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A dc voltage changed periodically with magnetic field is observed on segments of asymmetric aluminum loop without any external dc current at temperatures corresponded to superconducting transition. According to this experimental result a segment of the loop is a dc power source. A possibility of a persistent voltage on segments of an inhomogeneous normal metal mesoscopic loop follows from this result., Comment: 3 pages, 2 figures

Magnetic dependencies of the critical current of superconducting, aluminium rings, with homogeneous section and with small narrow spot, are measured. Only permitted state at each magnetic flux value is observed in the conventional ring because of strong discreteness of its spectrum. But two states are observed because of the small narrow spot., Comment: 3 pages, 2 figure, Presented at the 34 Meeting on the Low Temperature Physics, 26-30 September 2006, Loo, Russia

Magnetic field dependences of critical current, resistance, and rectified voltage of asymmetric (half circles of different widths) and symmetrical (half circles of equal widths) aluminum rings were measured in the temperature region close to the superconducting transition. All these dependences are periodic magnetic field functions with periods corresponding to the flux quantum in the ring. The periodic dependences of critical current measured in opposite directions were found to be close to each other for symmetrical rings and shifted with respect to each other by half the flux quantum in asymmetric rings with ratios between half circle widths of from 1.25 to 2. This shift of the dependences by a quarter of the flux quantum as the ring becomes asymmetric makes critical current anisotropic, which explains the rectification effect observed for asymmetric rings. Shifts of the extrema of the periodic dependences of critical current by a quarter of the flux quantum contradict directly to the results obtained by measuring asymmetric ring resistance oscillations, whose extrema are, as for symmetrical rings, observed at magnetic fluxes equal to an integer and a half of flux quanta., Comment: 6 pages, 6 figures

The obtained periodic magnetic-field dependencies of the critical current, measured in opposite directions on asymmetric superconducting aluminum rings, allow to explain observed earlier quantum oscillations of a dc voltage as a result of alternating current rectification. It is found, that the high efficiency of the rectification of both individual rings and ring systems is connected to a hysteresis of the current-voltage characteristics. The asymmetry of the current-voltage characteristics providing the rectification effect is due to the relative shifts of the magnetic dependencies of the critical current measured in opposite directions. This shift means that position of the critical current minimums does not correspond to n + 0.5 magnetic flux quantum which is in the direct contradiction with measurement results of the Little-Parks resistance oscillations. Despite of this contradiction the amplitude of the critical current anisotropy oscillations and its variations with temperature correspond to expected amplitude of the persistent current oscillations and to its variations with temperature., Comment: 16 pages, 19 figures

We analyze theoretically and experimentally vortex configurations in mesoscopic superconducting squares. Our theoretical approach is based on the analytical solution of the London equation using Green's-function method. The potential-energy landscape found for each vortex configuration is then used in Langevin-type molecular-dynamics simulations to obtain stable vortex configurations. Metastable states and transitions between them and the ground state are analyzed. We present our results of the first direct visualization of vortex patterns in micrometer-sized Nb squares, using the Bitter decoration technique. We show that the filling rules for vortices in squares with increasing applied magnetic field can be formulated, although in a different manner than in disks, in terms of formation of vortex "shells"., Comment: 12 pages, 9 figures

Little-Parks oscillations are observed in a system of 110 series-connected aluminum rings 2000 nm in diameter with the use of measuring currents from 10 nA to 1000 nA. The measurements show that the amplitude and character of the oscillations are independent of the relation between the measuring current and the amplitude of the persistent current. By using asymmetric rings, it is demonstrated that the persistent current has clockwise or contra-clockwise direction. This means that the total current in one of the semi-rings may be directed against the electric field at measurement of the Little-Parks oscillations. The measurements at zero and low measuring current have revealed that the persistent current, like the conventional circulating current, causes a potential difference on the semi-rings with different cross sections in spite of the absence of the Faraday's voltage., Comment: 5 pages, 6 figures

The interaction between the quantum states of two aluminum superconducting rings forming an 8-shape circular-asymmetric microstructure was examined under a threading magnetic flux and bias by an alternating current without a dc component. Quantum oscillations of the rectified dc voltage Vdc(B) as a function of magnetic field were measured in the 8-shape microstructure at various bias ac currents and temperatures close to critical. Fourier and wavelet analyses of Vdc(B) functions revealed the presence of various combination frequencies in addition to two ring fundamental frequencies, which suggests the interaction in the structure. Deviation of the Vdc(B) function from oddness with respect to the magnetic field direction was found for the first time., Comment: author english version, 3 pages, 3 figires, Proc. of the XXXIV Conference on Low-Temperature Physics "NT-34" (Russia, 2006)

Periodic quantum oscillations of a rectified dc voltage Vdc(B) vs the perpendicular magnetic field B were measured near the critical temperature Tc in a single superconducting aluminum almost symmetric ring (without specially created circular asymmetry) biased by alternating current with a zero dc component. With varying bias current and temperature, these Vdc(B) oscillations behave like the Vdc(B) oscillations observed in a circular-asymmetric ring but are of smaller amplitude. The Fourier spectra of the Vdc(B) functions exhibit a fundamental frequency, corresponding to the ring area, and its higher harmonics. Unexpectedly, satellite frequencies depending on the structure geometry and external parameters were found next to the fundamental frequency and around its higher harmonics., Comment: author english version, 2 pages, 3 figires, Proc. of the XXXIV Conference on Low-Temperature Physics "NT-34" (Russia, 2006)

We have measured periodic oscillations of rectified dc voltage versus magnetic field V_{dc}(B) in a superconducting aluminum thin-film circular-asymmetric figure-of-eight microstructure threaded by a magnetic flux and biased with a sinusoidal alternating current (without a dc component) near the critical temperature. The Fourier spectra of these V_{dc}(B) functions contain fundamental frequencies representing periodic responses of the larger and smaller asymmetric circular loops, composing the microstructure, to the magnetic field. The higher harmonics of the obtained fundamental frequencies result from the non-sinusoidal character of loop circulating currents. The presence of the difference and summation frequencies in these spectra points to the interaction between the quantum states of both loops. Magnitudes of the loop responses to the bias ac and magnetic field vary with temperature and the bias current amplitude, both in absolute values and with respect to each other. The strongest loop response appears when the average resistive state of the loop corresponds to the midpoint of the superconducting-normal phase transition., Comment: 5 pages; 2 figures; minor changes in grammar; shortened title

In order to clear up a question on possibility of a dc voltage proportional to the persistent current in normal metal and semiconductor mesoscopic loops conjectural causes of this phenomenon observed in superconductor loops is investigated., Comment: 3 pages, 2 figures

Multi-quanta, or giant, vortices (GVs) are known to appear in very small superconductors near the superconducting transition due to strong confinement of magnetic flux. Here we present evidence for a new, pinning-related, mechanism for the formation of GVs. Using Bitter decoration to visualise vortices in small Nb disks, we show that confinement in combination with strong disorder causes individual vortices to merge into clusters or even GVs well below Tc and Hc2, in contrast to well-defined shells of individual vortices found in the absence of pinning., Comment: 12 pages, 5 figures; the size of Figure 2 on p. 9 was reduced, as some information on it was lost in original submission

Multiple and single measurements of quantum states of mesoscopic superconducting loops are carried out in order to investigate a possibility of macroscopic quantum superposition and of creation of a superconductor quantum register. Asymmetric superconducting rings are used in order to be convinced that single measurement gives result corresponding to one of permitted states and multiple one gives an average value on these states. We have measured magnetic dependencies of resistance, rectified voltage and critical current on these rings. The observed quantum oscillations of the resistance and the rectified voltage, corresponding to multiple measurement of quantum states, give evidence of two permitted states at the magnetic flux inside the ring divisible by half of the flux quantum. But the observed quantum oscillations of the critical current, corresponding to single measurement, not only does not confirm these two quantum states, but are in a direct contradiction with the observed oscillations of the resistance. It is assumed that the observed contradiction between the results of measurements made on the same ring can testify to violation of the principle of realism on the mesoscopic level that is a necessary condition for an opportunity of creation of a quantum computer., Comment: 10 pages, 8 figures

Mesoscopic loop is proposed in many works as possible solid-state quantum bit, i.e. two-state quantum system. The quantum oscillations of resistance and of rectified voltage observed on asymmetric superconducting loops give evidence of the two states at magnetic flux divisible by half of the flux quantum. But our measurements of quantum oscillations of the critical current of these loops have given results coming into irreconcilable contradictions with result of the observations of the quantum oscillations of resistance., Comment: 3 pages, 3 figures

The Little-Parks oscillations of the resistance and the quantum oscillations of the rectified voltage observed for asymmetric superconducting Al rings give experimental evidence of two degenerate energy states at the magnetic flux $\Phi_{0}$/2. The quantum oscillations of the critical current as a function of magnetic field have also been measured. On the one hand, these oscillations confirm that the quantum oscillations of the rectified voltage are a consequence of periodical dependence of the asymmetry of the current-voltage curves and, on the other hand, comparison of the oscillations with Little-Parks measurements results in contradiction., Comment: 4 pages, 6 figes

The quantum oscillations of the dc voltage are induced on segments of asymmetric superconducting loops by an external ac current or noise. The dependencies of the amplitude of the quantum oscillations on amplitude of inducing ac current are measured at different temperatures below superconducting transition Tc on aluminum asymmetric loops and systems of the loops connected in series. The measured values of the maximum amplitude of the quantum oscillations, the amplitude of the ac current inducing this maximum dc voltage and the critical amplitude of the ac current decrease with temperature increase to Tc. The extrapolation of these measured dependencies to the region near superconducting transition allows to make a calibration of asymmetric superconducting loops as quantum detector of noise. The calibration restores an amplitude profile of the noise pulses from a measured temperature dependence of an amplitude of the quantum oscillations induced by this noise. It is found that rectification efficiency, determined as relation of the maximum amplitude of the quantum oscillations to the ac current amplitude inducing it, decreases near superconducting transition Tc. High efficiency of rectification observed below Tc is consequence of irreversibility of the current-voltage curves. Increase of the rectification efficiency is achieved in multiple series connected loop structures., Comment: 9 pages, 10 figures, paper for the Proceedings of the International Conference "Micro- and nanoelectronics - 2005" (ICMNE-2005), 3-7 October 2005, Moscow region, Russia

The current-voltage curves and magnetic dependence of the critical current of asymmetric superconducting loops are measured. It was found that sign and value of the asymmetry of the current-voltage curves changes with value of magnetic field, periodically for single loop and system of identical loops. The obtained results allow to explain the quantum oscillation of the dc voltage, observed below superconducting transition in the previous works, as rectification of ac current or noise., Comment: 3 pages, 3 figures

The quantum rectification effect observed on asymmetric superconducting loops is proposed to use as a basic of a noise detector with maximum sensitivity. The measurements show that a critical amplitude of noise or ac current decreases down to zero near superconducting transition, Tc, just as superconducting critical current. Therefore any how weak noise, right down to the equilibrium one, can induce the quantum oscillations of the dc voltage near Tc. The transformation of the power of random noise into the dc power observed on asymmetric superconducting loops gives very important advantage: even very weak noise can give enough high output power in a system with large number of loops., Comment: 3 pages, 4 figures, WOCSDICE 2005, p.97-99

The periodical dependencies in magnetic field of the asymmetry of the current-voltage curves of asymmetric aluminum loop are investigated experimentally at different temperatures below the transition into the superconducting state T < Tc. The obtained periodical dependencies of the critical current on magnetic field allow to explain the quantum oscillations of the dc voltage as consequence of the rectification of the external ac current and to calculate the persistent current at different values of magnetic flux inside the loop and temperatures., Comment: 2 pages, 2 figures, will be published in the Proceedings of the 24th International Conference on Low Temperature Physics

Electronic properties of materials are commonly described by quasiparticles that behave as non-relativistic electrons with a finite mass and obey the Schroedinger equation. Here we report a condensed matter system where electron transport is essentially governed by the Dirac equation and charge carriers mimic relativistic particles with zero mass and an effective "speed of light" c* ~10^6m/s. Our studies of graphene - a single atomic layer of carbon - have revealed a variety of unusual phenomena characteristic of two-dimensional (2D) Dirac fermions. In particular, we have observed that a) the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; b) graphene's conductivity never falls below a minimum value corresponding to the conductance quantum e^2/h, even when carrier concentrations tend to zero; c) the cyclotron mass m of massless carriers with energy E in graphene is described by equation E =mc*^2; and d) Shubnikov-de Haas oscillations in graphene exhibit a phase shift of pi due to Berry's phase.

We have visualised and studied vortex configurations in mesoscopic superconducting disks using the Bitter decoration technique. For a broad range of vorticities L the circular geometry is found to result in the formation of concentric shells of vortices. From images obtained on disks of different sizes in a range of magnetic fields we were able to trace the evolution of vortex states and identify stable and metastable configurations. Furthermore, quantitative analysis of shell filling with increasing L allowed us to identify 'magic' numbers corresponding to the appearance of consecutive new shells.

We report high-quality two-dimensional (2D) electron and hole gases induced at the surface of graphite by the electric field effect. The 2D carriers reside within a few near-surface atomic layers and exhibit mobilities up to 15,000 and 60,000 cm2/Vs at room and liquid-helium temperatures, respectively. The mobilities imply ballistic transport at micron scale. Pronounced Shubnikov-de Haas oscillations reveal the existence of two types of carries in both 2D electron and hole gases., Comment: related to cond-mat/0410631 where preliminary data for this experimental system were reported

The ability to control electronic properties of a material by externally applied voltage is at the heart of modern electronics. In many cases, it is the so-called electric field effect that allows one to vary the carrier concentration in a semiconductor device and, consequently, change an electric current through it. As the semiconductor industry is nearing the limits of performance improvements for the current technologies dominated by silicon, there is a constant search for new, non-traditional materials whose properties can be controlled by electric field. Most notable examples of such materials developed recently are organic conductors [1], oxides near a superconducting or magnetic phase transition [2] and carbon nanotubes [3-5]. Here, we describe another system of this kind - thin monocrystalline films of graphite - which exhibits a pronounced electric field effect, such that carriers in the conductive channel can be turned into either electrons or holes. The films remain metallic, continuous and of high quality down to a few atomic layers in thickness. The demonstrated ease of preparing such films of nearly macroscopic sizes and of their processing by standard microfabrication techniques, combined with submicron-scale ballistic transport even at room temperature, offer a new two-dimensional system controllable by electric-field doping and provide a realistic promise of device applications., Comment: This is a paper submitted to Nature on Feb 5, 2004. Our latest report in Science (cond-mat 0410550) covers more ground but we had several inquiries in recent days, concerning the earlier results on thicker graphitic films, as the Nature e-preprint seems to diffuse much wider than we expected. The earlier manuscript contains significant information not covered by Science

We report a naturally-occurring two-dimensional material (graphene that can be viewed as a gigantic flat fullerene molecule, describe its electronic properties and demonstrate all-metallic field-effect transistor, which uniquely exhibits ballistic transport at submicron distances even at room temperature.

We report a new nonlocal effect in vortex matter, where an electric current confined to a small region of a long and sufficiently narrow superconducting wire causes vortex flow at distances hundreds of inter-vortex separations away. The observed remote traffic of vortices is attributed to a very efficient transfer of a local strain through the one-dimensional vortex lattice, even in the presence of disorder. We also observe mesoscopic fluctuations in the nonlocal vortex flow, which arise due to "traffic jams" when vortex arrangements do not match a local geometry of a superconducting channel., Comment: a slightly longer version of a tentatively accepted PRL

Movements of individual domain walls in a ferromagnetic garnet were studied with angstrom resolution. The measurements reveal that domain walls can be locked between adjacent crystallographic planes and propagate by distinct steps matching the lattice periodicity. Domain walls are found to be weakly mobile within valleys of the atomic washboard but become unexpectedly flexible on Peierls ridges, where they can be kept in a bi-stable state by ac magnetic field. We describe the latter observation in terms of a single magnetic kink propagating along a domain wall.

A theoretical prediction published in Phys.Rev. B 64, 012505 (2001) is corroborated experimentally. This corroboration of the theoretical result published in Physical Review B was rejected for publication in the same journal. Such inconsistency is connected with a contradiction to the second law of thermodynamics. According to the theory Phys.Rev. B 64, 012505 (2001) the energy of a noise can be transformed to a dc power in superconducting loop and therefore a dc voltage oscillating with magnetic field can be observed on segments of an inhomogeneous loop in the temperature region close to the superconducting transition. Such quantum voltage oscillations observed in the present work can be induced both by an external electrical noise and by internal equilibrium noise (thermal fluctuations). Violation of the second law takes place in the second case. First of all the theoretical result published by Phys.Rev.B is challenge to the second law but about this contradiction was openly written only in the first version (see physics/0105059) of the experimental paper rejected by Referees of Phys.Rev.B. The transformation of an external electrical noise to the dc voltage was confirmed recently in the paper published in JETP Letters 77, 371 (2003) (see also cond-mat/0303538)., Comment: 4 pages, 5 figures

A dc voltage induced by an external ac current is observed in system of asymmetric mesoscopic superconducting loops. The value and sign of this dc voltage, like the one of the persistent current, depend in a periodical way on a magnetic field with period corresponded to the flux quantum within the loop. The amplitude of the oscillations does not depend on the frequency of the external ac current (in the investigated region 100 Hz - 1 MHz) and depends on its amplitude. The latter dependence is not monotonous. The observed phenomenon of rectification is interpreted as a consequence of a dynamic resistive state induced by superposition of the external current and the persistent current. It is shown that the dc voltage can be added in system of loops connected in series: the dc voltage oscillations with amplitude up to 0.00001 V were observed in single loop, up to 0.00004 V in a system of 3 loops and up to 0.0003 V in a system of 20 loops., Comment: 5 pages, 6 figures

The proximity effect in SF structures was examined. It is shown that, due to the oscillations of the induced superconducting order parameter in a ferromagnet, the critical temperature of an SF-bilayer becomes minimal when the thickness of the ferromagnetic layer is close to a quarter of the period of spatial oscillations. It is found that the spontaneous vortex state arisen in the superconductor due to the proximity of the magnetic domain structure of a ferromagnet brings about noticeable magnetoresistive effects., Comment: 9 pages, 5 figures, published in JETP Lett

An experimental and theoretical investigation was made of flux jumps and irreversible magnetization curves of mesoscopic Al superconducting rings. In the small magnetic field region the change of vorticity with magnetic field can be larger than unity. This behavior is connected with the existence of several metastable states of different vorticity. The intentional introduction of a defect in the ring has a large effect on the size of the flux jumps. Calculations based on the time-dependent Ginzburg-Landau model allows us to explain the experimental results semi-quantitatively., Comment: 6 pages, 6 figures

It was shown as long ago as 1998 cond-mat/9811051 that the vortex lattice melting theories are science fiction because the Abrikosov state is not the vortex lattice with crystalline long-range order. Nevertheless this false conception is used up to now in many works including the lecture notes cond-mat/0111052 providing a pedagogical introduction. This false conception has resulted from visual but incorrect ideas. In spite of outward appearances only long-range order - long-range phase coherence exists in the Abrikosov state. The phase transition interpreted erroneously as the vortex lattice melting is in reality a disappearance of long-range phase coherence. The investigation of the nonlocal resistivity made in this work is experimental evidence that a state without phase coherence, differed qualitatively from mythical vortex liquid, is observed above this transition., Comment: 4 pages, 3 figures

In order to verify a possibility of a dc voltage predicted on segments of an inhomogeneous superconducting loop the Little-Parks oscillations are investigated on symmetrical and asymmetric Al loops. The amplitude of the voltage oscillations $\Delta V$ measured on segments of symmetrical loop increases with the measuring current $I_{m}$ and $\Delta V = 0$ at $I_{m}= 0$ in accordance with the classical Little-Parks experiment. Whereas the $\Delta V$ measured on segments of asymmetric loop has a maximum value at $I_{m}= 0$. The observation of the dc voltage at $I_{m}= 0$ means that one of the loop segments is a dc power source and others is a load. The dc power can be induced by both thermal fluctuation and a external electric noise., Comment: 4 pages, 4 figures

As first pointed out by Bardeen and Ginzburg in the early sixties, the amount of magnetic flux carried by vortices depends on their distance to the sample edge and can be smaller than one flux quantum, f0 = h/2e. In bulk superconductors, this reduction of flux becomes negligible already at submicron distances from the edge but, in thin films, the effect may survive at much larger distances. In the absence of any experimental observation, such flux reduction is perceived to be an exotic or unimportant effect, and it is often assumed that magnetic field enters type-II superconductors in units of f0. Here we report the measurements of the amount of flux associated with the entrance of individual vortices in a superconducting film and show that the flux that they bring in, always differs substantially from f0. We have observed vortices that carry as little as 0.001 f0 as well as seemingly "negative vortices" whose penetration leads to the expulsion of magnetic field. We distinguish two phenomena responsible for non-quantized flux penetration: the finite-size effect and a non-linear screening of magnetic field in the presence of a surface barrier. The latter effect has previously not been considered but is likely to cause non-quantized penetration in many cases., Comment: pdf-file of a slighly longer version than appeared in Nature

Each time a vortex enters or exits a small superconductor, a different fluxoid state develops. We have observed splitting and sharp kinks on magnetization curves of such individual states. The features are the manifestation of first and second order transitions, respectively, and reveal the existence of distinct vortex phases within a superconducting state with a fixed number of fluxoids. We show that the kinks indicate the merger of individual vortices into a single giant vortex while the splitting is attributed to transitions between different arrays of the same number of vortices., Comment: in PDF format; 12 pages including 3 pages of figures. Slightly extended version of Phys. Rev. Lett. 85, 1528-1531 (2000)