material particles through a classically impenetrable barrier constitutes one of the hallmark effects of quantum physics. When interactions between the particles compete with their mobility through a tunnel junction, intriguing dynamical behaviour can arise because the particles do not tunnel independently. In single-electron or Bloch transistors, for example, the tunnelling of an electron or Cooper pair can be enabled or suppressed by the presence of a second charge carrier due to Coulomb blockade. Here we report direct, time-resolved observations of the correlated tunnelling of two interacting ultracold atoms through a barrier in a double-well potential. For the regime in which the interactions between the atoms are weak and tunnel coupling dominates, individual atoms can tunnel independently, similar to the case of a normal Josephson junction. However, when strong repulsive interactions are present, two atoms located on one side of the barrier cannot separate, but are observed to tunnel together as a pair in a second-order co-tunnelling process. By recording both the atom position and phase coherence over time, we fully characterize the tunnelling process for a single atom as well as the correlated dynamics of a pair of atoms for weak and strong interactions. In addition, we identify a conditional tunnelling regime in which a single atom can only tunnel in the presence of a second particle, acting as a single atom switch. Such second-order tunnelling events, which are the dominating dynamical effect in the strongly interacting regime, have not been previously observed with ultracold atoms. Similar second-order processes form the basis of superexchange interactions between atoms on neighbouring lattice sites of a periodic potential, a central component of proposals for realizing quantum magnetism.     

On-demand single-electron transfer between distant quantum dots

Single-electron circuits of the future, consisting of a network of quantum dots, will require a mechanism to transport electrons from one functional part of the circuit to another. For example, in a quantum computer decoherence and circuit complexity can be reduced by separating quantum bit (qubit) manipulation from measurement and by providing a means of transporting electrons between the corresponding parts of the circuit. Highly controlled tunnelling between neighbouring dots has been demonstrated, and our ability to manipulate electrons in single- and double-dot systems is improving rapidly. For distances greater than a few hundred nanometres, neither free propagation nor tunnelling is viable while maintaining confinement of single electrons. Here we show how a single electron may be captured in a surface acoustic wave minimum and transferred from one quantum dot to a second, unoccupied, dot along a long, empty channel. The transfer direction may be reversed and the same electron moved back and forth more than sixty times-a cumulative distance of 0.25 mm-without error. Such on-chip transfer extends communication between quantum dots to a range that may allow the integration of discrete quantum information processing components and devices.