A gentle introduction to the functional renormalization group: the Kondo effect in quantum dots

The functional renormalization group provides an efficient description of the interplay and competition of correlations on different energy scales in interacting Fermi systems. An exact hierarchy of flow equations yields the gradual evolution from a microscopic model Hamiltonian to the effective action as a function of a continuously decreasing energy cutoff. Practical implementations rely on suitable truncations of the hierarchy, which capture nonuniversal properties at higher energy scales in addition to the universal low-energy asymptotics. As a specific example we study transport properties through a single-level quantum dot coupled to Fermi liquid leads. In particular, we focus on the temperature T=0 gate voltage dependence of the linear conductance. A comparison with exact results shows that the functional renormalization group approach captures the broad resonance plateau as well as the emergence of the Kondo scale. It can be easily extended to more complex setups of quantum dots.Comment: contribution to Les Houches proceedings 2006, Springer styl

Observation of a One-Dimensional Spin-Orbit Gap in a Quantum Wire

Understanding the flow of spins in magnetic layered structures has enabled an increase in data storage density in hard drives over the past decade of more than two orders of magnitude1. Following this remarkable success, the field of 'spintronics' or spin-based electronics is moving beyond effects based on local spin polarisation and is turning its attention to spin-orbit interaction (SOI) effects, which hold promise for the production, detection and manipulation of spin currents, allowing coherent transmission of information within a device. While SOI-induced spin transport effects have been observed in two- and three-dimensional samples, these have been subtle and elusive, often detected only indirectly in electrical transport or else with more sophisticated techniques. Here we present the first observation of a predicted 'spin-orbit gap' in a one-dimensional sample, where counter-propagating spins, constituting a spin current, are accompanied by a clear signal in the easily-measured linear conductance of the system.Comment: 10 pages, 5 figures, supplementary informatio

Quantum Point Contacts and Coherent Electron Focusing

I. Introduction II. Electrons at the Fermi level III. Conductance quantization of a quantum point contact IV. Optical analogue of the conductance quantization V. Classical electron focusing VI. Electron focusing as a transmission problem VII. Coherent electron focusing (Experiment, Skipping orbits and magnetic edge states, Mode-interference and coherent electron focusing) VIII. Other mode-interference phenomenaComment: #3 of a series of 4 legacy reviews on QPC'

Supercurrent reversal in quantum dots

When two superconductors become electrically connected by a weak link a zero-resistance supercurrent can flow. This supercurrent is carried by Cooper pairs of electrons with a combined charge of twice the elementary charge, e. The 2e charge quantum is clearly visible in the height of Shapiro steps in Josephson junctions under microwave irradiation and in the magnetic flux periodicity of h/2e in superconducting quantum interference devices. Several different materials have been used to weakly couple superconductors, such as tunnel barriers, normal metals, or semiconductors. Here, we study supercurrents through a quantum dot created in a semiconductor nanowire by local electrostatic gating. Due to strong Coulomb interaction, electrons only tunnel one-by-one through the discrete energy levels of the quantum dot. This nevertheless can yield a supercurrent when subsequent tunnel events are coherent. These quantum coherent tunnelling processes can result in either a positive or a negative supercurrent, i.e. in a normal or a pi-junction, respectively. We demonstrate that the supercurrent reverses sign by adding a single electron spin to the quantum dot. When excited states of the quantum dot are involved in transport, the supercurrent sign also depends on the character of the orbital wavefunctions

Keldysh technique and non-linear sigma-model: basic principles and applications

The purpose of this review is to provide a comprehensive pedagogical introduction into Keldysh technique for interacting out-of-equilibrium fermionic and bosonic systems. The emphasis is placed on a functional integral representation of underlying microscopic models. A large part of the review is devoted to derivation and applications of the non-linear sigma-model for disordered metals and superconductors. We discuss such topics as transport properties, mesoscopic effects, counting statistics, interaction corrections, kinetic equation, etc. The sections devoted to disordered superconductors include Usadel equation, fluctuation corrections, time-dependent Ginzburg-Landau theory, proximity and Josephson effects, etc. (This review is a substantial extension of arXiv:cond-mat/0412296.)Comment: Review: 103 pages, 19 figure

Industrialised building system in Malaysia: Issues for research in a changing financial and property market

Industrialised Building System in its different guises appears to have gained popularity in recent years. Through a thorough review of literature, this paper presents a historical appraisal of the definitions offered for the different guises of IBS, the characteristics of IBS, and the benefits it purports to offer. In the same vein, the factors that have fuelled the popularity of IBS is discussed together with the impact of the changing financial and property market crisis on the future of IBS. The implications of the current financial and property market prices on IBS in Malaysia shall also be discussed. The paper concludes by drawing inferences on the implications of the current financial and property market crisis on research in IBS from a Malaysian construction industry perspective