Fluctuations and correlations in rotating Bose-Einstein condensates

We investigate the effects of correlations on the properties of the ground state of the rotating harmonically-trapped Bose gas by adding Bogoliubov fluctuations to the mean-field ground state of an $N$-particle single-vortex system. We demonstrate that the fluctuation-induced correlations lower the energy compared to that of the mean-field ground state, that the vortex core is pushed slightly away from the center of the trap, and that an unstable mode with negative energy (for rotations slower than a critical frequency) emerges in the energy spectrum, thus, pointing to a better state for slow rotation. We construct mean-field ground states of 0-, 1-, and 2-vortex states as a function of rotation rate and determine the critical frequencies for transitions between these states, as well as the critical frequency for appearance of a metastable state with an off-center vortex and its image vortex in the evanescent tail of the cloud.Comment: Added a paragraph to Section III; Revised arguments in Section III.A, results unchanged; Added reference

Strong spin-orbit coupling and magnetism in (111) (La0.3_{0.3}Sr0.7_{0.7})(Al0.65_{0.65}Ta0.35)_{0.35})/SrTiO3_3

Strong correlations, multiple lattice degrees of freedom, and the ease of doping make complex oxides a source of great research interest. Complex oxide heterointerfaces break inversion symmetry and can host a two dimensional carrier gas, which can display a variety of coexisting and competing phenomena. In the case of heterointerfaces based on SrTiO$_3$, many of these phenomena can be effectively tuned by using an electric gate, due to the large dielectric constant of SrTiO$_3$. Most studies so far have focused on (001) oriented heterostructures; however, (111) oriented heterostructures have recently gained attention due to the possibility of finding exotic physics in these systems due their hexagonal surface crystal symmetry. In this work, we use magnetoresistance to study the evolution of spin-orbit interaction and magnetism in a new system, (111) oriented (La$_{0.3}$Sr$_{0.7}$)(Al$_{0.65}$Ta$_{0.35}$)/SrTiO$_3$. At more positive values of the gate voltage, which correspond to high carrier densities, we find that transport is multiband, and dominated by high mobility carriers with a tendency towards weak localization. At more negative gate voltages, the carrier density is reduced, the high mobility bands are depopulated, and weak antilocalization effects begin to dominate, indicating that spin-orbit interaction becomes stronger. At millikelvin temperatures, and gate voltages corresponding to the strong spin-orbit regime, we observe hysteresis in magnetoresistance, indicative of ferromagnetism in the system. Our results suggest that in the (111) (La$_{0.3}$Sr$_{0.7}$)(Al$_{0.65}$Ta$_{0.35}$)/SrTiO$_3$ system, low mobility carriers which experience strong spin-orbit interactions participate in creating magnetic order in the system.Comment: 15 pages, 3 figure

Quantum signatures of self-trapping transition in attractive lattice bosons

We consider the Bose-Hubbard model describing attractive bosonic particles hopping across the sites of a translation-invariant lattice, and compare the relevant ground-state properties with those of the corresponding symmetry-breaking semiclassical nonlinear theory. The introduction of a suitable measure allows us to highlight many correspondences between the nonlinear theory and the inherently linear quantum theory, characterized by the well-known self-trapping phenomenon. In particular we demonstrate that the localization properties and bifurcation pattern of the semiclassical ground-state can be clearly recognized at the quantum level. Our analysis highlights a finite-number effect.Comment: 9 pages, 8 figure

Noninteracting Fermions in infinite dimensions

Usually, we study the statistical behaviours of noninteracting Fermions in finite (mainly two and three) dimensions. For a fixed number of fermions, the average energy per fermion is calculated in two and in three dimensions and it becomes equal to 50 and 60 per cent of the fermi energy respectively. However, in the higher dimensions this percentage increases as the dimensionality increases and in infinite dimensions it becomes 100 per cent. This is an intersting result, at least pedagogically. Which implies all fermions are moving with Fermi momentum. This result is not yet discussed in standard text books of quantum statistics. In this paper, this fact is discussed and explained. I hope, this article will be helpful for graduate students to study the behaviours of free fermions in generalised dimensionality.Comment: To appear in European Journal of Physics (2010

Electrostatic tuning of magnetism at the conducting (111) (La0.3_{0.3}Sr0.7_{0.7})(Al0.65_{0.65}Ta0.35_{0.35})/SrTiO3_3 interface

We present measurements of the low temperature electrical transport properties of the two dimensional carrier gas that forms at the interface of $(111)$ (La$_{0.3}$Sr$_{0.7}$)(Al$_{0.65}$Ta$_{0.35}$)/SrTiO$_3$ (LSAT/STO) as a function of applied back gate voltage, $V_g$. As is found in (111) LaAlO$_3$/SrTiO$_3$ interfaces, the low-field Hall coefficient is electron-like, but shows a sharp reduction in magnitude below $V_g \sim$ 20 V, indicating the presence of hole-like carriers in the system. This same value of $V_g$ correlates approximately with the gate voltage below which the magnetoresistance evolves from nonhysteretic to hysteretic behavior at millikelvin temperatures, signaling the onset of magnetic order in the system. We believe our results can provide insight into the mechanism of magnetism in SrTiO$_3$ based systems.Comment: 5 pages, 3 figure

Spontaneous current generation in the gapless 2SC phase

It is found that, except chromomagnetic instability, the gapless 2SC phase also exhibits a paramagnetic response to the perturbation of an external color neutral baryon current. The spontaneously generated baryon current driven by the mismatch is equivalent to the one-plane wave LOFF state. We describe the 2SC phase in the nonlinear realization framework, and show that each instability indicates the spontaneous generation of the corresponding pseudo Nambu-Golstone current. We show this Nambu-Goldstone currents generation state covers the gluon phase as well as the one-plane wave LOFF state. We further point out that, when charge neutrality condition is required, there exists a narrow unstable LOFF (Us-LOFF) window, where not only off-diagonal gluons but the diagonal 8-th gluon cannot avoid the magnetic instability. We discuss that the diagonal magnetic instability in this Us-LOFF window cannot be cured by off-diagonal gluon condensate in color superconducting phase, and it will also show up in some constrained Abelian asymmetric superfluid/superconducting system.Comment: 8 pages, no figure, final version to appear in PR

Magnetoresistance in the superconducting state at the (111) LaAlO3_3/SrTiO3_3 interface

Condensed matter systems that simultaneously exhibit superconductivity and ferromagnetism are rare due the antagonistic relationship between conventional spin-singlet superconductivity and ferromagnetic order. In materials in which superconductivity and magnetic order is known to coexist (such as some heavy-fermion materials), the superconductivity is thought to be of an unconventional nature. Recently, the conducting gas that lives at the interface between the perovskite band insulators LaAlO$_3$ (LAO) and SrTiO$_3$ (STO) has also been shown to host both superconductivity and magnetism. Most previous research has focused on LAO/STO samples in which the interface is in the (001) crystal plane. Relatively little work has focused on the (111) crystal orientation, which has hexagonal symmetry at the interface, and has been predicted to have potentially interesting topological properties, including unconventional superconducting pairing states. Here we report measurements of the magnetoresistance of (111) LAO/STO heterostructures at temperatures at which they are also superconducting. As with the (001) structures, the magnetoresistance is hysteretic, indicating the coexistence of magnetism and superconductivity, but in addition, we find that this magnetoresistance is anisotropic. Such an anisotropic response is completely unexpected in the superconducting state, and suggests that (111) LAO/STO heterostructures may support unconventional superconductivity.Comment: 6 Pages 4 figure

Anisotropic, multi-carrier transport at the (111) LaAlO3_3/SrTiO3_3 interface

The conducting gas that forms at the interface between LaAlO$_3$ and SrTiO$_3$ has proven to be a fertile playground for a wide variety of physical phenomena. The bulk of previous research has focused on the (001) and (110) crystal orientations. Here we report detailed measurements of the low-temperature electrical properties of (111) LAO/STO interface samples. We find that the low-temperature electrical transport properties are highly anisotropic, in that they differ significantly along two mutually orthogonal crystal orientations at the interface. While anisotropy in the resistivity has been reported in some (001) samples and in (110) samples, the anisotropy in the (111) samples reported here is much stronger, and also manifests itself in the Hall coefficient as well as the capacitance. In addition, the anisotropy is not present at room temperature and at liquid nitrogen temperatures, but only at liquid helium temperatures and below. The anisotropy is accentuated by exposure to ultraviolet light, which disproportionately affects transport along one surface crystal direction. Furthermore, analysis of the low-temperature Hall coefficient and the capacitance as a function of back gate voltage indicates that in addition to electrons, holes contribute to the electrical transport.Comment: 11 pages, 9 figure

Superconductivity and Frozen Electronic States at the (111) LaAlO3_3/SrTiO3_3 Interface

In spite of Anderson's theorem, disorder is known to affect superconductivity in conventional s-wave superconductors. In most superconductors, the degree of disorder is fixed during sample preparation. Here we report measurements of the superconducting properties of the two-dimensional gas that forms at the interface between LaAlO$_3$ (LAO) and SrTiO$_3$ (STO) in the (111) crystal orientation, a system that permits \emph{in situ} tuning of carrier density and disorder by means of a back gate voltage $V_g$. Like the (001) oriented LAO/STO interface, superconductivity at the (111) LAO/STO interface can be tuned by $V_g$. In contrast to the (001) interface, superconductivity in these (111) samples is anisotropic, being different along different interface crystal directions, consistent with the strong anisotropy already observed other transport properties at the (111) LAO/STO interface. In addition, we find that the (111) interface samples "remember" the backgate voltage $V_F$ at which they are cooled at temperatures near the superconducting transition temperature $T_c$, even if $V_g$ is subsequently changed at lower temperatures. The low energy scale and other characteristics of this memory effect ($<1$ K) distinguish it from charge-trapping effects previously observed in (001) interface samples.Comment: 6 pages, 5 Figure