Since the formulation of the geometric phase by Berry, its relevance has been demonstrated in a large variety of physical systems. However, a geometric phase of the most fundamental spin-1/2 system, the electron spin, has not been observed directly and controlled independently from dynamical phases. Here we report experimental evidence on the manipulation of an electron spin through a purely geometric effect in an InGaAs-based quantum ring with Rashba spin-orbit coupling. By applying an in-plane magnetic field, a phase shift of the Aharonov–Casher interference pattern towards the small spin-orbit-coupling regions is observed. A perturbation theory for a one-dimensional Rashba ring under small in-plane fields reveals that the phase shift originates exclusively from the modulation of a pure geometric-phase component of the electron spin beyond the adiabatic limit, independently from dynamical phases. The phase shift is well reproduced by implementing two independent approaches, that is, perturbation theory and non-perturbative transport simulations.

We study electronic structures of two-dimensional quantum dots in strong magnetic fields using mean-field density-functional theory and exact diagonalization. Our numerically accurate mean-field solutions show a reconstruction of the uniform-density electron droplet when the magnetic field flux quanta enter one by one the dot in stronger fields. These quanta correspond to repelling vortices forming polygonal clusters inside the dot. We find similar structures in the exact treatment of the problem by constructing a conditional operator for the analysis. We discuss important differences and limitations of the methods used.

Spin-transistor designs relying on spin-orbit interaction suffer from low signal levels resulting from low spin-injection efficiency and fast spin decay. Here, we present an alternative approach in which spin information is protected by propagating this information adiabatically. We demonstrate the validity of our approach in a cadmium manganese telluride diluted magnetic semiconductor quantum well structure in which efficient spin transport is observed over device distances of 50 micrometers. The device is turned "off" by introducing diabatic Landau-Zener transitions that lead to a backscattering of spins, which are controlled by a combination of a helical and a homogeneous magnetic field. In contrast to other spin-transistor designs, we find that our concept is tolerant against disorder.

The main theme of this review is the many-body physics of vortices in quantum droplets of bosons or fermions, in the limit of small particle numbers. Systems of interest include cold atoms in traps as well as electrons confined in quantum dots. When set to rotate, these in principle very different quantum systems show remarkable analogies. The topics reviewed include the structure of the finite rotating many-body state, universality of vortex formation and localization of vortices in both bosonic and fermionic systems, and the emergence of particle-vortex composites in the quantum Hall regime. An overview of the computational many-body techniques sets focus on the configuration interaction and density-functional methods. Studies of quantum droplets with one or several particle components, where vortices as well as coreless vortices may occur, are reviewed, and theoretical as well as experimental challenges are discussed. 12 F. Mapping between fermions and bosons 13III. Computational many-body methods 13 A. The Gross-Pitaevskii approach for trapped bosons 14 * Present address:

Published online zzz PACS 71.15.Ap, 71.15.Dx A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the main approaches include finite-difference methods, various types of finite-elements and wavelets. This paper reports on the results of several code development projects that approach problems related to the electronic structure using these three different discretization methods. We review the ideas behind these methods, give examples of their applications, and discuss their similarities and differences.

We study the ground state properties of rectangular quantum dots by using the spin-density-functional theory and quantum Monte Carlo methods. The dot geometry is determined by an infinite hard-wall potential to enable comparison to manufactured, rectangular-shaped quantum dots. We show that the electronic structure is very sensitive to the deformation, and at realistic sizes the non-interacting picture determines the general behavior. However, close to the degenerate points where Hund's rule applies, we find spin-density-wave-like solutions bracketing the partially polarized states. In the quasi-one-dimensional limit we find permanent charge-density waves, and at a sufficiently large deformation or low density, there are strongly localized stable states with a broken spin-symmetry.Comment: 8 pages, 9 figures, submitted to PR

We show that topological transitions in electronic spin transport are feasible by a controlled manipulation of spin-guiding fields. The transitions are determined by the topology of the fields texture through an effective Berry phase (related to the winding parity of spin modes around poles in the Bloch sphere), irrespective of the actual complexity of the nonadiabatic spin dynamics. This manifests as a distinct dislocation of the interference pattern in the quantum conductance of mesoscopic loops. The phenomenon is robust against disorder, and can be experimentally exploited to determine the magnitude of inner spin-orbit fields.PACS numbers: 71.70. Ej, 75.76.+j, In the early 1980s Berry showed that quantum states in a cyclic motion may acquire a phase component of geometric nature [1]. This opened a door to a class of topological quantum phenomena in optical and material systems [2]. With the development of quantum electronics in semiconducting nanostructures, a possibility emerged to manipulate electronic quantum states via the control of spin geometric phases driven by magnetic field textures [3]. After several experimental attempts An early proposal for the topological manipulation of electron spins by Lyanda-Geller involved the abrupt switching of Berry phases in spin interferometers [12]. These are conducting rings of mesoscopic size subject to Rashba spin-orbit (SO) coupling, where a radial magnetic texture B SO steers the electronic spin (Fig. 1a). For relatively large field strengths (or, alternatively, slow orbital motion) the electronic spins follow the local field direction adiabatically during transport, acquiring a Berry phase factor π of geometric origin (equal to half the solid angle subtended by the spins in a roundtrip) leading to destructive interference effects. By introducing an additional in-plane uniform field B, it was assumed that the spin geometric phase undergoes a sharp transition at the critical point beyond which the corresponding solid angle vanishes together with the Berry phase, and interference turns constructive. The transition should manifest as a step-like characteristic in the ring's conductance as a function of the coupling fields (so far unreported). However, this reasoning appears to be oversimplified: the adiabatic condition can not be satisfied in the vicinity of the transition point, since the local steering field vanishes and reverses direction abruptly at the rim of the ring. Moreover, typical experimental conditions correspond to moderate field strengths, resulting in nonadiabatic effects in analogy to the case of spin transport in helical magnetic fields [13]. Hence, a more sophisticated approach is required. This includes identifying the role played by nonadiabatic Aharonov-Anandan (AA) geometric phases [14].Here, we report transport simulations showing that a topological phase transition is possible in loop-shaped spin interferometers away from the adiabatic limit. The transition is determined by the topology of the field texture through an effective Berry phase ...

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