Dans ma thèse, j'ai étudié le transport électronique quantique dans des nanofils semiconducteurs couplés aux supraconducteurs, avec le but de comprendre les conditions nécessaires pour observer des états liés de Majorana. De manière inattendue, au cours de mes expériences j'ai trouvé des exemples notables de l'omniprésence de la localisation spatiale des électrons dans des nanofils apparemment balistiques et unidimensionnels (1D). Ses effets peuvent imiter des signatures d'unidimensionnalité, d’hélicité et des états liés de Majorana, jetant un doute sur leur interprétation.La conductance d’un nanofil 1D est quantifiée et censée montrer des plateaux a des multiples entiers du quantum de conductance. Curieusement, le transport dans un nanofil d'InAs qui hébergeait une boite quantique à un seul niveau a montré qu'il pouvait répliquer les deux premiers plateaux résolus en spin. Une mesure du courant Josephson sous un champ magnétique a révélé les transitions d'état fondamental d'un électron qui occupait ce niveau et confirmé sa nature localisé.Dans le régime hélicoïdal, une chute de la conductance est prédite au milieu de chaque plateau de conductance. De façon étonnante, des dispositifs à base de nanofils uniques d'InSb hébergeant une boite quantique qui conduisait en parallèle avec le canal 1D ont reproduit la même signature.Enfin, la présence des états liés de Majorana, devrait être décelée par un pic à tension de biais nul (ZBP) lors d’une spectroscopie tunnel. Dans un des échantillons à deux canaux mentionnés précédemment, lorsque le canal unidimensionnel était fermé, un ZBP a émergé dans le gap supraconducteur sous un champ magnétique parallèle au nanofil. Ce ZBP a été attribué aux états liés d'Andreev de la boite quantique. Dans une expérience différente faite avec une jonction Josephson à base d'un nanofil d'InAs hébergeant une boite quantique, un ZBP relié au courant Josephson est apparu dans le gap supraconducteur comme le résultat d'une transition de l'état fondamental singlet de la boite quantique vers un état doublet.Malgré la localisation, il a été possible d'extraire des informations significatives sur le régime 1D. Le rôle des grilles a été majeur dans la détermination des dégénérescences sous un champ magnétique des sous-bandes d’un nanofil d'InSb présentant deux canaux de conduction en parallèle. En jouant avec leurs tensions de seuil, effets orbitaux, et facteurs gyromagnétiques, la tension de grille pouvait changer les énergies des sous-bandes appartenant à chaque canal, de manière à les verrouiller ensemble. Grace à ce mécanisme, il a été possible d’observer un plateau à 2e^2/h jusque à de forts champ magnétiques sans aucune apparition d'un plateau à 1e^2/h. La possible existence des deux fils quantiques dans un seul nanofil ouvre la voie à l'observation des états hélicoïdaux et des états liés de Majorana de nature fractionnel.Dans l'ensemble, ces résultats pointent vers la nécessité d'une meilleure compréhension de la physique des dispositifs à base de nanofils d'InAs et d'InSb. Des études supplémentaires dans l'état supraconducteur et normal doivent être réalisées sur des dispositifs plus simples avec un faible nombre de grilles, avant de faire l'étude et manipulations des états liés de Majorana dans des systèmes plus complexes, dont les signatures de localisation pourraient être mieux cachées. Ces résultats originaux vont être publiés dans les mois qui suivent dans quatre articles différents. / In my thesis, I studied low-temperature electronic transport in semiconductor nanowires coupled to superconductors, with the goal of understanding the requirements to observe Majorana bound states. Unexpectedly, I found dramatic examples of the pervasiveness of spatial localization of electrons even in seemingly ballistic one-dimensional (1D) nanowires. Localization could replicate signatures of one-dimensionality, helicity and Majorana bound states, casting a shadow of doubt on their interpretation.1D nanowires are expected to show plateaus of quantized conductance. Curiously, transport through an InAs nanowire hosting a single-level quantum dot showed that it could mimic the first two spin-resolved plateaus. A measurement of the Josephson supercurrent under magnetic field revealed the ground-state transitions of an electron occupying this level, confirming its localized nature.In the helical regime, a conductance dip is predicted to appear in each of the conductance plateaus. Surprisingly, InSb nanowire devices hosting a quantum dot conducting in parallel with a 1D channel reproduced this signature.The presence of Majorana bound states, in turn, should be revealed by a zero-bias peak (ZBP) in tunnel spectroscopy. In one of the two-path devices mentioned above, when the 1D path was closed, a zero-bias peak emerged inside the superconducting gap under a magnetic field parallel to the nanowire. This ZBP was related to trivial Andreev bound states from the quantum dot in parallel to the 1D channel. In a different experiment done in an InAs nanowire Josephson junction device hosting a quantum dot, a ZBP related to a Josephson supercurrent appeared inside of the superconducting gap as a result of a transition of the ground-state of the dot from a singlet to a doublet.In spite of localization, it was possible to extract some meaningful information about the 1D regime. The role of the gates was major in determining the degeneracy of the subbands in an InSb nanowire with two 1D conduction paths in parallel under magnetic field. Through a direct influence on their threshold voltages, orbital effects, and g-factors, the gate voltage could shift the energies of the subbands and lock them together. Via this mechanism, it was possible to observe a 2e^2/h plateau lasting until very large field without the appearance of a 1e^2/h plateau. The possible existence of two quantum wires in a single nanowire opens the door for novel helical and Majorana bound states of fractional nature.Altogether, these results point to the need of a better understanding of the physics of simpler few-gates short-channel InAs and InSb nanowire superconducting and normal-state devices, before committing to the utterly complex devices that should be fabricated to study and manipulate Majorana bound states, in which signatures of localization could be better hidden. These original results will be published in the coming months in four different articles.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / One of the devices most important in mesoscopic physics is the quantum dot. This device consists of a cavity of submicrometrics dimensions formed in the interface plane of a electron gas two-dimensional (2DEG) in a semiconductor heterostructure, wherein is possible to study the properties of electronic transport coupling to the two reservoirs and establishing an electric current in the system. In this dissertation we studied the quantum theory of circuits by means of numerical methods with the goal to calculate the observables of transport, such as the conductance and the shot-noise power in a single quantum dot and in two quantum dots coupled in series. In a quantum dot was implemented the numerical method of bisection in Fortran to find the pseudocurrent and, through this, to calculate the conductance and the shotnoise power in a symmetric quantum dot and also in a assymmetric quantum dot. In the case of a symmetric dot were compared the numerical results obtained by bisection method with the analytical results found in the literature and was shown that there is a perfect agreement. We also implemented Newton’s method for two quantum dots associated in series and we calculate the conductance and the shot-noise power. The numerical results obtained by the Newton’s method, for two symmetric quantum dots in series, were also compared with the analytical results founds in the literature and showed excellent agreement. / Um dos dispositivos mais importantes em física mesoscópica é o ponto quântico. Este dispositivo consiste de uma cavidade de dimensões submicrométricas formada no plano da interface de um gás de elétrons bidimensional (2DEG) em heteroestruturas semicondutoras, em que é possível estudar as propriedades de transporte eletrônico acoplando o ponto quântico a dois reservatórios e estabelecendo-se uma corrente elétrica no sistema. Nesta dissertação estudamos a teoria quântica de circuitos por meio de métodos numéricos com o objetivo de calcular os observáveis de transporte, como a condutância e a potência do ruído de disparo, em um único ponto quântico e em dois pontos quânticos acoplados em série. Em um ponto quântico foi implementado o método numérico da bisseção em Fortran para encontrar a pseudocorrente e, através desta, calcular a condutância e a potência do ruído de disparo em um ponto quântico simétrico e também em um ponto quântico assimétrico. No caso de um ponto simétrico foram comparados os resultados numéricos, obtidos pelo método da bisseção, com os resultados analíticos encontrados na literatura e foi mostrado que há uma perfeita concordância. Também implementamos o método de Newton para dois pontos quânticos associados em série e calculamos a condutância e a potência do ruído de disparo. Os resultados numéricos obtidos pelo método de Newton para dois pontos quânticos simétricos em série também foram comparados com os resultados analíticos encontrados na literatura e mostraram ótima concordância.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The scientific advances we have experienced in recent decades have enabled us to produce systems in the mesoscopic scale. These systems have become very useful as research tools in various areas of science. In mesoscopic physics the ondulatory characteristic of electrons is more evident than in classical physics and the electron conduction process is better represented by the wave function that describes it. Examples of application of mesoscopic systems are quantum dots which are open cavities where electrons are limited to flow through. Thus, the objective of this work is to study the effects of decoherence in the transport of electrons in two systems: i) quantum dot with a fictitious guide and ii) quantum dot with stub, where we take into account ondulatory properties of electrons. The formalism that we use is the scattering matrix, which relates the incoming and outgoing amplitudes in the scattering of waves coming in and out of the scattering region. Since the studied systems are chaotic, the scattering matrices can be treated as random. These matrices were generated by computational simulation and then the conductance values were computed. The conductance distribution was obtained by means of probabilistic analysis. / Os avanços científicos que temos experimentado nas últimas décadas proporcionaram a construção de sistemas em escala mesoscópica. Esses sistemas tornaram-se muito úteis como ferramentas de investigação em diversas áreas da ciência. Na física mesoscópica a característica ondulatória dos elétrons é mais evidente do que na física clássica e o processo de condução dos elétrons é melhor representado pela função de onda que os descreve. Exemplos da aplicação de sistemas mesoscópicos são os pontos quânticos que são cavidades abertas por onde os elétrons são limitados a fluirem. Dessa forma, o objetivo deste trabalho é estudar os efeitos da decoerência no transporte de elétrons em dois sistemas: i) ponto quântico com guia fictício e ii) ponto quântico com estube, onde levamos em consideração as propriedades ondulatórias dos elétrons. O formalismo que utilizamos é o da matriz de espalhamento, a qual relaciona as amplitudes das ondas que entram e saem da região de espalhamento. Como os sistemas estudados são caóticos, as matrizes de espalhamento podem ser tratadas como aleatórias. Geramos estas matrizes por meio de simulação computacional e delas extraímos a condutância do sistema. A distribuição da condutância foi obtida por meio de uma análise probabilística.

In this thesis, we investigate the quantum transport properties of disordered three dimensional topological insulator (3DTI) nanostructures of BiSe and BiTe in detail. Despite their intrinsic bulk conductivity, we show the possibility to study the specific transport properties of the topological surface states (TSS), either with or without quantum confinement. Importantly, we demonstrate that unusual transport properties not only come from the Dirac nature of the quasi-particles, but also from their spin texture. Without quantum confinement (wide ribbons), the transport properties of diffusive 2D spin-helical Dirac fermions are investigated. Using high magnetic fields allows us to measure and separate all contributions to charge transport. Band bending is investigated in BiSe nanostructures, revealing an inversion from upward to downward bending when decreasing the bulk doping. This result points out the need to control simultaneously both the bulk and surface residual doping in order to produce bulk-depleted nanostructures and to study TSS only. Moreover, Shubnikov-de-Haas oscillations and transconductance measurements are used to measure the ratio of the transport length to the electronic mean free path ltr/le. This ratio is measured to be close to one for bulk states, whereas it is close to 8 for TSS, which is a hallmark of the anisotropic scattering of spin-helical Dirac fermions. With transverse quantum confinement (narrow wires or ribbons), the ballistic transport of quasi-1D surface modes is evidenced by mesoscopic transport measurements, and specific properties due to their topological nature are revealed at very low temperatures. The metallic surface states are directly evidenced by the measure of periodic Aharonov-Bohm oscillations (ABO) in 3DTI nanowires. Their exponential temperature dependence gives an unusual power-law temperature dependence of the phase coherence length, which is interpreted in terms of quasi-ballistic transport and decoherence in the weak-coupling regime. This remarkable finding is a consequence of the enhanced transport length, which is comparable to the perimeter. Besides, the ballistic transport of quasi-1D surface modes is further evidenced by the observation of non-universal conductance fluctuations in a BiSe nanowire, despite the long-length limit (L > ltr) and a high metallicity (many modes). We show that such an unusual property for a mesoscopic conductor is related to the limited mixing of the transverse modes by disorder, as confirmed by numerical calculations. Importantly, a model based on the modes' transmissions allows us to describe our experimental results, including the full temperature dependence of the ABO amplitude.

The quantitative measurement of structural alterations at the nanoscale level is important for understanding the physical states of weakly disordered optical mediums such as cells/tissues. Progress in certain diseases, such as cancer or abnormalities in the brain, is associated with the nanoscale structural alterations at basic building blocks of the cells/tissues. Elastic light scattering, especially at visible wavelengths range provides non-invasive ways to probe the cells/tissues up to nanoscale level. Therefore, a mesoscopic physics-based open light scattering technique with added finer focusing, partial wave spectroscopy (PWS), is developed to probe nanoscale changes. Then, molecular-specific light localization technique, a close scattering approach called inverse participation ratio (IPR) is proposed that is sensitive to nano to microstructural cell/tissue alterations. In this dissertation, we have introduced the further engineered PWS system with the finer focus for precise volume scattering and molecular-specific light localization IPR techniques. As an application of PWS, we first probe precise scattering volume in commercially available tissue microarrays (TMA) tissue samples to standardize the existing cancer diagnostic methods by distinguishing the cancer stages. We also apply the PWS technique to probe chemotherapy drug-treated metastasizing cancer patients by xenografting prostate cancer cells using a mouse model and identify drug-sensitive and drug-resistance treatment cases. On the other hand, as an illustration of another mesoscopic physics-based molecular specific light localization technique, Confocal-IPR, we study the effects of a probiotic on chronic alcoholic mice brains by targeting the molecular specific alteration in glial cells, astrocytes and microglia, and chromatin of the brain cells through staining with appropriate dyes/proteins. Using structural disorder of IPR as a biomarker, the results show that probiotics in the presence of alcohol are beneficial and help overall brain health. Finally, a TEM-IPR study was performed using nanoscale resolution TEM imaging to support the optical IPR method by studying the anti-cancerous drug effect in ovarian cancer cells. The result shows that we can quantitatively measure the effect of anti-cancerous drugs in cancer treatment and the level of tumorigenicity far below the diffraction limit, and it has a similar effect and supports the optical IPR method.

The results reported in this thesis contribute to the understanding of disordered systems, to mesoscopic physics on the one hand, and to the physics of spin glasses on the other hand. The first part of this thesis studies numerically coherent electronic transport in a non magnetic metal accurately doped with frozen magnetic impurities (a low temperature spin glass). Thanks to a recursive code that calculates the two terminal conductance of the system, we study in detail the metallic regime of conduction (large conductance) as well as the insulating regime (small conductance). In both regimes, we highlight a universal behavior of the system. Moreover, a study of correlations between the conductance of different spin configurations of impurities allows us to link these correlations with correlations between spin configurations. This study opens the route for the first experimental determination of the overlap via transport measurements. A second part of this thesis deals with the study of the mean field Sherrington-Kirkpatrick model, which describes the low temperature phase of an Ising spin glass. We are interested here in the generalization of this model to quantum spins (i.e including the possibility to flip by quantum tunneling) of this classical model that was well studied during the past thirty years. We deduce analytically motion equations at the semi-classical level, for which the influence of quantum tunneling is weak, and we compare them with the classical case. We finally solve numerically these equations using a pseudo-spectral method.

La microscopie de grille à balayage (SGM pour Scanning GateMicroscopy), développée à la fin des années 1990, est devenue un outilpuissant pour étudier les propriétés électroniques locales dans lesnano-dispositifs semi-conducteurs. La SGM est basée sur la techniqueAFM, mais la pointe métallique est utilisée comme une grille mobilecouplée capacitivement au dispositif, et les propriétés de transportélectronique sont étudiées sous l'influence de cette grille,fournissant des informations spatiales à haute résolution. Cette thèsedécrit d'abord le remplacement de la détection optique de notresystème AFM par une détection piézo-électrique utilisant un diapason àquartz, puis les résultats de mesures SGM sur divers nano-dispositifs,qui sont tous fabriqués à partir d'hétérostructures InGaAs / InAlAscontenant un gaz d'électrons bi-dimensionnel (2DEG) de grande mobilitésitué à quelques dizaines de nanomètres sous la surface. Sur unesimple constriction, nous étudions l'interaction pointe-échantillonavec deux approches: la force électrostatique et l'effet capacitif.Sur une boite quantique, nous étudions les phénomènes de blocage deCoulomb lorsque la pointe est utilisée comme une grille pour modulerla charge à l'intérieur de la boite. Dans un travail sur le paradoxede Braess, avec l'aide de simulations numériques, nous découvrons uneffet paradoxal en modulant la largeur du canal central dans undispositif mésoscopique en forme de double anneau, en analogie avec leparadoxe qui se produit dans un réseau classique. Par une étudedétaillée de l'évolution de la conductance, nous découvrons enfinplusieurs pièges de charge dans les images SGM, et proposons un modèlepour interpréter le changement de conductance en présence de pièges decharge. Nous développons alors une méthode pour imager directement lespièges de charge par des mesures de transconductance avec unemodulation de la tension sur la pointe. / Scanning gate microscopy (SGM), developed in the late 1990's, has become a powerful tool to investigate the local electronic properties in semiconductor nano devices. SGM is based on the AFM technique but the metallic tip is used as a movable gate capacitively coupled to the device, and the electron transport property is studied on influence of this gate, providing spatial information with high resolution. This thesis presents the update of the force detection mode of our AFM system from optical method to force sensing by a quartz tuning fork, and the SGM measurement results on various nano devices, all of which are fabricated from InGaAs/InAlAs heterostructures containing a high mobility 2DEG located a few tens of nanometers below the surface. On a 2DEG constriction, we investigate the tip-sample interaction with two approaches: the capacitive force and the gate effect. On a quantum dot, we study the Coulomb blockade phenomena where the tip is used as a gate to modulate the charging/discharging inside the dot. In a work on Braess paradox, with the help of numerical simulations, we discover a Braess paradox effect by modulating a channel width in a ‘double-ring' shaped mesoscopic device in analogy with the one that occurs in a classical network. By a detailed study of the conductance changes, we discover several charge traps from the SGM map, and propose a model to interpret the conductance change with the presence of charge traps. We develop a method to directly image the charge traps by transconductance measurements with a voltage modulation on the tip.

Cette thèse est consacrée à l'étude expérimentale du bruit quantique électronique d'un système mésoscopique. Dans une première partie, nous nous sommes intéressés au bruit de partition d'un conducteur unidimensionnel balistique : un contact ponctuel quantique (QPC). Nous avons montré que, lorsque l'un des contacts du QPC est modulé par une onde radio-fréquence, il apparaît un bruit de partition en l'absence de courant moyen à travers le conducteur. Nous avons ainsi validé la théorie de la diffusion appliquée au bruit photo-assisté, d'une part en mesurant le facteur de Fano en l'absence de tension appliquée au QPC, et d'autre part en mesurant le bruit en présence d'une tension continue et d'une irradiation micro-onde. Dans une seconde partie, nous avons testé le système de mesure d'une nouvelle expérience qui, à terme, permettra de mesurer le bruit à haute fréquence d'un conducteur mésoscopique, ainsi que la statistique des photons qu'il émet dans le circuit de mesure. Le test a consisté à réaliser des expériences de type Hanbury-Brown et Twiss (interférométrie d'intensité) avec deux types de sources de photons micro-ondes. D'abord, nous avons utilisé une source thermique incohérente (résistance macroscopique de 50 Ohms) qui présente une statistique super-poissonnienne : les fluctuations de puissance sont proportionnelles au carré de la puissance moyenne émise par la source. Puis nous avons mis en évidence la statistique poissonnienne d'une source classique monochromatique, et nous avons montré que le facteur de Fano géant mesuré est parfaitement expliqué par le bruit des chaînes d'amplification.

We report on conductance measurements in carbon nanotube based double quantum dots connected to two normal electrodes and a central superconducting finger. By operating our devices as Cooper pair beam splitters, we provide evidence for Crossed Andreev Reflection (CAR). We inject Cooper pairs in the superconducting electrode and measure the differential conductance at both left and right arm. The contacts split the device into two coupled quantum dots. Each of the quantum dots can be tuned by a lateral sidegate. If the two sidegates are tuned such that both quantum dots are at a transmission resonance, a considerable part of the injected Cooper pairs splits into different normal contacts. On the contrary, if only one of the two dots is at resonance, nearly all pairs tunnel to the same normal contact. By comparing different triple points in the double dot stability diagram, we demonstrate the contribution of split Cooper pairs to the total current. In this manner, we are able to extract a splitting efficiency of up to 50% in the resonant case. Carbon Nanotubes ensure ballistic transport and long spin-flip scattering lengths. Due to these properties they are promising candidates to investigate EPR-type correlations in solid state systems.

This thesis reports our work on transport related problems in mesoscopic physics using analytical as well as numerical techniques. Some of the problems we studied are: effect of interactions and static impurities on the conductance of a ballistic quantum wire[1], aspects of quantum charge pumping [2, 3, 4], DC and AC conductivity of a (dissipative) quantum Hall (edge) line junctions[5, 6], and junctions of three or more Luttinger liquid (LL)quantum wires[7]. This thesis begins with an introductory chapter which gives a brief glimpse of the underlying physical systems and the ideas and techniques used in our studies. In most of the problems we will look at the physical effects caused by e-e interactions and static scattering processes. In the second chapter we study the effects of a static impurity and interactions on the conductance of a 1D-quantum wire numerically. We use the non-equilibrium Green’s function (NEGF) formalism along with a self-consistent Hartree-Fock approximation to numerically study the effects of a single impurity and interactions between the electrons (with and without spin) on the conductance of a quantum wire [1]. We study the variation of the conductance with the wire length, temperature and the strength of the impurity and electron-electron interactions. We find our numerical results to be in agreement with the results obtained from the weak interaction RG analysis. We also discover that bound states produce large density deviations at short distances and have an appreciable effect on the conductance which is not captured by the renormalization group analysis. In the third chapter we use the equations of motion (EOM) for the density matrix and Floquet scattering theory to study different aspects of charge pumping of non-interacting electrons in a one-dimensional system. We study the effects of the pumping frequency, amplitude, band filling and finite bias on the charge pumped per cycle, and the spectra of the charge and energy currents in the leads[2]. The EOM method works for all values of parameters, and gives the complete time-dependences of the current and charge at any site of the system. In particular we study a system with oscillating impurities at several sites and our results agree with Floquet and adiabatic theory where these are applicable, and provides support for a mechanism proposed elsewhere for charge pumping by a traveling potential wave in such systems. For non-adiabatic and strong pumping, the charge and energy currents are found to have a marked asymmetry between the two leads, and pumping can work even against a substantial bias. We also study one-parameter charge pumping in a system where an oscillating potential is applied at one site while a static potential is applied in a different region [3]. Using Floquet scattering theory, we calculate the current up to second order in the oscillation amplitude and exactly in the oscillation frequency. For low frequency, the charge pumped per cycle is proportional to the frequency and therefore vanishes in the adiabatic limit. If the static potential has a bound state, we find that such a state has a significant effect on the pumped charge if the oscillating potential can excite the bound state into the continuum states or vice versa. In the fourth chapter we study the current produced in a Tomonaga-Luttinger liquid (TLL) by an applied bias and by weak, point-like impurity potentials which are oscillating in time[4]. We use bosonization to perturbatively calculate the current up to second order in the impurity potentials. In the regime of small bias and low pumping frequency, both the DC and AC components of the current have power law dependences on the bias and pumping frequencies with an exponent 2K−1 for spinless electrons, where Kis the interaction parameter. For K<1/2, the current grows large for special values of the bias. For non-interacting electrons with K= 1, our results agree with those obtained using Floquet scattering theory for Dirac fermions. We also discuss the cases of extended impurities and of spin-1/2 electrons. In chapter five, we present a microscopic model for a line junction formed by counter or co-propagating single mode quantum Halledges corresponding to different filling factors and calculate the DC [5] and AC[6] conductivity of the system in the diffusive transport regime. The ends of the line junction can be described by two possible current splitting matrices which are dictated by the conditions of both lack of dissipation and the existence of chiral commutation relations between the outgoing bosonic fields. Tunneling between the two edges of the line junction then leads to a microscopic understanding of a phenomenological description of line junctions introduced by Wen. The effect of density-density interactions between the two edges is considered exactly, and renormalization group (RG) ideas are used to study how the tunneling parameter changes with the length scale. The RG analysis leads to a power law variation of the conductance of the line junction with the temperature (or other energy scales) and the line junction may exhibit metallic or insulating phase depending on the strength of the interactions. Our results can be tested in bent quantum Hall systems fabricated recently. In chapter six, we study a junction of several Luttinger Liquid (LL) wires. We use bosonization with delayed evaluation of boundary conditions for our study. We first study the fixed points of the system and discuss RG flow of various fixed points under switching of different ‘tunneling’ operators at the junction. Then We study the DC conductivity, AC conductivity and noise due to tunneling operators at the junction (perturbative).We also study the tunneling density of states of a junction of three Tomonaga-Luttinger liquid quantum wires[7]. and find an anomalous enhancement in the TDOS for certain fixed points even with repulsive e-e interactions.