Abstract:We demonstrate that a field effect transistor ( Main Text:Few-layer black phosphorus (BP) has received in recent years much attention due to its unique properties making this layered material attractive for technological applications(1-3). This twodimensional crystal has an anisotropic structure (Fig.1a) and is characterized by a BP thickness dependent direct band gap(4). In contrast to graphene, the presence of a band gap in BP permits for a selective depletion of charge carriers by electrostatic gating, which is an essential feature in field effect transistors (FETs). A high charge carrier mobility reaching 1000 cm 2 /Vs at room temperature accentuates this material for applications at room temperature(5). However, the exposure of BP crystals to ambient conditions causes the oxidation of BP and significantly degrades the quality of BP channels. Nevertheless, the encapsulation of BP layers by hexagonal boron nitride (h-BN) sheets in air or in an inert gas environment is found to be very effective for preventing BP oxidation(6-8). Surface impurity effects are largely reduced, and high charge carrier mobility up to several 10 3 cm 2 /Vs has been obtained in BP FETs at cryogenic temperature(6-8). The charge carrier scattering at the impurities encapsulated along with the BP layers hinders further mobility increase. Figure 1a shows Fig.1c). The mobility values are more than four times larger compared with that in previous studies, which indicates the improved quality of h-BN/BP interfaces(7). In spite of using the advanced fabrication technique,  FET and  H saturate at T<20 K, which implies that the disorder scattering dominates over the phonon scattering in this temperature regime, which limits the hole mobility at cryogenic temperature(9). The increase of  H with the carrier density p (Fig. 1c) suggests that the disorder potential is likely created by residual impurities and can be screened by the mobile carriers (7,10,11). The scattering behavior changes at high temperatures (T>100 K).  FET and  H decrease with increasing T and follow the dependence T    , where  =1.9 and 2.0 characterize the dependence for  H and  FET , respectively (black line in Fig. 1c). The large  values imply that the acoustic phonon rather than the optical phonon scattering dominates over the scattering by the residual impurities in this temperature regime. It is very noticeable that the room temperature hole mobility  H = 5200 cm 2 /Vs closely approaches the theoretically predicted hole mobility for a clean five-layer BP sheets, which lies in the range between 4,800 cm 2 V -1 s -1 and 6,400 cm 2 V -1 s -1 (9). The realization 4 of the predicated mobility value, which is solely limited by the phonon scattering at room temperature, is another demonstration of the improved BP heterostructure quality. Quantum Hall Effect (QHE) in BP 2DHGFigure 2a shows Hall resistance R yx and magnetoresistance R xx as a function of the magnetic field, which is measured in a clean heterostructure at the base temperature of the experim...

The quantum Hall effect arises from the cyclotron motion of charge carriers in two-dimensional systems. However, the ground states related to the integer and fractional quantum Hall effect, respectively, are of entirely different origin. The former can be explained within a single-particle picture; the latter arises from electron correlation effects governed by Coulomb interaction. The prerequisite for the observation of these effects is extremely smooth interfaces of the thin film layers to which the charge carriers are confined. So far, experimental observations of such quantum transport phenomena have been limited to a few material systems based on silicon, III-V compounds and graphene. In ionic materials, the correlation between electrons is expected to be more pronounced than in the conventional heterostructures, owing to a large effective mass of charge carriers. Here we report the observation of the fractional quantum Hall effect in MgZnO/ZnO heterostructures grown by molecular-beam epitaxy, in which the electron mobility exceeds 180,000 cm(2) V(-1) s(-1). Fractional states such as ν = 4/3, 5/3 and 8/3 clearly emerge, and the appearance of the ν = 2/5 state is indicated. The present study represents a technological advance in oxide electronics that provides opportunities to explore strongly correlated phenomena in quantum transport of dilute carriers.

The fractional quantum Hall (FQH) e ect emerges in high-quality two-dimensional electron systems exposed to a magnetic field when the Landau-level filling factor, ν e , takes on a rational value. Although the overwhelming majority of FQH states have odd-denominator fillings, the physical properties of the rare and fragile even-denominator states are most tantalizing in view of their potential relevance for topological quantum computation. For decades, GaAs has been the preferred host for studying these even-denominator states, where they occur at ν e = 5/2 and 7/2. Here we report an anomalous series of quantized evendenominator FQH states outside the realm of III-V semiconductors in the MgZnO/ZnO 2DES electron at ν e = 3/2 and 7/2, with precursor features at 9/2; all while the 5/2 state is absent. The e ect in this material occurs concomitantly with tunability of the orbital character of electrons at the chemical potential, thereby realizing a new experimental means for investigating these exotic ground states.T he framework for the wide range of ground states observed in two-dimensional electron systems (2DES) resides in the discretized energy spectrum with a high degeneracy of the allowed states which emerges with the addition of a perpendicular magnetic field, B p . A ladder of spin-split Landau-levels (LLs) results with B p , inducing quantization of the orbital motion and lifting of the spin degeneracy. Each level is characterized by its orbital index N e = 0, 1, . . . and spin orientation (↑ or ↓). These levels can host as many charge carriers as magnetic flux quanta thread the sample and the filling factor, ν e , indicates how many levels are occupied. With increasing B p these LLs are successively depopulated and, on emptying a level completely, ν e takes on an integer value and the bulk of the 2DES becomes incompressible (see ref. 1 for an overview). The system exhibits the integer quantum Hall effect: vanishing longitudinal resistance (R xx ) and a Hall resistance (R xy ) quantized in units of h/e 2 . Further incompressible ground states may form at fractional fillings p/q when the electron number and number of flux quanta are commensurable. In contrast to FQH states at odd-denominator fillings, where the anti-symmetry constraint on the many-particle wavefunction imposed by the Pauli exclusion principle for fermions is automatically fulfilled, the development of even-denominator states 2-11 requires some mechanism which either restores the anti-symmetry of the manyparticle wavefunction or simply lifts the need to fulfil the Pauli exclusion principle. For systems where the charge carriers possess another degree of freedom, such as a layer or subband index, the anti-symmetry issue at even-denominator fillings may be solved by a two-component wavefunction. Indeed, in wide GaAs quantum wells with two subbands or in double-layer systems evendenominator states have been observed 2-7 and consensus has been reached that they are described by many-particle wavefunctions like the two-component ψ 331 -Laughlin sta...

We report NMR experiments using high-power, RF decoupling techniques to show that a 29 Si nuclear spin qubit in a solid silicon crystal at room temperature can preserve quantum phase for 10 9 precessional periods. The coherence times we report are longer than for any other observed solid-state qubit by more than four orders of magnitude. In high quality crystals, these times are limited by residual dipolar couplings and can be further improved by isotopic depletion. In defect-heavy samples, we provide evidence for decoherence limited by 1/f noise. These results provide insight toward proposals for solid-state nuclear-spin-based quantum memories and quantum computers based on silicon.PACS numbers: 03.67. Lx, 03.67.Pp, 76.60.Lz, 82.56.Jn Quantum information processing devices outperform their classical counterparts by preserving and exploiting the correlated phases of their constituent quantum oscillators, which are usually two-state systems called "qubits." An increasing number of theoretical proposals have shown that such devices allow secure long-distance communication and improved computational power [1]. Solid-state implementations of these devices are favored for reasons of both scalability and integration with existing hardware, although previous experiments have shown limited coherence times for solid-state qubits. The development of quantum error correcting codes [2] and fault tolerant quantum computation [3] showed that largescale quantum algorithms are still theoretically possible in the presence of decoherence. However, the coherence time must be dauntingly long: approximately 10 5 times the duration of a single quantum gate, and probably longer depending on the quantum computer architecture [1]. The question of whether a scalable implementation can surpass this coherence threshold is not only important for the technological future of quantum computation, but also for fundamental understanding of the border between microscopic quantum behavior and macroscopic classical behavior.Experimentally observed coherence times (T 2 ) for various qubit implementations are shown in Table I. The atomic systems shown -trapped ions and molecular nuclei in liquid solution -have already been employed for small quantum algorithms [6,13]; not coincidentally, they show very high values of Q, the product of the qubit frequency ω 0 /2π and πT 2 . Most solid-state qubits show smaller values of Q; as we demonstrate in this Letter, however, the long coherence times we observe in solid-state 29 Si nuclei afford them a Q and ΩT 2 as high or higher than atomic systems, indicating this system's promise for solid-state quantum computing.Many promising qubits and coherence time measurements are not mentioned in Table I either because reliable experimental data are not available, or because the existing experimental data are taken under conditions not sufficiently similar to the corresponding quantum computer architecture. For example, electron spins bound to phosphorous donors in pure, isotopically depleted silicon also show prom...

The magnesium content in MgxZn1-xO/ZnO heterostructures grown by molecular beam epitaxy enables the careful control of the carrier density of the two-dimensional electron system down to 5.6×1010 cm-2 while retaining a mobility of 200,000 cm2 V-1 s-1 when pursuing magnesium concentrations as low as x = 0.0038. By selecting an optimum magnesium content (x∼0.01), the mobility is enhanced to over 700,000 cm2 V-1 s-1 due to reduced impurity levels associated with the use of pure distilled ozone and avoiding interface roughness scattering. This control technique allows access to the coherent transport region with strong electron–electron interaction.

The quantum Hall effect is a macroscopic quantum phenomenon in a two-dimensional electron system. The two-dimensional electron system in SrTiO3 has sparked a great deal of interest, mainly because of the strong electron correlation effects expected from the 3d orbitals. Here we report the observation of the quantum Hall effect in a dilute La-doped SrTiO3-two-dimensional electron system, fabricated by metal organic molecular-beam epitaxy. The quantized Hall plateaus are found to be solely stemming from the low Landau levels with even integer-filling factors, ν=4 and 6 without any contribution from odd ν's. For ν=4, the corresponding plateau disappears on decreasing the carrier density. Such peculiar behaviours are proposed to be due to the crossing between the Landau levels originating from the two subbands composed of d orbitals with different effective masses. Our findings pave a way to explore unprecedented quantum phenomena in d-electron systems.

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The sequence of prominent fractional quantum Hall states up to ν = 5/11 around ν = 1/2 in a high mobility two-dimensional electron system confined at oxide heterointerface (ZnO) is analyzed in terms of the composite fermion model. The temperature dependence of Rxx oscillations around ν = 1/2 yields an estimation of the composite fermion effective mass, which increases linearly with the magnetic field. This mass is of similar value to an enhanced electron effective mass, which in itself arises from strong electron interaction. The energy gaps of fractional states and the temperature dependence of Rxx at ν = 1/2 point to large residual interactions between composite fermions. [3,6] transitions. Essential to the evolution of this field has been the material SrTiO 3 and its derived heterostructures, which has recently displayed an electron mobility exceeding 100,000 cm 2 /Vs [7]. However, in recent years, the MgZnO/ZnO heterostructure has emerged as an outstanding material for two-dimensional (2D) high-mobility electron system in this new realm of materials science, where steady improvements in growth technique have realized mobilities as high as 800,000 cm 2 /Vs [2,4,8]. In such a clean 2D system, the Coulomb interaction can dominate the physics in magnetic fields [9][10][11]. In low fields, interact- ), where n is the charge carrier density, m b the band mass and ǫ the dielectric constant of the hosting material. In a high magnetic field B, the kinetic energy of charge carriers is quenched, where the Coulomb interaction ( e 2 ǫlB ) on the magnetic length scale l B = /eB leads to the fractional quantum Hall effect(FQHE). This sequence of FQHE is described by the composite fermion picture, which maps the original system in a magnetic field B to a fermion system in an effective magnetic field B eff = B − 2nφ 0 by attaching an even number of flux quanta φ 0 to each electron [13]. At ν = 1/2 in particular, the state is mapped to a CF system interacting with a Chern-Simons gauge field with a zero B eff at a mean-field level. Conversely, beyond the mean field approximation, density fluctuations of CFs cause the fluctuation of effective magnetic field, and this dictates the inter-CF interaction, which is totally different from the original interaction at B = 0. The inter-CF interaction also determines the renormalized mass m CF of a composite fermion [14]. Now the appearance of correlation effects, both in low and high magnetic fields, depends on the material parameters. Table I compares them for ZnO-based 2D electron system (2DES) with the well-established GaAs and SrTiO 3 systems, which shows that large r s and strong Coulomb interaction in high magnetic fields distinguish ZnO from other materials. Therefore we anticipate the electron transport in this material to be strongly affected by the Coulomb interaction in weak as well as strong