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We have studied the Coulomb anomaly in the conductance of a phase-coherent disordered 2-dimensional electron gas. Its average magnitude of δGEEI≈−0.3 e2/h is obtained by applying a bias voltage to suppress the Coulomb anomaly. This Coulomb anomaly is suppressed by a parallel magnetic field in contrast to theoretical predictions. Surprisingly, the magnitude of this Coulomb anomaly exhibits reproducible fluctuations in perpendicular magnetic fields on a magnetic field scale much larger than that for universal conductance fluctuations.

We present an overview of sample-specific transport properties tuned by the superconducting phase difference between two superconductors connected to a disordered 2-dimensional electron gas (2DEG). We demonstrate a crossover from ensemble-averaged to sample-specific resistance oscillations of a T-shaped 2DEG interferometer by increasing the magnetic field. Multi-terminal resistances of a cross-shaped 2DEG interferometer are analyzed in terms of an extended Landauer-Buttiker transport formalism. We show that the extended reciprocity relations hold and that three-terminal resistances become negative. (C) 1998 Elsevier Science B.V. All rights reserved.

We study the conductance fluctuations in the quasi-ballistic transport regime by an analytical method based on the Lippmann–Schwinger equation and the Landauer formula. The contribution of single impurity scattering events, impurity potential fluctuations, multiple scattering between an impurity and sample boundaries as well as multiple scattering involving many impurities are discussed. The amplitude of the fluctuations cannot be measured by tuning the Fermi energy or an external magnetic field because the single impurity scattering events dominate the fluctuations, implying that the ergodic hypothesis breaks down in the quasi-ballistic transport regime. Absence of aperiodic oscillations in the experimental parametric conductance does not always mean an absence of defects in the sample.

We have investigated ballistic transport through a sub-micron-sized Sinai billiard fabricated using a high-mobility two-dimensional electron gas. The geometry of the billiard is defined by a circular surface gate surrounded by an outer square gate with two quantum point contacts. When both gates are biased negatively, the Sinai billiard is formed and collisions with the confining potential walls generate chaotic classical motion. Recent experiments have revealed novel ‘self-similar’ fluctuation patterns in the conductance of the Sinai billiard, measured as a function of magnetic field perpendicular to the plane of the electron gas. We have undertaken quantum mechanical calculations of the device conductance using a detailed model for the potential landscape under the surface gates. We compare these results with predictions for a hard-walled billiard and show that the surface gate geometry can have a large effect on the observed transport properties.

Millikelvin magnetoconductance studies performed in mesoscopic spin-glass n+-Cd1−xMnxTe wires reveal strong effects of Mn spins upon universal conductance fluctuations. In particular, scattering potential of the frozen spins leads to magnetic and thermal irreversibilities of the fluctuation patterns. Slowly fluctuating spins, on the other hand, are an efficient source of conductance noise providing a real-time probe of spin dynamics.

We have studied the magnetic properties of self-organized ErAs aggregates embedded in a GaAs matrix using telegraph noise spectroscopy. The electrical transport through the samples is mesoscopic and exhibits universal conductance fluctuations and two-level fluctuations (TLF's). A statistical analysis of a TLF allows us to measure the extremely small magnetization of an isolated ErAs cluster. Rotating the sample in a magnetic field reveals the sixfold magnetic anisotropy expected for ErAs with a rocksalt structure. At high temperatures the switching is thermally activated, while at low temperatures it is the tunneling of the magnetization which dominates. The magnetic-field dependence of the crossover temperature between the thermally activated and tunneling regimes can be explained with a simple model. ispartof: Physical Review B, Condensed Matter vol:57 issue:12 pages:7182-7189 status: published

An overview is given of selected novel effects observed recently by various groups in modulated structures of Cd 1− x Mn x Te. Millikelvin studies of submicron wires doped with either indium or iodine have demonstrated the existence of a new mechanism, by which the universal conductance fluctuations can be generated in mesoscopic systems containing magnetic ions. Moreover, 1/ f conductance noise as well as thermal and magnetic irreversibilities have been observed, providing important information on spin-glass dynamics. Finite size effects in magnetic properties have been probed by direct static and dynamic SQUID measurements on superlattices consisting of few-monolayer spin-glass films separated by nonmagnetic barriers. The confined holes have been found to exert a strong influence upon the magnetic ions and to induce a ferromagnetic phase transition above 1 K in quantum wells modulation doped by nitrogen. Finally, it has been shown also that the giant spin-splitting of the bands offers a tool to tune the coupling between confined photon and exciton modes in photonic structures.

We have measured the $1/f$ resistance noise of quench-condensed mesoscopic Li wires as a function of magnetic field over the range 0--9 T at low temperatures. The noise versus field reflects the crossover behavior of universal conductance fluctuations. Since Li has negligible spin-orbit scattering, the $1/f$ noise versus magnetic field shows two distinct reductions by factors of 2. The first results from the breaking of time-reversal invariance and the second from Zeeman splitting of the conduction-electron-spin degeneracy. In the experiment the thermal energy is larger than the Thouless energy; in this case the former energy governs the characteristic magnetic-field scale for the Zeeman crossover. In mesoscopic Li wires with finite spin-flip scattering due to magnetic impurities, the $1/f$ noise also shows a reduction by a factor of 2 in a weak magnetic field. At high magnetic field, however, the $1/f$ noise increases dramatically when the Zeeman splitting of the magnetic impurities is larger than the temperature. We analyze the data from both experiments quantitatively and find good agreement with theory.

Two types of quantum magnetotransport behavior were observed in pristine bundles of helicoidal carbon nanotubes. Universal conductance fluctuations for $Tl10$ K and an underlying positive magnetoconductance to very high magnetic fields for $Tl100$ K are the most notable features of one of these types. Remarkably, this behavior was observed after intercalation of potassium guest atoms into pristine bundles of the other type. This range of phenomena is explained within the theory of weak localization and interaction effect in three dimensions. However, the observed inelastic scattering mechanism for K-intercalated bundles cannot be described by the present theory for a common mechanism of the same dimensionality.

We investigate fluctuations in the magnetoconductance (measured at T o 50 mK) of noble-metal nanowires in a mesoscopic two-lead configuration, with lengths 500 and 1000 nm and widths w between 45 and 360 nm. We determine the dependence of the correlation field Bc on the angle u between the direction of the magnetic field and the long axis of the wires. u is changed at low T continuously from 90± (usual geometry) to 0±. We present a calculation taking into account the 3D diffusive motion of the conduction electrons describing the angular dependence of Bc. We compare this Bcsud dependence with conductance fluctuations observed while sweeping u at constant magnetic field. [S0031-9007(97)03042-1]

The conductance distribution of metallic mesoscopic systems is considered. The variance of this distribution describes the universal conductance fluctuations, yielding a Gaussian distribution of the conductance. We calculate diagrammatically the third cumulant of this distribution, the leading deviation from the Gaussian. We confirm random matrix theory calculations that the leading contribution in quasi-one dimension vanishes. However, in quasi two dimensions the third cumulant is negative, whereas in three dimensions it is positive., 9 pages, Revtex, with eps figures,to appear in Phys Rev B

Normal-conducting mesoscopic systems in contact with a superconductor are classified by the symmetry operations of time reversal and rotation of the electron's spin. Four symmetry classes are identified, which correspond to Cartan's symmetric spaces of type C, CI, D, and DIII. A detailed study is made of the systems where the phase shift due to Andreev reflection averages to zero along a typical semiclassical single-electron trajectory. Such systems are particularly interesting because they do not have a genuine excitation gap but support quasiparticle states close to the chemical potential. Disorder or dynamically generated chaos mixes the states and produces forms of universal level statistics different from Wigner-Dyson. For two of the four universality classes, the n-level correlation functions are calculated by the mapping on a free one-dimensional Fermi gas with a boundary. The remaining two classes are related to the Laguerre orthogonal and symplectic random-matrix ensembles. For a quantum dot with a normal-metal--superconducting geometry, the weak-localization correction to the conductance is calculated as a function of sticking probability and two perturbations breaking time-reversal symmetry and spin-rotation invariance. The universal conductance fluctuations are computed from a maximum-entropy S-matrix ensemble. They are larger by a factor of 2 than what is naively expected from the analogy with normal-conducting systems. This enhancement is explained by the doubling of the number of slow modes: owing to the coupling of particles and holes by the proximity to the superconductor, every cooperon and diffusion mode in the advanced-retarded channel entails a corresponding mode in the advanced-advanced (or retarded-retarded) channel.

Mesoscopic phenomena in quantum structures which incorporate magnetic impurities with localized spins may exhibit a number of novel features driven by spin-disorder scattering, exchange spin-splitting of electron bands, and the formation of bound magnetic polarons. After brief information on these effects, their influence on universal conductance fluctuations as well as on low frequency noise and quantum localization is presented. Millikelvin investigations of diffusive charge transport, which have been carried out for submicron wires of n+-Cdi_ xMnx Te epilayers, are reviewed in some details. These studies have provided information on the significance of spin-disorder scattering in semiconductors and put into the evidence a new driving mechanism of the magnetoconductance fluctuations — the redistribution of the electrons between energy levels of the system, induced by the giant s-d exchange spin-splitting. Important implications of these findings for previous interpretations of spin effects in semiconductor and metal nanostructures are discussed. PACS numbers: 72.15.Rn, 73.20.Fz, 73.61.Ga, 75.50.Pp

Periodic Aharonov–Bohm and Altshuler–Aronov–Spivak oscillations have traditionally been observed in lateral transport through patterned mesoscopic loops of diffusive conductors. However, our studies of perpendicular-to-plane magnetotransport in straight-channel, diffusive devices of epitaxial Bi2Se3 surprisingly reveal signatures of Aharonov–Bohm orbits, periodic conductance fluctuation magneto-fingerprints, even though the devices are not explicitly patterned into loops. We show that the length scale of these orbits corresponds to the typical perimeter of triangular terraces found on the surface of these thin film devices, strongly suggesting that the periodic magneto-fingerprint arises from coherent scattering of electron waves from the step-edges. Our interpretation is bolstered by control measurements in devices without such surface morphology that only show a conventional, aperiodic magneto-fingerprint. These results show that lithographically patterned Bi2Se3 devices provide a novel class of mesoscopic physical systems for systematic studies of coherent surface sensitive transport.

We study conductance fluctuations (CF) and the sensitivity of the conductance to the motion of a single scatterer in two-dimensional massless Dirac systems. Our extensive numerical study finds limits to the predicted universal value of CF. We find that CF are suppressed for ballistic systems near the Dirac point and approach the universal value at sufficiently strong disorder. The conductance of massless Dirac fermions is sensitive to the motion of a single scatterer. CF of order $e^2/h$ result from the motion of a single impurity by a distance comparable to the Fermi wavelength. This result applies to graphene systems with a broad range of impurity strength and concentration while the dependence on the Fermi wavelength can be explored {\em via} gate voltages. Our prediction can be tested by comparing graphene samples with varying amounts of disorder and can be used to understand interference effects in mesoscopic graphene devices., 15 Pages, 3 Figures. Related papers at this http URL

n-p-n and n-2D TI-n junctions. The resistance reveals the fractional plateau 2h/e 2 in n-p-n regime in the presence of the strong perpendicular magnetic field. We found that in n-2D TI-n regime the plateaux in resistance in not universal and results from the edge state equilibration at the interface between chiral and helical edge modes. We provided the simple model describing the resistance quantization in n-2D TI-n regime. Recently interest in the edge state transport in the integer quantum Hall effect (QHE) has been renewed due to observation of the conductance quantization in the locally gated graphene layers in the bipolar regime [1–3]. It has been demonstrated that the density variation across the charge neutrality point results in a p-n junction with interesting transport properties that are absent in the QHE regime in the unipolar case. In particular, the twoterminal resistance reveals fractional quantization in the graphene p-n [1] or n-p-n [2, 3] junctions, which has been attributed to chiral edge states equilibration at the pn interfaces [4]. In general, the character of the QHE transport in unipolar and bipolar regimes is quite different. In the unipolar regime the edge states propagate in the same direction (figure 1a), while in the bipolar regime the edge states counter-circulate in the p and n regions, propagating parallel to each other along the interface (figure 1c). The intermode scattering across the interface in the presence of the disorder leads to interference between channels, and conductance should exhibit fractional quantization superimposed by universal conductance fluctuations (UCF)[4]. Note, however, that UCF in the bipolar regime have not been observed, which has been attributed to several extrinsic and intrinsic mechanisms [4]. Further study demonstrated that UCF in a sufficiently small (mesoscopic) system are robust to sample disorder [5], but could be suppressed in the absence of the intervalley scattering [6]. In the latter case, the plateaux value is expected to be shifted up or down from the quantized value, which disagrees with experiments. Therefore, the microscopic mechanism providing plateaux quantization in graphene p-n and p-n-p structures still remains unclear. The semiclassical approach [7] confirms this conclusion. Another interesting system, which provides for realization of the p-n junction and study of the QHE in the bipolar regime is the HgTe-based quantum well. The transport properties of such a system depends on the well width d. In particular, when d exceeds the ”critical” width approximately equal to 6.3 nm, the energy spectrum becomes inverted and one changes to a two

A recent Drude model description of the metallic regime and of a channel- averaged elastic mean free path (mfp), $\ell_0$, in an $N$-channel tight-binding wire identifies the Thouless localization length, $N\ell_0$, as a proper lower bound of macroscopic length scales ("mean free path") for the DMPK equation describing the localized regime of the wire. The mfp $\ell_0$ leads to a metallic regime which is consistent with Dorokhov's microscopic transmission analysis in terms of a nominal elastic mfp. On the other hand, the validity of Mello's derivation of universal conductance fluctuations in the metallic regime based on the DMPK equation is restored if the mfp $\ell'$, of order $N\ell_0$, in that equation is replaced by the correct mean free path $\ell_0$., To be published in Solid State Communications

We present the study of low-frequency noise, or 1/f noise, in degenerately doped Si: P and Ge: P delta-layers at low temperatures. For the Si: P d-layers we find that the noise is several orders of magnitude lower than that of bulk Si: P systems in the metallic regime and is one of the lowest values reported for doped semiconductors. Ge: P d-layers as a function of perpendicular magnetic field, shows a factor of two reduction in noise magnitude at the scale of B-phi, where B-phi is phase breaking field. We show that this is a characteristic feature of universal conductance fluctuations.

We demonstrate that the universal conductance fluctuations (UCF) can be used as a direct probe to study the valley quantum states in disordered graphene. The UCF magnitude in graphene is suppressed by a factor of four at high carrier densities where the short-range disorder essentially breaks the valley degeneracy of the K and K' valleys, leading to a density dependent crossover of symmetry class from symplectic near the Dirac point to orthogonal at high densities.

The earth's crust and outer space are rich sources of technologically relevant materials which have found application in a wide range of fields. Well-established examples are diamond, one of the hardest known materials, or graphite as a suitable precursor of graphene. The ongoing drive to discover novel materials useful for (opto)electronic applications has recently drawn strong attention to topological insulators. Here, we report that Kawazulite, a mineral with the approximate composition Bi$_2$(Te,Se)$_2$(Se,S), represents a naturally occurring topological insulator whose electronic properties compete well with those of its synthetic counterparts. Kawazulite flakes with a thickness of a few tens of nanometers were prepared by mechanical exfoliation. They exhibit a low intrinsic bulk doping level and correspondingly a sizable mobility of surface state carriers of more than $1000 \text{cm}^2/(\text{V s})$ at low temperature. Based on these findings, further minerals which due to their minimized defect densities display even better electronic characteristics may be identified in the future.

The transport properties of manganite thin films characterized by a weak-localization transition have been studied. Detailed voltage noise measurements show a specific $1/f$ noise spectrum below the transition temperature. A theoretical interpretation in terms of universal conductance fluctuations explains the nature of the unconventional electric noise, suggesting a direct connection between the weak-localization phenomenon and universal conductance fluctuations. The universal nature of the mechanism allows its detection in different systems under the weak-localization regime.

The works presented in this thesis intend to contribute to condensed matter physics in the understanding of the electronic properties of a recently discovered class of materials : the topological insulators.The first part of this memoir is an introduction to topological insulators, focusing on their specifities compared to "trivial" insulators : helical edge states (in the two dimensional quantum spin Hall effect) or relativistic surface states (for three dimensional topological insulators) both robust agiant disorder.The second part proposes a new way to probe the unique properties of the helical edge states of quantum spin Hall effect via the injection of Cooper pair from a superconductor.The third part deals with the diffusion of the three dimensional topological insulator surface states, in the phase coherent regime. The diffusion, the quantum correction to conductivity, and the amplitude of the universal conductance fluctuations are studied. This study is also led in the experimentally relevant case where the Fermi surface presents a hexagonal deformation., Les travaux présentés dans cette thèse ont pour objectif d’apporter à la physique mésoscopique un éclairage concernant la compréhension des propriétés de transport électroniques d’une classe de matériaux récemment découverts : les isolants topologiques.La première partie de ce manuscrit est une introduction aux isolants topologiques, mettant en partie l’accent sur leurs spécificités par rapport aux isolants "triviaux" : des états de bords hélicaux (dans le cas de l’effet Hall quantique de spin en 2 dimensions) ou de surface relativistes (pour les isolants topologiques tridimensionnels) robustes vis-à-vis du désordre.La deuxième partie propose une sonde de l’hélicité des états de bords de l’effet Hall quantique de spin en étudiant les propriétés remarquables de l’injection de paires de Cooper dans cette phase topologique.La troisième partie étudie la diffusion des états de surface des isolants topologiques tridimensionnels dans le régime cohérent de phase. L’étude de la diffusion, de la correction quantique à la conductance (antilocalisation faible) et de l’amplitude des fluctuations universelles de conductance de fermions de Dirac sans masse est présentée. Cette étude est aussi menée dans la cas d’états de surface dont la surface de Fermi présente la déformation hexagonale observée expérimentalement.

We study origin of Rashba spin-orbit interaction at SrTiO${}_{3}$ surfaces and LaAlO${}_{3}$/SrTiO${}_{3}$ interfaces by considering the interplay between atomic spin-orbit coupling and inversion asymmetry at the surface or interface. We show that in a simple tight-binding model involving $3d$ ${t}_{2g}$ bands of Ti ions, the induced spin-orbit coupling in the ${d}_{xz}$ and ${d}_{yz}$ bands is cubic in momentum whereas the spin-orbit interaction in the ${d}_{xy}$ band has linear momentum dependence. We also find that the spin-orbit interaction in one-dimensional channels at LaAlO${}_{3}$/SrTiO${}_{3}$ interfaces is linear in momentum for all bands. We discuss implications of our results for transport experiments on SrTiO${}_{3}$ surfaces and LaAlO${}_{3}$/SrTiO${}_{3}$ interfaces. In particular, we analyze the effect of a given spin-orbit interaction term on magnetotransport of LaAlO${}_{3}$/SrTiO${}_{3}$ by calculating weak antilocalization corrections to the conductance and to universal conductance fluctuations.

Mesoscopic phenomena in nanostructures that incorporate diluted magnetic semiconductors may exhibit a number of novel features driven by spin interactions between mobile electrons and localized spins. Millikelvin studies of linear and nonlinear diffusive charge transport, which have been carried out for submicron wires of epilayers as well as for microstructures of bicrystals, are reviewed. These studies have provided information on the significance of spin-disorder scattering and evidence of a new driving mechanism of the magnetoconductance fluctuations - the redistribution of the electrons between energy levels of the system, induced by the giant s - d exchange spin-splitting. Important implications of these findings for previous interpretations of spin effects in semiconductor and metal nanostructures are discussed.

We review the methods of fabrication and transport properties of submicron II-VI, IV-VI and IlI-V semiconductor wires. Devices were prepared by electron-beam lithograply and used for detailed magnetotransport studies, carried out at low (down to 30 mK) temperatures. We discuss a number of novel features obtained in ballistic, diffusive and localized transport regimes. In particular, we describe the universal conductance fluctuations for semimagnetic materials (CdMnTe) and discuss the edge channel transport for PbTe, PbSe and GaAs/GaA1As systems.

We study the magnetic field dependence of the correlation field ΔB c and amplitude δg of the conductance fluctuations, observed in the low-temperature magnetoresistance of a quasi-ballistic split-gate wire. With increasing the fields, there exists a crossover from diffusive to ballistic motions in the quasi-ballistic transport. Scattering processes have been discussed by analyzing a linear field dependence of ΔB c above the crossover. The crossover behaviors are considered to be a precursor effect on the formation of the edge channel accompanied with a rapid increase of inelastic scattering length l in .

We study the resistance of narrow AlGaAs/GaAs in-plane gate quantum wires versus gate voltage and magnetic field at 1.2 K. A practical method of determining the effective width of the wire is presented. A tarnsition to boundary dominant scattering occurs as the effective width is decreased and becomes comparable to the mean free path. Beyond this transition, an alternative mean free path, l = αW , is used. Results for effective width compare well to those from the estimate due to the onset of Landau quantization at W ≈ r C . The in-plane gate structure is proposed as a suitable system for studying mesoscopic phenomena, specifically the scaling of universal conductance fluctuations.

We have studied the dynamics of single bistable defects in submicron disordered Bi wires at temperatures 0.1--2 K. The wires are sufficiently small so that the motion of a single defect can be detected as a random telegraph signal in the resistance time trace. The amplitude of the resistance jumps increases as the temperature is lowered due to the physics of universal conductance fluctuations. The defect transitions obey Poisson statistics and detailed balance, indicating that the defect is a two-state system. We interpret the signal as arising from incoherent tunneling of an atom or group of atoms between the two wells of a double-well potential. The temperature dependence of the tunneling rates agrees quantitatively with the predictions of dissipative quantum tunneling theory, which describes tunneling of a defect in the presence of strong dissipation from the electron bath. Our measurements exploit the previous discovery that the energy asymmetry \ensuremath{\varepsilon} of the defect varies with magnetic field. By varying both the temperature and magnetic field, we can probe the behavior of the tunneling rates spanning two very different regimes, from kT\ensuremath{\ll}\ensuremath{\varepsilon} to kT\ensuremath{\gg}\ensuremath{\varepsilon}. Data from a single defect at several values of magnetic field suggest that the defect-bath coupling constant \ensuremath{\alpha} and the renormalized tunneling matrix element ${\mathrm{\ensuremath{\Delta}}}_{\mathit{r}}$ are nearly independent of magnetic field. \textcopyright{} 1996 The American Physical Society.

Weak-field magnetoresistance and universal conductance fluctuations have been studied at millikelvin temperatures in submicron wires of In-doped n + -CdTe and n + -Cd 0.99 Mn 0.01 Te. The fluctuations contain a periodic component of unknown origin. The giant spin-splitting of the electron states, caused by the s-d exchange interaction with the Mn spins, results in the positive magnetoresistance and the temperature dependence of the fluctuation pattern.

A novel class of interference phenomena originating from the geometric phase is discussed. Spin-orbit interaction results in the geometric phase and leads to the destructive interference and a phase shift of the Aharonov-Bohm conductance oscillations in ballistic and diffusive rings. In-plane magnetoresistance of rings exhibits abrupt “topological” transitions from destructive to constructive interference. The origin of the phase breaking due to the spin-orbit interaction in the weak localization conductance and in the universal conductance fluctuations is clarified.

We have studied the negative magnetoresistance and universal conductance fluctuations ~UCF’s ! in a twodimensional electron gas ~2DEG! grown on substrates with prepatterned, submicrometer dimples. Since the 2DEG is sensitive only to the normal component of B, electrons move in a spatially inhomogeneous ( B perpendicular to the substrate: B’) or sign-alternating random magnetic field (B parallel to the substrate: Bi). Quantum interference effects in a random magnetic field due to the magnetic flux appear only due to second-order effects. The UCF’s are found to be 1.5‐2 times smaller for Bi than for B’ . @S01631829~96!09419-2#

We study the magnetic field dependence of the correlation field ΔBcand amplitude δgof the conductance fluctuations, observed in the low temperature magnetoresistance of GaAs/AlGaAs split-gate wires. Near zero field, universality of quantum interference is retained and the magnetoresistance shows universal conductance fluctuations. At high magnetic fields, although the discrete Landau level quantization becomes resolved. ΔBcand δgare found to increase linearly with magnetic field, with a slope which depends upon the nature of electron scatterings in the wire.

We have investigated the transmission of an electron in quasi-one-dimensional systems in the presence of nonuniform magnetic fields. The subband energy and the wave function in a magnetic field, whose strength varies parabolically in the transverse direction, are calculated. This model is expected to describe a composite fermion in quantum wires. The parabolic magnetic field is found to increase the band-edge energies and modify the probability distribution significantly. When a moderate negative offset magnetic field is added, the subband energy takes a minimum value for a finite parabolic magnetic-field strength and the wave function of the lowest subband is double peaked. We have calculated magnetic-field dependencies of the bend resistance and the Hall resistance in a cross junction, in which the parabolic magnetic field is assumed. The positions in magnetic field of the peak in the bend resistance due to ballistic transport and of the zero Hall resistance are shifted and generally do not coincide as the parabolic field is imposed. We also examine the conductance of quantum wires in the presence of random magnetic fields. The nonuniform magnetic fields lead to universal conductance fluctuations in the metallic regime and to exponential decay of the conductance as the length is increased in the localized regime. In contrast to the impurity scattering case, the localization length is found to be smaller for larger average magnetic fields.

We study carrier scattering processes in GaAs/AlGaAs quantum wires by a correlation field analysis of the conductance fluctuations observed in their low temperature magnetoresistance. In the diffusive transport regime, the magneto-resistance at low magnetic fields shows universal conductance fluctuations (UCF) and the correlation field Bc is field independent. However, at higher fields, where the Landau level quantization is resolved, Bc is found to increase as a power law of the magnetic field. We compare our results with recent theoretical predictions for the diffusive nature and also with our own semi-classical explanations for the dynamical transport.

We report magnetoresistance measurements on a two-dimensional electron gas at low magnetic field and near Landau filling factor v = 1 2 in mesoscopic samples. Aperiodic reproducible resistance fluctuations have been found in both cases. In order to show that the fluctuations in a strong field are due to the quantum interference of the composite Fermions, we have compared coherence properties for the electrons and composite particles.

Single, sub-micrometer wide quantum wires have been fabricated using molecular beam epitaxy on mesa-etched GaAs substrates, where the GaAs wire is embedded in AlGaAs. By using a Hall bar pattern, potential probes were directly attached to the wires while grown. To avoid problems associated with anisotropic etching and regrowth, the wire structures were oriented along the 100 crystallographic directions. From this fabrication technique, described in detail by Shitara et al., Appl. Phys. Lett. 66, 2385 (1995), one can expect the formation of high quality �self-aligned� quantum wires with a confinement potential determined by the conduction band discontinuity of AlGaAs and GaAs. Here we study the four-point magnetoresistance of 50 im long single quantum wires with widths between 250 and 700 nm from 1.3 to 21 K. A distinct weak localization peak and universal conductance fluctuations dominate the low magnetic field regime and are used to estimate the phase- coherence length of the electrons. Pronounced 1/B periodic quantum oscillations at magnetic fields above 1 T are consistent with the picture of wires with a square-well shaped confining potential.

Using field-angle, temperature, and back-gate-voltage dependence of the weak anti-localization (WAL) and universal conductance fluctuations of thin Bi1.5Sb0.5Te1.7Se1.3 topological-insulator single crystals, in combination with gate-tuned Hall resistivity measurements, we reliably separated the surface conduction of the topological nature from both the bulk conduction and topologically trivial surface conduction. We minimized the bulk conduction in the crystals and back-gate tuned the Fermi level to the topological bottom-surface band while keeping the top surface insensitive to back-gating with the optimal crystal thickness of ~?100 nm. We argue that the WAL effect occurring by the coherent diffusive motion of carriers in relatively low magnetic fields is more essential than other transport tools such as the Shubnikov-de Hass oscillations for confirming the conduction by the topologically protected surface state. Our approach provides a highly coherent picture of the surface transport properties of TIs and a reliable means of investigating the fundamental topological nature of surface conduction and possible quantum-device applications related to momentum-locked spin polarization in surface states.

Single-crystalline iridium dioxide nanowires show the time-dependent universal conductance fluctuations (TUCFs) at cryogenic temperatures. The conductance fluctuations persist up to temperature T as high as nearly 10 K. The root-mean-square TUCF magnitudes increase with decreasing T, reaching approximately 0.1 e2 / h at 1.7 K. We ascribe these conductance fluctuations to originating from the conduction electrons scattering upon mobile defects (moving scattering centers). Our measured TUCF characteristics are satisfactorily explained in terms of the existing TUCF theory in its three-dimensional form. The extracted electron dephasing length Lφ(1.7 K) ≃90 nm is smaller than the diameter (≈ 180 nm) of our nanowires.

Numerical simulations of conduction through a disordered microbridge between a normal metal and a superconductor have revealed an anomalous insensitivity of the conductance fluctuations to a magnetic field. A theory for the anomaly is presented: Both an exact analytical calculation (using random-matrix theory) and a qualitative symmetry argument (involving the exchange of time-reversal for reflection symmetry)., 8 pages, REVTeX-3.0, 2 figures

We investigated the magneto-conductance of gold nano-wires in a mesoscopic 2-probe configuration. The nano-structures were fabricated using a four-layer resist system and electron beam lithography. The samples consisted of a wire of length L = 1001000 nm and cross section 30 × 30 nm2 connected to two funnel-shaped contacts. At very low temperatures T⋍ 100 mK the magneto-conductance of all measured devices showed a rms-value δG ≈ 0.1e2/h. Our measurements demonstrate that the conductance fluctuations are strongly influenced by the contacts. This is most significant in the correlation field Bc ∼ 1Fα which decreases with decreasing wire length. We also observed a weak dependence of δG on the wire length L which can be interpreted as a dimensional crossover from 1D (L ≥ 400 nm) to 2D (L ≤ 200 nm).

Magnetoresistance (MR) oscillations of multiple periodicities are recorded in singly connected silicon nanowires of diameter . At 100 K we observe oscillations of periodicity and 0.444 T corresponding to h / e and Aharonov-Bohm (AB) oscillations, whereas at 10 K we record periodicities of 0.98 T, 0.49 T and 0.25 T corresponding to h / e , (Al'tshuler-Aronov-Spivak (AAS)) and oscillations. At 2.5 K we find magnetoresistance oscillations with multiple periodicities of 1.3 T, 0.52 T, and 0.325 T corresponding to AB and AAS oscillations. The and peaks can be attributed to the interference of time-reversed paths originating from the core orbits that scatter coherently on the surface of the nanowires multiple times. We also observed 20 mT and 60 mT oscillations of small amplitude superimposed on a quasi-periodic background which we attribute to the quantum interference of special surface states associated with skipping orbits that propagate quasi-ballistically. The aperiodic fluctuations in the MR at all temperatures are universal conductance fluctuations (UCF) originating from randomly spaced impurity scattering in the core of the nanowire.

We describe the transport properties of mesoscopic devices based on the two dimensional electron gas (2DEG) present at the LaAlO$_3$/SrTiO$_3$ interface. Bridges with lateral dimensions down to 500~nm were realized using electron beam lithography. Their detailed characterization shows that processing and confinement do not alter the transport parameters of the 2DEG. The devices exhibit superconducting behavior tunable by electric field effect. In the normal state, we measured universal conductance fluctuations, signature of phase-coherent transport in small structures. The achievement of reliable lateral confinement of the 2DEG opens the way to the realization of quantum electronic devices at the LaAlO$_3$/SrTiO$_3$ interface., 10 pages, 4 figures

We have experimentally investigated quantum interference corrections to the conductivity of graphene nanoribbons at temperatures down to 20 mK studying both weak localization (WL) and universal conductance fluctuations (UCF). Since in individual nanoribbons at millikelvin temperatures the UCFs strongly mask the weak localization feature we employ both gate averaging and ensemble averaging to suppress the UCFs. This allows us to extract the phase coherence length from both WL and UCF at all temperatures. Above 1 K, the phase coherence length is suppressed due to Nyquist scattering whereas at low temperatures we observe a saturation of the phase coherence length at a few hundred nanometers, which exceeds the ribbon width, but stays below values typically found in bulk graphene. To better describe the experiments at elevated temperatures, we extend the formula for 1D weak localization in graphene, which was derived in the limit of strong intervalley scattering, to include all elastic scattering rates., 8 pages, 6 figures, accepted by PRB

The universal conductance fluctuations (UCFs), one of the most important manifestations of mesoscopic electronic interference, have not yet been demonstrated for the two-dimensional surface state of topological insulators (TIs). Even if one delicately suppresses the bulk conductance by improving the quality of TI crystals, the fluctuation of the bulk conductance still keeps competitive and difficult to be separated from the desired UCFs of surface carriers. Here we report on the experimental evidence of the UCFs of the two-dimensional surface state in the bulk insulating Bi2Te2Se nanoribbons. The solely-B\perp-dependent UCF is achieved and its temperature dependence is investigated. The surface transport is further revealed by weak antilocalizations. Such survived UCFs of the topological surface states result from the limited dephasing length of the bulk carriers in ternary crystals. The electron-phonon interaction is addressed as a secondary source of the surface state dephasing based on the temperature-dependent scaling behavior.

Magnetic field dependent universal conductance fluctuations (UCF's) are observed in weakly disordered indium tin oxide nanowires from 0.26 K up to $\sim 25$ K. The fluctuation magnitudes increase with decreasing temperature, reaching a fraction of $e^2/h$ at $T \lesssim 1$ K. The shape of the UCF patterns is found to be very sensitive to thermal cycling of the sample to room temperatures, which induces irreversible impurity reconfigurations. On the other hand, the UCF magnitudes are insensitive to thermal cycling. Our measured temperature dependence of the root-mean-square UCF magnitudes are compared with the existing theory [C. W. J. Beenakker and H. van Houten, Phys. Rev. B \textbf{37}, 6544 (1988)]. A notable discrepancy is found, which seems to imply that the experimental UCF's are not cut off by the thermal diffusion length $L_T$, as would be expected by the theoretical prediction when $L_T < L_\varphi$, where $L_\varphi$ is the electron dephasing length. The approximate electron dephasing length is inferred from the UCF magnitudes and compared with that extracted from the weak-localization magnetoresistance studies. A reasonable semiquantitative agreement is observed., Comment: 11 pages, 9 figures

We study the propagation of waves in quasi-one-dimensional finite periodic systems whose classical (ray) dynamics is diffusive. By considering a random matrix model for a chain of $L$ identical chaotic cavities, we show that its average conductance as a function of $L$ displays an ohmic behavior even though the system has no disorder. This behavior, with an average conductance decay $N/L$, where $N$ is the number of propagating modes in the leads that connect the cavities, holds for $1\ll L \lesssim \sqrt{N}.$ After this regime, the average conductance saturates at a value of ${\mathcal O}(\sqrt{N})$ given by the average number of propagating Bloch modes $$ of the infinite chain. We also study the weak localization correction and conductance distribution, and characterize its behavior as the system undergoes the transition from diffusive to Bloch-ballistic. These predictions are tested in a periodic cosine waveguide., Comment: 9 pages, 10 figures

The universal conductance fluctuations of quasi-two-dimensional systems are analyzed with experimental considerations in mind. The traditional statistical metrics of these fluctuations (such as variance) are shown to have large statistical errors in such systems. An alternative characteristic is identified, the inflection point of the correlation function in magnetic field, which is shown to be significantly more useful as an experimental metric and to give a more robust measure of phase coherence., Comment: 9 pages, 7 figures

We have measured the low-temperature magnetoresistance of long (>50 mu m), narrow (similar to 1 mu m) quantum wires fabricated from a high-mobility two-dimensional electron gas. In the quantum Hall regime at high magnetic fields we observe that the Shubnikov-de Haas oscillations split into a series of aperiodic sharp peaks. Both the amplitude and sharpness of the peaks are strongly dependent on temperature below 1 K. We attribute the peaks to resonant tunneling between edge states through localized states in the bulk. The results are in quantitative agreement with the theoretical model of Jain and Kivelson.

Using a finite-frequency recursive Green's function technique, we calculate the dynamic magneto-conductance fluctuations and oscillations in disordered mesoscopic normal metal systems, incorporating inter-particle Coulomb interactions within a self-consistent potential method. In a disordered metal wire, we observe ergodic behavior in the dynamic conductance fluctuations. At low $\omega$, the real part of the conductance fluctuations is essentially given by the dc universal conductance fluctuations while the imaginary part increases linearly from zero, but for $\omega$ greater than the Thouless energy and temperature, the fluctuations decrease as $\omega^{-1/2}$. Similar frequency-dependent behavior is found for the Aharonov-Bohm oscillations in a metal ring. However, the Al'tshuler-Aronov-Spivak oscillations, which predominate at high temperatures or in rings with many channels, are strongly suppressed at high frequencies, leading to interesting crossover effects in the $\omega$-dependence of the magneto-conductance oscillations., Comment: 4 pages, REVTeX 3.0, 5 figures(ps file available upon request), #phd09

A maximum-entropy model describing the conductance statistics of disordered mesoscopic quantum wires is presented. The model, closely related to the Laguerre ensemble of random matrices, predicts a weak localization effect and universal conductance fluctuations, in qualitative agreement with microscopic theory. A simple interpretation of the maximum-entropy model is given and the relation with other maximum-entropy models is discussed.