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The Kitaev model on the honeycomb lattice recently attracted considerable attention. However, in candidate materials, other interactions are present, and 
among them the off-diagonal $\Gamma$ interaction has been particularly challenging. While several numerical studies on a minimal Kitaev-$\Gamma$ $(K\Gamma)$ model found multiple quantum disordered phases, definite conclusions on existence of quantum spin liquids remain elusive due to various numerical limitations. Here we present a classical phase diagram of the $K\Gamma$ model in the presence of the bond-anisotropy, which reveals intriguing competing phases and extended frustration. The stability of the classical phases to quantum fluctuations using a linear spin wave theory will be also discussed.

CAP Virtual Congress 2021

Extent of Frustration in the Classical Kitaev-$\Gamma$ Model

kitaev

spin

classical

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Morphogens (often acting as transcription activators or repressors) govern pattern formation and cell differentiation during early embryogenesis. Abnormal distributions of morphogens can result in developmental defects or even death. Oftentimes, thresholds of concentrations of morphogens behave like an ON/OFF switch for the activation or repression of downstream genes. Thus accurate measurements of morphogen concentration and mobility in space and time can help tackle the puzzle of how exactly cascades of hundreds of morphogens coordinate their targets precisely and promptly amidst crowded and complicated cellular environments. 

In principle, Fluorescence Correlation Spectroscopy (FCS) allow for accurate measurements of both protein dynamics and concentration. Here, we demonstrate how to use FCS and confocal imaging to achieve extremely low (~ nM) concentration measurements in live Drosophila embryos expressing recombinant fluorescent morphogens, by carefully taking account background noise and photobleaching effects. The dynamics of both an activator and a repressor morphogens were further studied using FCS and Fluorescence Recovery After Photobleaching. We found that both type of morphogens are very mobile in nuclei, explaining how that are able to turn on or off gene expression in only a few minutes.

Concentration and Mobility of Activator and Repressor Morphogens in live early Drosophila Embryos

Recently, there has been an increasing interest in the study of optical/microwave cavity-confined photon-magnon interaction due to their potential applications in quantum information processing
and spintronics [1,2]. In those studies, a number of unique features have been observed at frequencies in the GHz range. On the other hand, less is known about the dynamics of antiferromagnets, which are characterized by frequencies in the THz range [3].


We report results from an analytical study of the coupling of an antiferromagnetic domain wall to optical photons via the inverse Faraday effect. We consider spin canting and complex spin textures in antiferromagnetic materials that can arise from Dzyaloshinskii-Moriya interactions (DMI) [4]. DMI is not easily measurable and is often inferred from other quantities. In this work, we find that the presence of DMI enables spin interactions with cavity photons in a geometry which otherwise allows no magneto-optical coupling. This result may be used to measure the DMI constant in optomagnonic experiments by measuring the interaction of antiferromagnetic resonances to optical modes in a cavity.

**Keywords**: optomagnonic, DMI, antiferromagnet, domain wall, spin texture

*This work was supported by NSERC, CFI-JELF, Research Manitoba and the University of Manitoba, Canada.*

**References**
1. Harder, M. & Hu, C. M. Cavity Spintronics: An Early Review of Recent Progress in the Study of
Magnon–Photon Level Repulsion. in Solid State Physics - Advances in Research and Applications (eds. Camley, R. E. & Stamps, R. L.) vol. 69 47–121 (Academic Press, 2018).
2. Bozhko, D. A., Vasyuchka, V. I., Chumak, A. V & Serga, A. A. Magnon-phonon interactions in
magnon spintronics (Review article). Low Temp. Phys. 46, 383–399 (2020).
3. Kampfrath, T. et al. Coherent terahertz control of antiferromagnetic spin waves. Nat. Photonics 5, 31–34 (2011).
4. Conzelmann, T., Selzer, S. & Nowak, U. Domain walls in antiferromagnets: The effect of Dzyaloshinskii-Moriya interactions. J. Appl. Phys. 127, 223908 (2020).

Collective dynamics of antiferromagnetic domain walls in an optical cavity

Geometrical frustration arises in systems whose structures support multiple degenerate ground states. Artificial spin ice (ASI), has been built in diverse configurations which allows us to control frustration by experimentally tuning suitable parameters[1]. We present computational results on ASI systems consisting
of planar arrays of nanosized elongated ferromagnetic islands where geometrical frustration takes place at the vertices due to dipolar interactions between elements. To date, most studies have employed two-dimensional geometries in order to study magnetic charge dynamics, phase transitions, vertex-based frustration, and other interesting effects[2]. Recently, there has been a surge of interest in realizing three-dimensional artificial spin ice[3]. The use of a third dimension allows increased configurability and optimization of the magnetostatic interaction between different elements of the system. The work mentioned here concerns non-
equilibrium dynamics of a bilayer artificial spin ice structure consisting of two identical arrays separated by some distance and rotated at an angle between the two array axes. Introducing an angle between the layers enables the observation of novel, emergent phenomena as it changes the nature of the interactions between
the spins. We consider pinwheel variants of a square ice geometry for each
array[4]. Using different Monte Carlo techniques, we examine ground state ordering as a function of the interaction strength between layers for different relative orientations. Avalanche processes are also investigated and contrasted with those found in single-layer arrays.

References:
[1] RF Wang, C Nisoli, RS Freitas, J Li, W McConville, BJ Cooley, MS Lund, N Samarth, C Leighton, VH Crespi, et al. Artificial `spin ice' in a geometrically frustrated lattice of nanoscale ferromagnetic islands. Nature, 439(7074):303{306, 2006.
[2] Cristiano Nisoli, Vassilios Kapaklis, and Peter Schier. Deliberate exotic magnetism via frustration and topology. Nature Physics, 13(3):200{203, 2017.
[3] Gia-Wei Chern, Charles Reichhardt, and Cristiano Nisoli. Realizing three-dimensional artificial spin ice by stacking planar nano-arrays. Applied Physics Letters, 104(1):013101, 2014.
[4] R. Mac^edo, G. M. Macauley, F. S. Nascimento, and Robert L. Stamps. Apparent ferromagnetism in the pinwheel artificial spin ice. Physical Review B,
98(1):014437, 2018.

Investigation of the dynamics of twisted bilayer artificial spin ice structure

Electron spins confined to quantum dots are a promising platform for scalable quantum computation. A necessary component of such a quantum processor is a microwave magnetic field (B$_1$) that implements single-qubit gate operations via electron spin resonance. A common method for generating a B$_1$ field is to place a micro-stripline close to the device. A second method is to place a micromagnet near the device and apply local voltage pulses to induce electric dipole spin resonance. Both methods involve elements that are bulky (> 1 µm) compared to the scale of an individual quantum dot (~60 nm), and are placed on the surface of the chip, taking up valuable space and preventing scalable, dense packing of qubits. Furthermore, the B$_1$ produced by both methods is local, limiting single-qubit rotations to only a few quantum dots per micro-stripline or micromagnet.

We have investigated a centimeter-scale bowtie-shaped microwave resonator design that produces a global B$_1$ field with minimal electric field over a relatively large area (~mm$^2$), which could enable single-qubit rotations for thousands of qubits. The design ensures that the magnetic field is maximal near the center of the resonator, whereas the electric field is expelled towards the edges of the resonator. A minimal electric field in the active area is necessary to prevent photon-assisted tunneling of the confined electrons. The resonator can be vertically integrated above the quantum device layer, removing the need for microwave interconnects or bulky components in the device layer. Individual qubits can be tuned in and out of resonance with this global B$_1$ field using the Stark effect, wherein the electronic $g$-factor shifts slightly as a function of applied electric field. Coupling an external microwave source to the resonator is achieved by an excitation stripline on the opposite side of a dielectric substrate. The resonator and stripline dimensions are optimized for operation at ~15 GHz, corresponding to a DC magnetic field of 0.53 T for a $g=2$ electron spin. At this field and a temperature of 100 mK, the spin qubit is initialized by relaxing into its ground state with a probability of 99.9 %. Our experimental implementation of lateral quantum dots in silicon will be discussed, along with progress in testing and integrating the global B$_1$ field resonator.

Microwave resonators for global control of electron spins qubits

With advances in nanofabrication, modelling the optical properties of nanoscale systems is critical.

The optical response of nanostructures can be simulated using the bulk permittivity of the constituent materials (1). The permittivity is generally assumed time-invariant and spatially dispersionless. While these approximations are enough for the simulations of most systems, in some cases the physics must be modelled more precisely.

We present three recent projects on the modelling of complex optical properties with implications in active nanophotonics (2), ultrafast physics and nonlinear plasmonics. The algorithms we developed are unavailable in commercial or open-source software.

1.) Nonlocal models: for small nanostructures (< 10 nm) spatial dispersion cannot be neglected, and we need to account for the electron degeneracy pressure (3).

2.) Nonlinear hydrodynamics: The hydrodynamic plasma model is required to properly model conduction electron dynamics in strong optical fields (4).

3.) Time-variant permittivity: Electrodynamics combined with two-temperature modelling is required to calculate the optical response induced by nonlinearity in ITO under strong optical fields (5).

Our models combined with high-performance computing allow us to achieve accurate results and significant agreement to experiments.

References

1. Pernice, W. H. P. Finite-Difference Time-Domain Methods and Material Models for the Simulation of Metallic and Plasmonic Structures. J. Comput. Theor. Nanosci. 7, 1–14 (2010).

2. Shaltout, A. M., Shalaev, V. M. & Brongersma, M. L. Spatiotemporal light control with active metasurfaces. Science 364, eaat3100 (2019).

3. Baxter, J., Lesina, A. C. & Ramunno, L. Parallel FDTD modelling of nonlocality in plasmonics. ArXiv200506997 Phys. (2020).

4. Bin-Alam, M. S. et al. Hyperpolarizability of plasmonic meta-atoms in metasurfaces. ArXiv200705142 Phys. (2020).

5. Alam, M. Z., Schulz, S. A., Upham, J., De Leon, I. & Boyd, R. W. Large optical nonlinearity of nanoantennas coupled to an epsilon-near-zero material. Nat. Photonics 12, 79–83 (2018)

Advanced modelling in computational nanophotonics

Majorana zero modes (MZM) have been a focal point of the condensed matter physics
community in recent times due in part to their potential applications in quantum computation.
Most notably, the exotic exchange statistics of MZMs form the basis of
topologically protected quantum gates. The physical exchange, or braiding, of MZMs is often modeled in networks of 1D topological superconducting wires. A key ingredient of these braiding protocols is the transport of MZMs across a superconductor. We consider a “piano key model” of transport, where segments of a superconductor are adiabatically tuned between the topologically trivial and the topologically non-trivial phases via electric gates. We examine the time scales over which the piano key tuning should be performed in order to minimize the likelihood of unwanted excitations of the ground state. We also examine the dynamical phase accrued by the ground state, which is of importance in the context of braiding.

Transport of Majorana zero modes in 1D topological superconductors

The discovery of time-reversal symmetry(TRS) breaking in elemental Re has ignited fresh interest in the Re based superconductors. The recent studies show that role of Re concentration and crystal symmetry is crucial in understanding the unconventional superconductivity of these compounds. Therefore, we studied two Re-based superconductors Re$_3$B (<var>TC</var> = 5.19 K) and Re$_7$B$_3$ 
(<var>TC</var> = 3.2 K) having a centrosymmetric and non-centrosymmetric crystal structure, respectively. In this talk, we will present a comprehensive study on superconducting properties of Re$_7$B$_3$ and Re$_3$B through specific heat, magnetic susceptibility, resistivity, and transverse and zero-field muon rotation/relaxation ($\mu$SR) experiments. This will include the temperature dependence of penetration depth using transverse-field $\mu$SR measurements, which will be used to determine the symmetry of the superconducting gap. To further explore these materials, we performed the zero-field $\mu$SR measurements, which show the evidence for TRS preserving superconducting state for both materials in the limits of our measurements.

$\mu$SR study of superconducting Re-B compounds

In the past few decades, scientists discovered that TiO2 was capable of purifying polluted water without any addition of strong oxidants. Active hydroxyl radicals can be produced through photodegradation process when TiO2 is illuminated under water, and such process is viewed as a favorable method for on-site decomposition of organic compounds. However, the main drawback of this process suffers from the range of wavelength TiO2 can absorb, which lies in Ultraviolet region. In previous studies, Fe (III) doping was used to broaden the band gap of titania and allow the material of absorb into the visible region. Yet, in our own work, the doping of TiO2 with iron does not provide the expected improvement during methylene blue photodegradation under simulated sun light illumination.

In this study, we characterized pure and Fe(III) doped TiO2 nanopowders using SEM, EDS, XRD, valence band XPS and UPS, to learn about the phase, particle size, chemical composition, and more importantly the influence of Fe (III) dopants on the valence band structure of TiO2 nanoparticles synthesized through Sol-Gel method. The relationship between the valence band structure and the material’s photocatalytic properties will be discussed.

Electronic properties of pure and iron(III) doped TiO2 nanomaterials

The ability to image magnetodynamics has proved key to the advancement of spintronics technology [1]. As technological size scales reduce and speeds increase, there is a need to provide commensurate advancement in experimental tools to image magnetodynamics down to the atomic scale with ultrafast time resolution. In pursuit of this goal, we are developing a custom designed scanning tunneling microscope which will be paired with a THz light source to create a THz-STM that achieves ultrafast time resolution [2]. THz-STM experiments require significant acquisition time and present an extreme challenge. To make such an instrument practical, the STM must be designed with optical access, long-term stability, and rigidity in mind. Progress on the design and construction of a variable temperature scanning tunneling microscope purpose built for the observation of magnetodynamics will be presented. 

1 https://science.sciencemag.org/content/294/5546/1484
2 https://www.nature.com/articles/nphoton.2013.151

Imaging Magnetic Dynamics on the Atomic Scale

Hydrogen terminated silicon has seen a recent resurgence in popularity due to several works demonstrating its use for ultra-dense memory, atomic electronics, and quantum devices. On this surface, individual hydrogen atoms can be removed with atomic precision through STM pulses, leaving a dangling bond (DB) behind. DBs are quantum dot-like entities that can hold either 0, 1, or 2 electrons, with their discrete energy levels in the bandgap. We are studying DBs to achieve true random number generators (RNG) on the atomic scale. Two DBs patterned in close proximity to each other on a highly n-doped crystal host a net extra electron, which can quantum mechanically tunnel to reside on either side. Through measurement of the extra electrons’ spatial location in the pair, it is expected that the electron will be found on either side with equal probability in the absence of any biasing effects. This opens the possibility of using the system as a true RNG, where the bits are generated by probing the electrons’ spatial location. Quantum processes are most desired for RNG because the randomness can be such that no common naturally occurring or imposed noise will alter the number generation. We study these DB pairs by DFT methods to establish the effect of geometry, external fields, and nearby dopants on charge localization and consequent RNG bit generation.
![Image abstract.][1]


[1]: https://i.ibb.co/jhvjz07/Image-Abstract.png

Extent of Frustration in the Classical Kitaev-$\Gamma$ Model

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Concentration and Mobility of Activator and Repressor Morphogens in live early Drosophila Embryos

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