Electronic spin transport and spin precession in single graphene layers at room temperature

Electronic transport in single or a few layers of graphene is the subject of intense interest at present. The specific band structure of graphene, with its unique valley structure and Dirac neutrality point separating hole states from electron states, has led to the observation of new electronic transport phenomena such as anomalously quantized Hall effects, absence of weak localization and the existence of a minimum conductivity. In addition to dissipative transport, supercurrent transport has also been observed. Graphene might also be a promising material for spintronics and related applications, such as the realization of spin qubits, owing to the low intrinsic spin orbit interaction, as well as the low hyperfine interaction of the electron spins with the carbon nuclei. Here we report the observation of spin transport, as well as Larmor spin precession, over micrometre-scale distances in single graphene layers. The 'non-local' spin valve geometry was used in these experiments, employing four-terminal contact geometries with ferromagnetic cobalt electrodes making contact with the graphene sheet through a thin oxide layer. We observe clear bipolar (changing from positive to negative sign) spin signals that reflect the magnetization direction of all four electrodes, indicating that spin coherence extends underneath all of the contacts. No significant changes in the spin signals occur between 4.2 K, 77 K and room temperature. We extract a spin relaxation length between 1.5 and 2 mum at room temperature, only weakly dependent on charge density. The spin polarization of the ferromagnetic contacts is calculated from the measurements to be around ten per cent.     

Two-dimensional gas of massless Dirac fermions in graphene

Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schr?dinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.     

Supercurrent reversal in quantum dots

When two superconductors are electrically connected by a weak link--such as a tunnel barrier--a zero-resistance supercurrent can flow. This supercurrent is carried by Cooper pairs of electrons with a combined charge of twice the elementary charge, e. The 2e charge quantum is clearly visible in the height of voltage steps in Josephson junctions under microwave irradiation, and in the magnetic flux periodicity of h/2e (where h is Planck's constant) in superconducting quantum interference devices. Here we study supercurrents through a quantum dot created in a semiconductor nanowire by local electrostatic gating. Owing to strong Coulomb interaction, electrons only tunnel one-by-one through the discrete energy levels of the quantum dot. This nevertheless can yield a supercurrent when subsequent tunnel events are coherent. These quantum coherent tunnelling processes can result in either a positive or a negative supercurrent, that is, in a normal or a pi-junction, respectively. We demonstrate that the supercurrent reverses sign by adding a single electron spin to the quantum dot. When excited states of the quantum dot are involved in transport, the supercurrent sign also depends on the character of the orbital wavefunctions.     

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.     

Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice

Dirac points are central to many phenomena in condensed-matter physics, from massless electrons in graphene to the emergence of conducting edge states in topological insulators. At a Dirac point, two energy bands intersect linearly and the electrons behave as relativistic Dirac fermions. In solids, the rigid structure of the material determines the mass and velocity of the electrons, as well as their interactions. A different, highly flexible means of studying condensed-matter phenomena is to create model systems using ultracold atoms trapped in the periodic potential of interfering laser beams. Here we report the creation of Dirac points with adjustable properties in a tunable honeycomb optical lattice. Using momentum-resolved interband transitions, we observe a minimum bandgap inside the Brillouin zone at the positions of the two Dirac points. We exploit the unique tunability of our lattice potential to adjust the effective mass of the Dirac fermions by breaking inversion symmetry. Moreover, changing the lattice anisotropy allows us to change the positions of the Dirac points inside the Brillouin zone. When the anisotropy exceeds a critical limit, the two Dirac points merge and annihilate each other-a situation that has recently attracted considerable theoretical interest but that is extremely challenging to observe in solids. We map out this topological transition in lattice parameter space and find excellent agreement with ab initio calculations. Our results not only pave the way to model materials in which the topology of the band structure is crucial, but also provide an avenue to exploring many-body phases resulting from the interplay of complex lattice geometries with interactions.     

GaAs原子链耦合石墨烯电子输运性质的理论计算

基于密度泛函理论,运用非平衡格林函数对(GaAs)_4原子链耦合石墨烯纳米条带的电子输运性质进行了第一性原理计算,结果发现通过改变原子链与石墨烯之间的距离可以有效调制系统的电子传输行为.当(GaAs)_4原子链与石墨烯之间的距离d在0.10~0.28nm的范围内变化时,石墨烯、原子链上各自的电子传输要相互影响,且系统的平衡电导在2G_0~7G_0之间发生G_0(G_0=2e~2/h)整数倍的变化,即表现出量子化电导现象;当d0.28nm时,总的电导等于各自的电导之和,此时(GaAs)_4原子链与石墨烯之间的耦合很弱,各自的电子输运相互影响很小.     

可调谐石墨烯光电子器件

凭借着良好的光电、力学和热学性能,石墨烯是目前凝聚态物理领域一个重要的研究热点.而且由于石墨烯的色散关系在狄拉克点附近呈现线性特性,石墨烯的光电特性可以通过外加电场、磁场和温度来加以调节.因此,石墨烯是研究可调谐器件的良好平台.基于石墨烯的电导率随费米能级有明显改变的特点,在分析石墨烯器件的调制机制的基础上,对石墨烯可调谐器件在太赫兹、中红外和近红外的应用发展进行了综述研究.     

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.     

Quantum supercurrent transistors in carbon nanotubes

Electronic transport through nanostructures is greatly affected by the presence of superconducting leads. If the interface between the nanostructure and the superconductors is sufficiently transparent, a dissipationless current (supercurrent) can flow through the device owing to the Josephson effect. A Josephson coupling, as measured by the zero-resistance supercurrent, has been obtained using tunnel barriers, superconducting constrictions, normal metals and semiconductors. The coupling mechanisms vary from tunnelling to Andreev reflection. The latter process has hitherto been observed only in normal-type systems with a continuous density of electronic states. Here we investigate a supercurrent flowing through a discrete density of states-that is, the quantized single particle energy states of a quantum dot, or 'artificial atom', placed between superconducting electrodes. For this purpose, we exploit the quantum properties of finite-sized carbon nanotubes. By means of a gate electrode, successive discrete energy states are tuned on- and off-resonance with the Fermi energy in the superconducting leads, resulting in a periodic modulation of the critical current and a non-trivial correlation between the conductance in the normal state and the supercurrent. We find, in good agreement with existing theory, that the product of the critical current and the normal state resistance becomes an oscillating function, in contrast to being constant as in previously explored regimes.     

短程相互作用对准粒子相对论动力学的影响

通过调节短程相互作用，在Su-Schrieffer-Heeger(SSH)模型中实现了Dirac点的移动与融合.该过程对应于一种由半金属相到能带绝缘相的拓扑相变(即Lifshitz相变).通过解析和数值研究的方法，对该相变过程中系统准粒子的相对论动力学特性进行了研究.结果表明:在短程相互作用很弱的情况下(即Dirac点融合前)，系统展现出相对论动力学特征; 然而，随着短程相互作用的增强，Dirac点会发生融合相变.此后，系统则表现为非相对论动力学特征.因此，相变过程是由相对论到非相对论动力学转变的过程.进一步通过数值模拟得到了融合前(相对论)后(非相对论)粒子的密度分布随时间演化的图像.在相变前，单色Dirac准粒子发生劈裂，而双色Dirac准粒子产生定向漂移现象.在相变后，无论初态如何改变，系统始终无组分劈裂现象出现.最后，展示了不同相互作用下准粒子的质心运动曲线(世界线).     

光子石墨烯中光传输特性的研究

光子石墨烯与电子石墨烯有相同的微结构,是具有三角晶格的二维光子晶体,其能带结构中存在中心奇异点,称为狄拉克点。这种狄拉克准粒子的存在导致了一种新的传输状态"赝扩散"。利用共面接地波导实现了单方向性窄的波束通过二维光子晶体。利用数值仿真的方法验证了"赝扩散"的传输特性。实验结果表明,对于二维光子晶体有些能带是不能被激发的。     

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.     

相对论效应对巯基金团簇电荷分布的影响

在巯基金团簇中尤其是部分巯基包裹的金核簇,Au原子和S原子的电荷分布是决定金核簇静电势的重要因素.Au是有强相对论效应的重元素,相对论效应对裸露的和有机分子保护的金团簇的几何结构和电子结构有不可忽略的影响.基于密度泛函理论,运用第一性原理研究了环状Au4(SCH3)4簇的电子结构.结果表明相对论效应对电荷分布有重要影响.根据Hirshfeld和Mulliken这两种方法对电子数进行分析,发现当考虑相对论效应时几乎没有电荷从Au转移到S,而不考虑相对论效应时有大量电荷从Au转移到S.     

强关联体系中的自旋与电荷密度涨落的共存性

对于具有晶格结构的固体、利用在相对论狄喇克方程的非相对论极限下得到的电子自旋－轨道相互作用，推导出自旋涨落一声子相互作用。利用此相互作用推导出自旋磁化率、电荷极化率、声子格林函数的一组自洽方程。然后，又讨论了自旋和电荷密度涨落的共存性及其对高温超导的影响。     

石墨烯双势垒结构中的输运特性

利用Landauer-Büttiker散射理论和传递矩阵方法研究了单层石墨烯双势垒结构中的隧穿几率和电导.计算结果表明:即使存在克莱因隧穿效应,单层石墨烯双势垒结构中的量子隧穿仍然与势阱宽度和势垒高度密切相关.隧穿几率和电导表现出复杂的振荡行为,振荡的振幅和周期敏感地依赖于势阱宽度、势垒高度、电子的入射能量和入射角度....     

掺杂armchair石墨烯纳米带电子结构和输运性质的研究

基于第一性原理计算,研究了B/N掺杂对宽度为N(a)=3p+2=11的扶手椅(Armchair)型石墨烯纳米带电子结构和输运性质的影响.杂质的存在使得扶手椅型石墨烯纳米带的能隙增大,并在能隙中出现了一条局域的杂质态能带,杂质的位置也影响其能带结构.另外,杂质的存在还引起输运过程中的电子共振散射,其特点与掺杂种类、掺杂位...     

The structure of suspended graphene sheets

The recent discovery of graphene has sparked much interest, thus far focused on the peculiar electronic structure of this material, in which charge carriers mimic massless relativistic particles. However, the physical structure of graphene--a single layer of carbon atoms densely packed in a honeycomb crystal lattice--is also puzzling. On the one hand, graphene appears to be a strictly two-dimensional material, exhibiting such a high crystal quality that electrons can travel submicrometre distances without scattering. On the other hand, perfect two-dimensional crystals cannot exist in the free state, according to both theory and experiment. This incompatibility can be avoided by arguing that all the graphene structures studied so far were an integral part of larger three-dimensional structures, either supported by a bulk substrate or embedded in a three-dimensional matrix. Here we report on individual graphene sheets freely suspended on a microfabricated scaffold in vacuum or air. These membranes are only one atom thick, yet they still display long-range crystalline order. However, our studies by transmission electron microscopy also reveal that these suspended graphene sheets are not perfectly flat: they exhibit intrinsic microscopic roughening such that the surface normal varies by several degrees and out-of-plane deformations reach 1 nm. The atomically thin single-crystal membranes offer ample scope for fundamental research and new technologies, whereas the observed corrugations in the third dimension may provide subtle reasons for the stability of two-dimensional crystals.     

Ballistic carbon nanotube field-effect transistors

A common feature of the single-walled carbon-nanotube field-effect transistors fabricated to date has been the presence of a Schottky barrier at the nanotube--metal junctions. These energy barriers severely limit transistor conductance in the 'ON' state, and reduce the current delivery capability--a key determinant of device performance. Here we show that contacting semiconducting single-walled nanotubes by palladium, a noble metal with high work function and good wetting interactions with nanotubes, greatly reduces or eliminates the barriers for transport through the valence band of nanotubes. In situ modification of the electrode work function by hydrogen is carried out to shed light on the nature of the contacts. With Pd contacts, the 'ON' states of semiconducting nanotubes can behave like ohmically contacted ballistic metallic tubes, exhibiting room-temperature conductance near the ballistic transport limit of 4e(2)/h (refs 4-6), high current-carrying capability (approximately 25 micro A per tube), and Fabry-Perot interferences at low temperatures. Under high voltage operation, the current saturation appears to be set by backscattering of the charge carriers by optical phonons. High-performance ballistic nanotube field-effect transistors with zero or slightly negative Schottky barriers are thus realized.     

H2O分子在石墨烯扶手型边缘吸附的研究

类似石墨表面,石墨烯可以吸附和脱附各种原子和分子,石墨烯比石墨具有更大表面积,因此,石墨烯的表面性能被广泛关注. 然而较少被关注的是石墨烯边缘C原子的性能. 石墨烯边缘C原子由于存在未配对的电子,因此具有更强的反应活性. 本文采用了SelfConsistentCharge Density Functional Tight Binding(SCCDFTB)方法对H2O分子在石墨烯扶手型边缘的吸附现象进行了研究. 研究发现,石墨烯边缘的峰位C原子具有很好的吸附性,吸附能大约为-0.109~-0.768     

Coulomb-blockade transport in single-crystal organic thin-film transistors

Coulomb-blockade transport--whereby the Coulomb interaction between electrons can prohibit their transport around a circuit--occurs in systems in which both the tunnel resistance, Rb between neighbouring sites is large (>h/e2) and the charging energy, E(C) (E(C) = e2/2C, where C is the capacitance of the site), of an excess electron on a site is large compared to kT. (Here e is the charge of an electron, k is Boltzmann's constant, and h is Planck's constant.) The nature of the individual sites--metallic, superconducting, semiconducting or quantum dot--is to first order irrelevant for this phenomenon to be observed. Coulomb blockade has also been observed in two-dimensional arrays of normal-metal tunnel junctions, but the relatively large capacitances of these micrometre-sized metal islands results in a small charging energy, and so the effect can be seen only at extremely low temperatures. Here we demonstrate that organic thin-film transistors based on highly ordered molecular materials can, to first order, also be considered as an array of sites separated by tunnel resistances. And as a result of the sub-nanometre sizes of the sites (the individual molecules), and hence their small capacitances, the charging energy dominates at room temperature. Conductivity measurements as a function of both gate bias and temperature reveal the presence of thermally activated transport, consistent with the conventional model of Coulomb blockade.