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.     

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.     

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.     

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.     

Erasable electrostatic lithography for quantum components

Quantum electronic components--such as quantum antidots and one-dimensional channels--are usually defined from doped GaAs/AlGaAs heterostructures using electron-beam lithography or local oxidation by conductive atomic force microscopy. In both cases, lithography and measurement are performed in very different environments, so fabrication and test cycles can take several weeks. Here we describe a different lithographic technique, which we call erasable electrostatic lithography (EEL), where patterns of charge are drawn on the device surface with a negatively biased scanning probe in the same low-temperature high-vacuum environment used for measurement. The charge patterns locally deplete electrons from a subsurface two-dimensional electron system (2DES) to define working quantum components. Charge patterns are erased locally with the scanning probe biased positive or globally by illuminating the device with red light. We demonstrate and investigate EEL by drawing and erasing quantum antidots, then develop the technique to draw and tune high-quality one-dimensional channels. The quantum components are imaged using scanned gate microscopy. A technique similar to EEL has been reported previously, where tip-induced charging of the surface or donor layer was used to locally perturb a 2DES before charge accumulation imaging.     

Tunnelling between the edges of two lateral quantum Hall systems

The edge of a two-dimensional electron system in a magnetic field consists of one-dimensional channels that arise from the confining electric field at the edge of the system. The crossed electric and magnetic fields cause electrons to drift parallel to the sample boundary, creating a chiral current that travels along the edge in only one direction. In an ideal two-dimensional electron system in the quantum Hall regime, all the current flows along the edge. Quantization of the Hall resistance arises from occupation of N one-dimensional edge channels, each contributing a conductance of e2/h. Here we report differential conductance measurements, in the integer quantum Hall regime, of tunnelling between the edges of a pair of two-dimensional electron systems that are separated by an atomically precise, high-quality, tunnel barrier. The resultant interaction between the edge states leads to the formation of new energy gaps and an intriguing dispersion relation for electrons travelling along the barrier: for example, we see a persistent conductance peak at zero bias voltage and an absence of tunnelling features due to electron spin. These features are unexpected and are not consistent with a model of weakly interacting edge states. Remnant disorder along the barrier and charge screening may each play a role, although detailed numerical studies will be required to elucidate these effects.     

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.     

Using photoemission spectroscopy to probe a strongly interacting Fermi gas

Ultracold atomic gases provide model systems in which to study many-body quantum physics. Recent experiments using Fermi gases have demonstrated a phase transition to a superfluid state with strong interparticle interactions. This system provides a realization of the 'BCS-BEC crossover' connecting the physics of Bardeen-Cooper-Schrieffer (BCS) superconductivity with that of Bose-Einstein condensates (BECs). Although many aspects of this system have been investigated, it has not yet been possible to measure the single-particle excitation spectrum (a fundamental property directly predicted by many-body theories). Here we use photoemission spectroscopy to directly probe the elementary excitations and energy dispersion in a strongly interacting Fermi gas of (40)K atoms. In the experiments, a radio-frequency photon ejects an atom from the strongly interacting system by means of a spin-flip transition to a weakly interacting state. We measure the occupied density of single-particle states at the cusp of the BCS-BEC crossover and on the BEC side of the crossover, and compare these results to that for a nearly ideal Fermi gas. We show that, near the critical temperature, the single-particle spectral function is dramatically altered in a way that is consistent with a large pairing gap. Our results probe the many-body physics in a way that could be compared to data for the high-transition-temperature superconductors. As in photoemission spectroscopy for electronic materials, our measurement technique for ultracold atomic gases directly probes low-energy excitations and thus can reveal excitation gaps and/or pseudogaps. Furthermore, this technique can provide an analogue of angle-resolved photoemission spectroscopy for probing anisotropic systems, such as atoms in optical lattice potentials.     

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).     

拓扑平带上的分数量子反常霍尔效应(二)

拓扑平带模型属于著名Haldane模型的扩展版本,至少有一个能带具有非平庸的拓扑性质,即有非零的陈数(Chern number),另外,该能带的带宽很窄,且与其他能带间有较大能隙.通过对拓扑平带上强关联相互作用的费米子和玻色子晶格体系的系统数值研究,发现了一类新奇的阿贝尔型和非阿贝尔型分数量子霍尔效应.新发现的分数量子霍尔效应不同于传统朗道能级上的连续型分数量子霍尔效应,无须外加强磁场,有较大特征能隙,可在较高温度下存在,无需单粒子朗道能级,不能用常规Laughlin波函数来描述.这些无外加磁场、无朗道能级的分数化现象,定义了一类新的分数拓扑相,也称为分数陈绝缘体,其中的分数量子霍尔效应也称为分数量子反常霍尔效应.该新领域在近期引起了国际凝聚态物理学界的研究热情与广泛关注.对笔者与合作者在该领域的系列研究工作进行了综述介绍,以期引起国内外同行的进一步研究兴趣.     

拓扑平带上的分数量子反常霍尔效应（一）

拓扑平带模型属于著名Haldane模型的扩展版本,至少有一个能带具有非平庸的拓扑性质,即有非零的陈数（Chernnumber）,而且该能带的带宽很窄,同时与其他能带间有较大能隙．最近通过对拓扑平带上强关联相互作用的费米子和玻色子品格体系的系统数值进行研究,发现了一类新奇的阿贝尔型和非阿贝尔型分数量子霍尔效应．新发现的分数量子霍尔效应不同于传统朗道能级上的连续型分数量子霍尔效应,无须外加强磁场,有较大特征能隙,可在较高温度下存在,无需单粒子朗道能级,不能用常规Laughlin波函数描述．这些无外加磁场、无朗道能级的分数化现象,定义了一类新的分数拓扑相,也称为分数陈绝缘体,其中的分数量子霍尔效应也称为分数量子反常霍尔效应．该新领域在近期引起了国际凝聚态物理学界的研究热情与广泛关注．对笔者与合作者在该领域的系列研究工作进行综述介绍,以期引起国内外同行的进一步研究兴趣．     

Coherent zero-state and pi-state in an exciton-polariton condensate array

The effect of quantum statistics in quantum gases and liquids results in observable collective properties among many-particle systems. One prime example is Bose-Einstein condensation, whose onset in a quantum liquid leads to phenomena such as superfluidity and superconductivity. A Bose-Einstein condensate is generally defined as a macroscopic occupation of a single-particle quantum state, a phenomenon technically referred to as off-diagonal long-range order due to non-vanishing off-diagonal components of the single-particle density matrix. The wavefunction of the condensate is an order parameter whose phase is essential in characterizing the coherence and superfluid phenomena. The long-range spatial coherence leads to the existence of phase-locked multiple condensates in an array of superfluid helium, superconducting Josephson junctions or atomic Bose-Einstein condensates. Under certain circumstances, a quantum phase difference of pi is predicted to develop among weakly coupled Josephson junctions. Such a meta-stable pi-state was discovered in a weak link of superfluid 3He, which is characterized by a 'p-wave' order parameter. The possible existence of such a pi-state in weakly coupled atomic Bose-Einstein condensates has also been proposed, but remains undiscovered. Here we report the observation of spontaneous build-up of in-phase ('zero-state') and antiphase ('pi-state') 'superfluid' states in a solid-state system; an array of exciton-polariton condensates connected by weak periodic potential barriers within a semiconductor microcavity. These in-phase and antiphase states reflect the band structure of the one-dimensional polariton array and the dynamic characteristics of metastable exciton-polariton condensates.     

Quantum computing in molecular magnets

Shor and Grover demonstrated that a quantum computer can outperform any classical computer in factoring numbers and in searching a database by exploiting the parallelism of quantum mechanics. Whereas Shor's algorithm requires both superposition and entanglement of a many-particle system, the superposition of single-particle quantum states is sufficient for Grover's algorithm. Recently, the latter has been successfully implemented using Rydberg atoms. Here we propose an implementation of Grover's algorithm that uses molecular magnets, which are solid-state systems with a large spin; their spin eigenstates make them natural candidates for single-particle systems. We show theoretically that molecular magnets can be used to build dense and efficient memory devices based on the Grover algorithm. In particular, one single crystal can serve as a storage unit of a dynamic random access memory device. Fast electron spin resonance pulses can be used to decode and read out stored numbers of up to 105, with access times as short as 10-10 seconds. We show that our proposal should be feasible using the molecular magnets Fe8 and Mn12.     

Bose-Einstein condensation of excitons in bilayer electron systems

An exciton is the particle-like entity that forms when an electron is bound to a positively charged 'hole'. An ordered electronic state in which excitons condense into a single quantum state was proposed as a theoretical possibility many years ago. We review recent studies of semiconductor bilayer systems that provide clear evidence for this phenomenon and explain why exciton condensation in the quantum Hall regime, where these experiments were performed, is as likely to occur in electron-electron bilayers as in electron-hole bilayers. In current quantum Hall excitonic condensates, disorder induces mobile vortices that flow in response to a supercurrent and limit the extremely large bilayer counterflow conductivity.     

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.     

硅量子点表面掺氮的电子结构计算

本文在量子点表面掺入氮原子,用第一性原理方法模拟计算硅量子点（111）面上的电子结构.本文主要解决两个问题：（1）比较研究六种不同大小的量子点结构掺杂和未掺杂氮原子情况下的带隙宽度和电子态密度变化;（2）分别用广义梯度近似（GGA）和局域密度近似（LDA）两种不同的算法计算六种量子点结构的带隙宽度和态密度,并比较GGA和LDA算法的特点.计算结果发现：带隙随着量子点的尺度变小而展宽,这符合量子受限规律;在量子点表面掺杂氮原子会减小带隙宽度;重要的是发现LDA算法对局域态更加敏感.     

Quantum phase transition in a single-molecule quantum dot

Quantum criticality is the intriguing possibility offered by the laws of quantum mechanics when the wave function of a many-particle physical system is forced to evolve continuously between two distinct, competing ground states. This phenomenon, often related to a zero-temperature magnetic phase transition, is believed to govern many of the fascinating properties of strongly correlated systems such as heavy-fermion compounds or high-temperature superconductors. In contrast to bulk materials with very complex electronic structures, artificial nanoscale devices could offer a new and simpler means of understanding quantum phase transitions. Here we demonstrate this possibility in a single-molecule quantum dot, where a gate voltage induces a crossing of two different types of electron spin state (singlet and triplet) at zero magnetic field. The quantum dot is operated in the Kondo regime, where the electron spin on the quantum dot is partially screened by metallic electrodes. This strong electronic coupling between the quantum dot and the metallic contacts provides the strong electron correlations necessary to observe quantum critical behaviour. The quantum magnetic phase transition between two different Kondo regimes is achieved by tuning gate voltages and is fundamentally different from previously observed Kondo transitions in semiconductor and nanotube quantum dots. Our work may offer new directions in terms of control and tunability for molecular spintronics.     

基于贝尔态的确定性量子密钥分配协议

提出了一种基于贝尔态的确定性量子密钥分配协议.它建立在纠缠量子系统的内部关联的基础上,双方通过共享纠缠量子系统和做单粒子量子测量建立起共享的密钥.与传统的只能生成随机字符串作为密钥的量子密钥分配协议不同,利用该协议,双方可以以任意指定的字符串作为共享的密钥.量子力学的定律保证了该协议的无条件安全性.除了单粒子量子测量之外,不需要做任何复杂的量子操作,因此它更容易实现,健壮性更好.     

Magnetic impurity formation in quantum point contacts

A quantum point contact (QPC) is a narrow constriction between two wider electron reservoirs, and is the standard building block of sub-micrometre devices such as quantum dots and qubits (the proposed basic elements of quantum computers). The conductance through a QPC changes as a function of its width in integer steps of G(0) = 2e2/h (where e is the charge on an electron, and h is Planck's constant), signalling the quantization of its transverse modes. But measurements of these conductance steps also reveal an additional shoulder at a value around 0.7G(0) (refs 1-4), an observation that has remained a puzzle for more than a decade. It has recently been suggested that this phenomenon can be explained by the existence of a magnetic 'impurity' in the QPC at low electron densities. Here we present extensive numerical density-functional calculations that reveal the formation of an electronic state with a spin-1/2 magnetic moment in the channel under very general conditions. In addition, we show that such an impurity will also form at large magnetic fields, for a specific value of the field, and sometimes even at the opening of the second transverse mode in the QPC. Beyond explaining the source of the '0.7 anomaly', these results may have far-reaching implications for spin-filling of electronic states in quantum dots and for the dephasing of quantum information stored in semiconductor qubits.     

Real-time detection of electron tunnelling in a quantum dot

Nanostructures in which strong (Coulomb) interactions exist between electrons are predicted to exhibit temporal electronic correlations. Although there is ample experimental evidence that such correlations exist, electron dynamics in engineered nanostructures have been observed directly only on long timescales. The faster dynamics associated with electrical currents or charge fluctuations are usually inferred from direct (or quasi-direct) current measurements. Recently, interest in electron dynamics has risen, in part owing to the realization that additional information about electronic interactions can be found in the shot noise or higher statistical moments of a direct current. Furthermore, interest in quantum computation has stimulated investigation of quantum bit (qubit) readout techniques, which for many condensed-matter systems ultimately reduces to single-shot measurements of individual electronic charges. Here we report real-time observation of individual electron tunnelling events in a quantum dot using an integrated radio-frequency single-electron transistor. We use electron counting to measure directly the quantum dot's tunnelling rate and the occupational probabilities of its charge state. Our results provide evidence in favour of long (10 micros or more) inelastic scattering times in nearly isolated dots.