Flow enhanced pairing and other novel effects in Fermi gases in synthetic gauge fields

Recent experiments on fermions in synthetic gauge fields result in systems with a spin-orbit coupling along one spatial axis, a detuning field, and a Zeeman field. We show theoretically that the presence of all three results in interesting and unusual phenomena in such systems in the presence of a contact singlet attraction between the fermions (described by a scattering length). For two particles, bound states appear over certain range of the centre of mass momenta when a critical positive scattering length is attained, with the deepest bound state appearing at a nonzero centre of mass momentum. For the centre of mass momenta without a bound state, the gauge field induces a resonance like feature in the scattering continuum resulting in a large scattering phase shift. For many particles, we demonstrate that the system, in a parameter range, shows flow enhanced pairing, i.e., a more robust superfluid at finite centre of mass momentum. Yet another regime of parameters offers the opportunity to study strongly interacting normal states of spin-orbit coupled fermionic systems utilizing the resonance like feature induced by the synthetic gauge field.Comment: 5 pages, 5 figure

Continuum Theory of Edge States of Topological Insulators: Variational Principle and Boundary Conditions

We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us derive natural boundary conditions valid for such systems. Our formulation is particularly suited to develop a continuum theory of the protected edge/surface excitations of topological insulators both in two and three dimensions. By a detailed comparison of our analytical formulation with tight binding calculations of ribbons of topological insulators modeled by the Bernevig-Hughes-Zhang (BHZ) hamiltonian, we show that the continuum theory with the natural boundary condition provides an appropriate description of the low energy physics. As a spin-off, we find that in a certain parameter regime, the gap that arises in topological insulator ribbons of finite width due to the hybridization of edges states from opposite edges, depends non-monotonically on the ribbon width and can nearly vanish at certain "magic widths".Comment: 8 pages, 5 figure

Size-dependent Rigidities of Nanosized Torsional Elements

A theory for the prediction of the size dependence of torsional rigidities of nanosized structural elements is developed. It is shown that, to a very good approximation, the torsional rigidity (D) of a nanosized bar differs from the prediction of standard continuum mechanics $(D_c)$ as $(D-D_c)/D_c = A h_0/a$ where A is a non-dimensional constant, a is the size scale of the cross-section of the bar and $h_0$ is a material length equal to the ratio of the surface elastic constant to the bulk elastic constant. The theory developed is compared with direct atomistic calculations (``numerical experiment'') of the torsional rigidity bars made of several FCC metals modeled using the embedded atom method. Very good agreement is obtained between theory and simulation. The framework presented here can aid the development of design methodologies for nanoscale structural elements without the need for full scale atomistic simulations.Comment: 18 Pages, 5 Figures, Submitted to Int. J. Sol. Struc

Synchronous and Asynchronous Mott Transitions in Topological Insulator Ribbons

We address how the nature of linearly dispersing edge states of two dimensional (2D) topological insulators evolves with increasing electron-electron correlation engendered by a Hubbard like on-site repulsion $U$ in finite ribbons of two models of topological band insulators. Using an inhomogeneous cluster slave rotor mean-field method developed here, we show that electronic correlations drive the topologically nontrivial phase into a Mott insulating phase via two different routes. In a synchronous transition, the entire ribbon attains a Mott insulating state at one critical $U$ that depends weakly on the width of the ribbon. In the second, asynchronous route, Mott localization first occurs on the edge layers at a smaller critical value of electronic interaction which then propagates into the bulk as $U$ is further increased until all layers of the ribbon become Mott localized. We show that the kind of Mott transition that takes place is determined by certain properties of the linearly dispersing edge states which characterize the topological resilience to Mott localization.Comment: 4+ pages, 5 figure

Strange Half Metals and Mott Insulators in SYK Models

We study a dual flavor fermion model where each of the flavors form a Sachdev-Ye-Kitaev (SYK) system with arbitrary and possibly distinct $q$-body interactions. The crucial new element is an arbitrary all-to-all $r$-body interaction between the two flavors. At high temperatures the model shows a strange metal phase where both flavors are gapless, similar to the usual single flavor SYK model. Upon reducing temperature, the coupled system undergoes phase transitions to previously unseen phases - first, a strange half metal (SHM) phase where one flavor remains a strange metal while the other is gapped, and, second, a Mott insulating phase where both flavors are gapped. At a fixed low temperature we obtain transitions between these phases by tuning the relative fraction of sites for each flavor. We discuss the physics of these phases and the nature of transitions between them. This work provides an example of an instability of the strange metal with potential to provide new routes to study strongly correlated systems through the rich physics contained in SYK like models.Comment: 7 pages, 3 figure

Possible ferro-spin nematic order in NiGa2S4

We explore the possibility that the spin-1 triangular lattice magnet NiGa2 S4 may have a ferro-nematic ground state with no frozen magnetic moment but a uniform quadrupole moment. Such a state may be stabilized by biquadratic spin interactions. We describe the physical properties of this state and suggest experiments to help verify this proposal. We also contrast this state with a `non-collinear' nematic state proposed earlier by Tsunetsugu and Arikawa for NiGa2S4