Differential conductance of a ballistic quantum wire in the presence of Rashba spin-orbit and Zeeman interactions : a thesis presented in partial fulfilment of the requirements for the degree of Master of Philosophy in Theoretical Condensed Matter Physics at Massey University

This thesis calculates the theoretical differential conductance of a ballistic quantum wire semiconductor nanostructure in the presence of Rashba spin-orbit and Zeeman interactions. In semiconductor heterostructures the Rashba spin-orbit interaction arises due to structure inversion asymmetry and couples the spin of the electron to its orbital momentum. In our work Zeeman interaction is induced by application of external magnetic fields in directions transverse, parallel, and perpendicular to the wire axis. Differential conductance is defined as the rate of change of current with respect to a voltage which is applied between two contacts, one on the left (source) and the other on the right (drain) side of the nanostructure. The dispersion relations of the wire are obtained and from these differential conductance is calculated. Differential conductance is presented for zero and strong spin-orbit interaction situations and for magnetic fields applied in the various directions. The wire is studied under two specific regimes, namely normal and full Rashba mediated by the Rashba spin-orbit Hamiltonian. In the normal Rashba regime the wire is modelled without Rashba intersubband coupling while the full Rashba model includes this coupling. Spin-orbit interaction and the direction of applied magnetic field significantly modifies dispersions and have drastic effects on the differential conductance profile. The application of magnetic field in directions parallel (and perpendicular) to the wire in the normal regime in the strong Rashba limit results in the formation of energy gaps. The presence of these gaps drastically reduces conductance. These gaps are suppressed in the full Rashba model of the wire in the strong Rashba limit and therefore reduction in conductance is not observed in the parallel and perpendicular field directions. In the normal Rashba regime in the strong Rashba limit conductance is enhanced for a greater range of source-drian bias voltages at low fields, especially for fields applied in the parallel (and perpendicular) directions. Whereas, in the full Rashba regime in the strong Rashba limit conductance is enhanced up to mid range fields and voltages for all field directions. In both Rashba regimes in the strong Rashba limit the overall conductance is reduced at low fields and voltages for all field directions. Hence, it is concluded that weak Zeeman and weak spin-orbit effects at low bias voltages favours electron transmission in ballistic quantum wires

Antiferromagnetic Order and Phase Coexistence in Antisite Disordered Double Perovskites

In addition to the well known ferromagnetism, double perovskites are also expected to exhibit antiferromagnetic (AF) order driven by electron delocalisation. This has been seen in model Hamiltonian studies and confirmed via ab initio calculations. The AF phases should occur, for example, on sufficient electron doping of materials like Sr_2FeMoO_6 (SFMO) via La substitution for Sr. Clear experimental indication of such AF order is limited, possibly because of increase in antisite disorder with La doping on SFMO, although intriguing signatures of non ferromagnetic behaviour are seen. We study the survival of electronically driven antiferromagnetism in the presence of spatially correlated antisite disorder and extract the signals in magnetism and transport. We discover that A and G type AF order, that is predicted in the clean limit, is actually suppressed less strongly than ferromagnetism by antisite disorder. The AF phases are metallic, and, remarkably, more conducting that the ferromagnet for similar antisite disorder. We also highlight the phase coexistence window that connects the ferromagnetic regime to the A type antiferromagnetic phase.Comment: 8 pages, pdflate

Ultra-low vibration pulse-tube cryocooler stabilized cryogenic sapphire oscillator with 10^-16 fractional frequency stability

A low maintenance long-term operational cryogenic sapphire oscillator has been implemented at 11.2 GHz using an ultra-low-vibration cryostat and pulse-tube cryocooler. It is currently the world's most stable microwave oscillator employing a cryocooler. Its performance is explained in terms of temperature and frequency stability. The phase noise and the Allan deviation of frequency fluctuations have been evaluated by comparing it to an ultra-stable liquid-helium cooled cryogenic sapphire oscillator in the same laboratory. Assuming both contribute equally, the Allan deviation evaluated for the cryocooled oscillator is sigma_y = 1 x 10^-15 tau^-1/2 for integration times 1 < tau < 10 s with a minimum sigma_y = 3.9 x 10^-16 at tau = 20 s. The long term frequency drift is less than 5 x 10^-14/day. From the measured power spectral density of phase fluctuations the single side band phase noise can be represented by L_phi(f) = 10^-14.0/f^4+10^-11.6/f^3+10^-10.0/f^2+10^-10.2/f+ 10^-11.0 for Fourier frequencies 10^-3<f<10^3 Hz in the single oscillator. As a result L_phi approx -97.5 dBc/Hz at 1 Hz offset from the carrier.Comment: 8 pages, 10 figures, presented at European Frequency and Time Forum, ESTEC, Noordwijk, Netherland, April 11-16th 2010 accepted in IEEE Trans. on Micro. Theory & Technique

Radio frequency spectroscopy of the attractive Hubbard model in a trap

Attractive interaction between fermions can lead to pairing and superfluidity in an optical lattice. In contrast to the `continuum', on a lattice the trap induced density variation can generate a non monotonic profile of the pairing amplitude, and completely modify the spectral signatures of any possible pseudogap phase. Using a tool that fully captures the inhomogeneity and strong thermal fluctuations, we demonstrate how the crucial radio frequency signatures of pairing are `inverted' in a trapped attractive fermion lattice compared to the traditional continuum case. These features would be central in interpreting any spectroscopic hint of fermion pairing and superfluidity.Comment: this article supersedes arXiv:1104.491

Ultra-low-phase-noise cryocooled microwave dielectric-sapphire-resonator oscillators with 1 x 10^-16 frequency instability

Two nominally identical ultra-stable cryogenic microwave oscillators are compared. Each incorporates a dielectric-sapphire resonator cooled to near 6 K in an ultra-low vibration cryostat using a low-vibration pulse-tube cryocooler. The phase noise for a single oscillator is measured at -105 dBc/Hz at 1 Hz offset on the 11.2 GHz carrier. The oscillator fractional frequency stability is characterized in terms of Allan deviation by 5.3 x 10^-16 tau^-1/2 + 9 x 10^-17 for integration times 0.1 s < tau < 1000 s and is limited by a flicker frequency noise floor below 1 x 10^-16. This result is better than any other microwave source even those generated from an optical comb phase-locked to a room temperature ultra-stable optical cavity.Comment: 4 pages, 5 figure