Nanophysics : Lecture Notes of the Les Houches Summer School 2004.
Title:
Nanophysics : Lecture Notes of the Les Houches Summer School 2004.
Author:
Bouchiat, Hélène.
ISBN:
9780080461243
Personal Author:
Edition:
1st ed.
Physical Description:
1 online resource (641 pages)
Series:
Les Houches ; v.81
Les Houches
Contents:
Lecturers -- Seminar speakers -- Participants -- Preface -- Contents -- Fundamental aspects of electron correlations and quantum transport in one-dimensional systems -- Introduction -- Non-Fermi liquid features of Fermi liquids: 1D physics in higher dimensions -- Long-range effective interaction -- 1D kinematics in higher dimensions -- Infrared catastrophe -- 1D -- 2D -- Dzyaloshinskii-Larkin solution of the Tomonaga-Luttinger model -- Hamiltonian, anomalous commutators, and conservation laws -- Reducible and irreducible vertices -- Ward identities -- Effective interaction -- Dyson equation for the Green's function -- Solution for the case g2 = g4 -- Physical properties -- Momentum distribution -- Tunneling density of states -- Renormalization group for interacting fermions -- Single impurity in a 1D system: scattering theory for interacting fermions -- First-order interaction correction to the transmission coefficient -- Hartree interaction -- Exchange -- Renormalization group -- Electrons with spins -- Comparison of bulk and edge tunneling exponents -- Bosonization solution -- Spinless fermions -- Bosonized Hamiltonian -- Bosonization of fermionic operators -- Attractive interaction -- Lagrangian formulation -- Correlation functions -- Fermions with spin -- Tunneling density of states -- Transport in quantum wires -- Conductivity and conductance -- Galilean invariance -- Kubo formula for conductivity -- Drude conductivity -- Landauer conductivity -- Dissipation in a contactless measurement -- Conductance of a wire attached to reservoirs -- Inhomogeneous Luttinger-liquid model -- Elastic-string analogy -- Kubo formula for a wire attached to reservoirs -- Experiment -- Spin component of the conductance -- Thermal conductance: Fabry-Perrot resonances of plasmons -- Polarization bubble for small q in arbitrary dimensionality.
Polarization bubble in 1D -- Small q -- q near 2kF -- Some details of bosonization procedure -- Anomalous commutators -- Bosonic operators -- Commutation relations for bosonic fields phi and nu -- Problem with backscattering -- References -- Impurity in the Tomonaga-Luttinger model: A functional integral approach -- Introduction -- Functional integral representation -- The effective action for the Tomonaga-Luttinger Model -- The bosonized action for free electrons -- Gauging out the interaction -- Tunnelling density of states near a single impurity -- Jacobian of the gauge transformation -- References -- Novel phenomena in double layer two-dimensional electron systems -- Introduction -- Overview of physics in the quantum hall regime -- Basics -- Quantized hall effects -- Integer QHE -- Fractional QHE -- Composite fermions -- Double layer systems -- Coulomb drag between parallel 2D electron gases -- Basic concept -- Experimental -- Elementary theory of Coulomb drag -- Comparison between theory and experiment -- Tunneling between parallel two-dimensional electron gases -- Ideal 2D-2D tunneling -- Lifetime broadening -- 2D-2D tunneling in a perpendicular magnetic field -- Strongly-coupled bilayer 2D electron systems and excitonic superfluidity -- Introduction -- Quantum hall ferromagnetism -- Tunneling and interlayer phase coherence at nuT = 1 -- Excitonic superfluidity at nuT = 1 -- Detecting excitonic superfluidity -- Conclusions -- References -- Many-body theory of non-equilibrium systems -- Introduction -- Motivation and outline -- Closed time contour -- Free boson systems -- Partition function -- Green functions -- Keldysh rotation -- Keldysh action and causality -- Free bosonic fields -- Collisions and kinetic equation -- Interactions -- Saddle point equations -- Dyson equation -- Self-energy -- Kinetic term -- Collision integral.
Particle in contact with an environment -- Quantum dissipative action -- Saddle-point equation -- Classical limit -- Langevin equations -- Martin-Siggia-Rose -- Thermal activation -- Fokker-Planck equation -- From Matsubara to Keldysh -- Dissipative chains and membranes -- Fermions -- Free fermion Keldysh action -- Keldysh rotation -- External fields and sources -- Tunneling current -- Interactions -- Kinetic equation -- Disordered fermionic systems -- Disorder averaging -- Non-linear sigma-model -- Usadel equation -- Fluctuations -- Spectral statistics -- Gaussian integration -- Single particle quantum mechanics -- References -- Non-linear quantum coherence effects in driven mesoscopic systems -- Introduction -- Weak Anderson localization in disordered systems -- Drude approximation -- Beyond Drude approximation -- Weak localization correction -- Non-linear response to a time-dependent perturbation -- General structure of nonlinear response function -- Approximation of single photon absorption/emission -- Quantum rectification by a mesoscopic ring -- Diffusion in the energy space -- Quantum correction to absorption rate -- Weak dynamic localization and no-dephasing points -- Conclusion and open questions -- References -- Noise in mesoscopic physics -- Introduction -- Poissonian noise -- The wave packet approach -- Generalization to the multi-channel case -- Scattering approach based on operator averages -- Average current -- Noise and noise correlations -- Zero frequency noise in a two terminal conductor -- General case -- Transition between the two noise regimes -- Noise reduction in various systems -- Double barrier structures -- Noise in a diffusive conductor -- Noise reduction in chaotic cavities -- Noise correlations at zero frequency -- General considerations -- Noise correlations in a Y-shaped structure -- Finite frequency noise.
Which correlator is measured? -- Noise measurement scenarios -- Finite frequency noise in point contacts -- Noise in normal metal-superconducting junctions -- Bogolubov transformation and Andreev current -- Noise in normal metal-superconductor junctions -- Noise in a single NS junction -- Below gap regime -- Diffusive NS junctions -- Near and above gap regime -- Hanbury-Brown and Twiss experiment with a superconducting source of electrons -- S-matrix for the beam splitter -- Sub-gap regime -- Near and above gap regime -- Noise and entanglement -- Filtering spin/energy in superconducting forks -- Tunneling approach to entanglement -- Bell inequalities with electrons -- Noise in Luttinger liquids -- Edge states in the fractional quantum Hall effect -- Transport between two quantum Hall edges -- Keldysh digest for tunneling -- Backscattering current -- Poissonian noise in the quantum Hall effect -- Effective charges in quantum wires -- Conclusions -- References -- Higher moments of noise -- Introduction -- The probability distribution P(i) -- A simple model for a tunnel junction -- Noise in Fourier space -- Consequences -- Effect of the environment -- Imperfect voltage bias -- dc current: dynamical Coulomb blockade -- The second moment -- The third moment -- Effect of an external fluctuating voltage -- Voltage vs. current fluctuations -- Imperfect thermalization -- Principle of the experiment -- Possible methods -- Experimental setup -- Experimental results -- Third moment vs. voltage and temperature -- Effect of the detection bandwidth -- Effect of the environment -- Perspectives -- Quantum regime -- Noise thermal impedance -- Conclusion -- References -- Electron subgap transport in hybrid systems combining superconductors with normal or ferromagnetic metals -- Introduction -- NS junctions in the clean limit.
Single particle tunnelling in a tunnel junction -- Introduction -- Tunnel Hamiltonian -- Perturbation theory: golden rule -- Higher order processes -- Bogoliubov-de Gennes equations -- BCS Hamiltonian and diagonalization -- Simple examples -- NS interface -- Disordered NIS junctions -- Introduction -- Perturbation theory for NIS junction -- Tunnel Hamiltonian and golden rule -- Real space representation -- Disorder averaging -- Example: quasi-one-dimensional diffusive wire connected to a superconductor -- Calculation of the spectral current -- Zero-temperature limit -- Subgap noise of a superconductor-normal-metal tunnel interface -- Current fluctuations in NS systems -- Current noise in tunnel systems -- Generalized Schottky relation -- An explicit example: a wire out of equilibrium -- Tunnelling in a three-terminal system containing ferromagnetic metals -- Introduction -- Co-tunnelling and crossed Andreev tunnelling rates -- Tunnel Hamiltonian -- Calculation of spin-dependent tunnel rates -- Spin-dependent conductance matrix -- Discussion -- Nonmagnetic probes -- Spin-polarized probes -- References -- Low-temperature transport through a quantum dot -- Introduction -- Model of a lateral quantum dot system -- Thermally-activated conduction -- Onset of Coulomb blockade oscillations -- Coulomb blockade peaks at low temperature -- Activationless transport through a blockaded quantum dot -- Inelastic co-tunneling -- Elastic co-tunneling -- Kondo regime in transport through a quantum dot -- Effective low-energy Hamiltonian -- Linear response -- Weak coupling regime: TK << T << deltaE -- Strong coupling regime: T << TK -- Beyond linear response -- Splitting of the Kondo peak in a magnetic field -- Kondo effect in quantum dots with large spin -- Concluding remarks -- References -- Transport through quantum point contacts -- Introduction.
Spin-density-functional calculations.
Abstract:
The developments of nanofabrication in the past years have enabled the design of electronic systems that exhibit spectacular signatures of quantum coherence. Nanofabricated quantum wires and dots containing a small number of electrons are ideal experimental playgrounds for probing electron-electron interactions and their interplay with disorder. Going down to even smaller scales, molecules such as carbon nanotubes, fullerenes or hydrogen molecules can now be inserted in nanocircuits. Measurements of transport through a single chain of atoms have been performed as well. Much progress has also been made in the design and fabrication of superconducting and hybrid nanostructures, be they normal/superconductor or ferromagnetic/superconductor. Quantum coherence is then no longer that of individual electronic states, but rather that of a superconducting wavefunction of a macroscopic number of Cooper pairs condensed in the same quantum mechanical state. Beyond the study of linear response regime, the physics of non-equilibrium transport (including non-linear transport, rectification of a high frequency electric field as well as shot noise) has received much attention, with significant experimental and theoretical insights. All these quantities exhibit very specific signatures of the quantum nature of transport, which cannot be obtained from basic conductance measurements. Basic concepts and analytical tools needed to understand this new physics are presented in a series of theoretical fundamental courses, in parallel with more phenomenological ones where physics is discussed in a less formal way and illustrated by many experiments. · Electron-electron interactions in one-dimensional quantum transport · Coulomb Blockade and Kondo physics in quantum dots · Out of equilibrium noise and quantum transport · Andreev reflection and subgap nonlinear transport in
hybrid N/S nanosructures. · Transport through atomic contacts · Solid state Q-bits · Written by leading experts in the field, both theorists and experimentalists.
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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