Exact operator solution of the Calogero-Sutherland model

The wave functions of the Calogero-Sutherland model are known to be expressible in terms of Jack polynomials. A formula which allows to obtain the wave functions of the excited states by acting with a string of creation operators on the wave function of the ground state is presented and derived. The creation operators that enter in this formula of Rodrigues-type for the Jack polynomials involve Dunkl operators.Comment: 35 pages, LaTeX2e with amslate

Magnetic structure of the antiferromagnetic half-Heusler compound NdBiPt

We present results of single crystal neutron diffraction experiments on the rare-earth, half-Heusler antiferromagnet (AFM) NdBiPt. This compound exhibits an AFM phase transition at $T_{\mathrm N}=2.18$~K with an ordered moment of $1.78(9)$~$\mu_{\mathrm B}$ per Nd atom. The magnetic moments are aligned along the $[001]$-direction, arranged in a type-I AFM structure with ferromagnetic planes, alternating antiferromagnetically along a propagation vector $\tau$ of $(100)$. The $R$BiPt ($R$= Ce-Lu) family of materials has been proposed as candidates of a new family of antiferromagnetic topological insulators (AFTI) with magnetic space group that corresponds to a type-II AFM structure where ferromagnetic sheets are stacked along the space diagonal. The resolved structure makes it unlikely, that NdBiPt qualifies as an AFTI.Comment: As resubmitted to PRB, corrected typos and changed symbols in Fig.

Tuning the exciton g-factor in single InAs/InP quantum dots

Photoluminescence data from single, self-assembled InAs/InP quantum dots in magnetic fields up to 7 T are presented. Exciton g-factors are obtained for dots of varying height, corresponding to ground state emission energies ranging from 780 meV to 1100 meV. A monotonic increase of the g-factor from -2 to +1.2 is observed as the dot height decreases. The trend is well reproduced by sp3 tight binding calculations, which show that the hole g-factor is sensitive to confinement effects through orbital angular momentum mixing between the light-hole and heavy-hole valence bands. We demonstrate tunability of the exciton g-factor by manipulating the quantum dot dimensions using pyramidal InP nanotemplates

The origin of switching noise in GaAs/AlGaAs lateral gated devices

We have studied the origin of switching (telegraph) noise at low temperature in lateral quantum structures defined electrostatically in GaAs/AlGaAs heterostructures by surface gates. The noise was measured by monitoring the conductance fluctuations around $e^2/h$ on the first step of a quantum point contact at around 1.2 K. Cooling with a positive bias on the gates dramatically reduces this noise, while an asymmetric bias exacerbates it. We propose a model in which the noise originates from a leakage current of electrons that tunnel through the Schottky barrier under the gate into the doped layer. The key to reducing noise is to keep this barrier opaque under experimental conditions. Bias cooling reduces the density of ionized donors, which builds in an effective negative gate voltage. A smaller negative bias is therefore needed to reach the desired operating point. This suppresses tunnelling from the gate and hence the noise. The reduction in the density of ionized donors also strengthens the barrier to tunneling at a given applied voltage. Support for the model comes from our direct observation of the leakage current into a closed quantum dot, around $10^{-20} \mathrm{A}$ for this device. The current was detected by a neighboring quantum point contact, which showed monotonic steps in time associated with the tunneling of single electrons into the dot. If asymmetric gate voltages are applied, our model suggests that the noise will increase as a consequence of the more negative gate voltage applied to one of the gates to maintain the same device conductance. We observe exactly this behaviour in our experiments.Comment: 8 pages, 7 figure

Shape Invariance in the Calogero and Calogero-Sutherland Models

We show that the Calogero and Calogero-Sutherland models possess an N-body generalization of shape invariance. We obtain the operator representation that gives rise to this result, and discuss the implications of this result, including the possibility of solving these models using algebraic methods based on this shape invariance. Our representation gives us a natural way to construct supersymmetric generalizations of these models, which are interesting both in their own right and for the insights they offer in connection with the exact solubility of these models.Comment: Latex file, 23 pages, no picture

Rodrigues Formula for the Nonsymmetric Multivariable Laguerre Polynomial

Extending a method developed by Takamura and Takano, we present the Rodrigues formula for the nonsymmetric multivariable Laguerre polynomials which form the orthogonal basis for the $B_{N}$-type Calogero model with distinguishable particles. Our construction makes it possible for the first time to algebraically generate all the nonsymmetric multivariable Laguerre polynomials with different parities for each variable.Comment: 6 pages, LaTe

Collective Field Description of Spin Calogero-Sutherland Models

Using the collective field technique, we give the description of the spin Calogero-Sutherland Model (CSM) in terms of free bosons. This approach can be applicable for arbitrary coupling constant and provides the bosonized Hamiltonian of the spin CSM. The boson Fock space can be identified with the Hilbert space of the spin CSM in the large $N$ limit. We show that the eigenstates corresponding to the Young diagram with a single row or column are represented by the vertex operators. We also derive a dual description of the Hamiltonian and comment on the construction of the general eigenstates.Comment: 14 pages, one figure, LaTeX, with minor correction

Coulomb and Spin blockade of two few-electrons quantum dots in series in the co-tunneling regime

We present Coulomb Blockade measurements of two few-electron quantum dots in series which are configured such that the electrochemical potential of one of the two dots is aligned with spin-selective leads. The charge transfer through the system requires co-tunneling through the second dot which is $not$ in resonance with the leads. The observed amplitude modulation of the resulting current is found to reflect spin blockade events occurring through either of the two dots. We also confirm that charge redistribution events occurring in the off-resonance dot are detected indirectly via changes in the electrochemical potential of the aligned dot.Comment: 6 pages, 5 figures, submitted to Phys. Rev.