The recent proposal of Romero-Isart et al. [Phys. Rev. Lett. 111, 145304 (2013)] to utilize the vortex lattice phases of superconducting materials to prepare a lattice for ultracold-atom-based quantum emulators raises the need to create and control vortex lattices of different symmetries. Here we propose a mechanism by which honeycomb, hexagonal, square, and kagome vortex lattices could be created in superconducting systems with multiscale intervortex interactions. Multiple scales of the intervortex interaction can be created and controlled in layered systems made of different superconducting materials or with differing interlayer spacings.
The recent proposal of Romero-Isart et al. [Phys. Rev. Lett. 111, 145304 (2013)] to utilize the vortex lattice phases of superconducting materials to prepare a lattice for ultracold-atom-based quantum emulators raises the need to create and control vortex lattices of different symmetries. Here we propose a mechanism by which honeycomb, hexagonal, square, and kagome vortex lattices could be created in superconducting systems with multiscale intervortex interactions. Multiple scales of the intervortex interaction can be created and controlled in layered systems made of different superconducting materials or with differing interlayer spacings.
It was recently proposed to use the stray magnetic fields of superconducting vortex lattices to trap ultracold atoms for building quantum emulators. This calls for new methods for engineering and manipulating of the vortex states. One of the possible routes utilizes type-1.5 superconducting layered systems with multi-scale inter-vortex interactions. In order to explore the possible vortex states that can be engineered, we present two phase diagrams of phenomenological vortex matter models with multi-scale inter-vortex interactions featuring several attractive and repulsive length scales. The phase diagrams exhibit a plethora of phases, including conventional 2D lattice phases, five stripe phases, dimer, trimer, and tetramer phases, void phases, and stable low-temperature disordered phases. The transitions between these states can be controlled by the value of an applied external field.
Vortices and vortex lattices play a major role in determining the transport properties of type-II superconductors[1–3], and enable a platform to investigate exotic superconducting physics[4,5]. The study of vortex matter has generally focused on novel states in 2D films and structures, and has recently moved to investigating systems with constrained dimensions and smaller vortex numbers[6–11]. Vortices are responsible, for example, for some electrical transport regimes in superconducting films, as well as the Berezinkskii-Kosterlitz-Thouless phase transition in superconducting films[12]. Unconventional forms of superconductivity, such as the spin triplet pairing predicted in Sr2RuO4, or in topological insulators paired to s-wave superconductors, contain two condensates that may support two vortex lattices, and may display Majorana modes, signatures of which may have been seen in other superconducting systems[13–17]. The vortex-vortex interactions, or inter and intra-condensate couplings in multicondensate systems, are important parameters that characterize the behavior of the systems that display such phenomena[18–20]. In investigating these parameters, a technique that can both probe the energies in a system, as well as manipulate the vortices therein, has long been desired. In this work, we report on progress in determining the energy scales of vortex systems, as well as limited control over the vortex motion. Using a technique based on magnetic force microscopy, we can directly measure the resonant motion of vortices present in a superconducting lattice. We use a scanning magnetic tip to trap a small number of vortices in a superconducting Josephson junction array near the tip. By observing the resonant motion of the configuration of vortices, a map of the location of energy degeneracies between different stable configurations is generated. From this data, we use a simulation to extract the relative strengths of the characteristic energy scales for the system, including the vortex-magnetic field interaction, the vortex-vortex interaction strength, and the chemical potential for the vortices. The simulations for small numbers of vortices fits the data well for multiple field profiles and lattice spacings. The ability to tune the vortex number and configurations by changing the magnetic field profile from the tip, as well as the lattice parameters of the superconducting surface, are key portions of this technique. We demonstrate that the relative strengths of the chemical potential and vortex-vortex interactions can be tuned relative to the vortex-magnetic field energy by changing the lattice spacing of the array. We also show that by moving the tip farther from or closer to the surface, which changes the potential well from the tip, that the configurations of vortices can be modified. From the experiments, we show that this technique can be used to both extract the strengths of the relative energy scales in this system and other superconducting systems, as well as for manipulating the vortex configurations for quantum computation applications.
We investigate a mixture of two repulsively interacting superfluids with different constituent particle masses: m_{1}≠m_{2}. Solutions to the Gross-Pitaevskii equation for homogeneous infinite vortex lattices predict the existence of rich vortex lattice configurations, a number of which correspond to Platonic and Archimedean planar tilings. Some notable geometries include the snub-square, honeycomb, kagome, and herringbone lattice configurations. We present a full phase diagram for the case m_{2}/m_{1}=2 and list a number of geometries that are found for higher integer mass ratios.
Spin-triplet superconductivity is actively pursued in condensed matter physics due to the potential applications in topological quantum computations. The related pairing mechanism involving the interaction remains an important research topic. Here we propose a universal approach to obtain p-wave triplet superconductivity in the Hubbard models by simply changing the sign of the hopping amplitudes of the spin-down electrons, and apply it to three prototype two-dimensional lattices (honeycomb, square, and triangular). The parent Hamiltonian at half filling has long-range magnetic order, which is ferromagnetic in all three directions for the frustrated triangular lattices, and ferromagnetic (antiferromagnetic) in the xy plane (z direction) for the bipartite honeycomb and square lattices. The magnetic transitions occur at some critical interactions on honeycomb and triangular lattices, which are estimated by finite-size scalings. When the systems are doped, we find the triplet p-wave pairing is a dominating superconducting instability. We demonstrate its emergence is closely related to the strong ferromagnetic spin fluctuations induced by the doping. Our results provide an understanding of the microscopical triplet-pairing mechanism, and will be helpful in the search for spin-triplet superconducting materials.
Motivated by recent numerical work, we use the boson-vortex duality to study the possible phases of the frustrated spin-$\frac{1}{2}\phantom{\rule{4pt}{0ex}}{J}_{1}\text{\ensuremath{-}}{J}_{2}$ XXZ models on the honeycomb lattice. By condensing the vortices, we obtain various gapped phases that either break certain lattice symmetry or preserve all the symmetries. The gapped phases breaking lattice symmetries occur when the vortex band structure has two minima. Condensing one of the two vortex flavors leads to an Ising ordered phase, while condensing both vortex flavors gives rise to a valence-bond-solid state. Both of those phases have been observed in the numerical studies of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ XXZ honeycomb model. Furthermore, by tuning the band structure of vortex and condensing it at the $\mathrm{\ensuremath{\Gamma}}$ point, we obtain a featureless paramagnet. But the precise nature of this featureless state is still unclear and needs future study.
Possible phases of spin-1/2XXZ model on honeycomb lattice by charge-vortex duality
Motivated by the recent numerical work, we use the boson-vortex duality to study the possible phases of the frustrated spin-1/2J1−J2 XXZ models on the honeycomb lattice. By condensing the vortices, we obtain various insulating phases that either break certain lattice symmetry or preserve all the symmetries. The lattice symmetry breaking insulating phases occur when the vortex band structure has two minima. Condensing one of the two vortex flavors leads to an Ising ordered phase phase, while condensing both two vortex flavors gives rise to a valence bond solid state. Both of those phases have been observed in the numerical study of the J1−J2 XXZ honeycomb models. Furthermore by fine tuning the band structure of vortex and condense it at the single minimum at the Γ point, we obtain a featureless paramagnet state. But the precise nature of this featureless state is still unclear and needs future study.