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1. Size dependence- and induced transformations- of fractional quantum Hall effects under tilted magnetic fields

   https://doi.org/10.1038/s41598-022-22812-x  

   Wijewardena, U. Kushan ; Nanayakkara, Tharanga R. ; Kriisa, Annika ; Reichl, Christian ; Wegscheider, Werner ; Mani, Ramesh G. ( November 2022 , Scientific Reports)

   Two-dimensional electron systems subjected to high transverse magnetic fields can exhibit Fractional Quantum Hall Effects (FQHE). In the GaAs/AlGaAs 2D electron system, a double degeneracy of Landau levels due to electron-spin, is removed by a small Zeeman spin splitting,$$g \mu _B B$$$g{\mu }_{B}B$, comparable to the correlation energy. Then, a change of the Zeeman splitting relative to the correlation energy can lead to a re-ordering between spin polarized, partially polarized, and unpolarized many body ground states at a constant filling factor. We show here that tuning the spin energy can produce fractionally quantized Hall effect transitions that include both a change in$$\nu$$$\nu$for the$$R_{xx}$$$R_{\mathrm{xx}}$minimum, e.g., from$$\nu = 11/7$$$\nu =11/7$to$$\nu = 8/5$$$\nu =8/5$, and a corresponding change in the$$R_{xy}$$$R_{\mathrm{xy}}$, e.g., from$$R_{xy}/R_{K} = (11/7)^{-1}$$$R_{\mathrm{xy}}/R_K={(11/7)}^{-1}$to$$R_{xy}/R_{K} = (8/5)^{-1}$$$R_{\mathrm{xy}}/R_K={(8/5)}^{-1}$, with increasing tilt angle. Further, we exhibit a striking size dependence in the tilt angle interval for the vanishing of the$$\nu = 4/3$$$\nu =4/3$and$$\nu = 7/5$$$\nu =7/5$resistance minima, including “avoided crossing” type lineshape characteristics, and observable shifts of$$R_{xy}$$$R_{\mathrm{xy}}$at the$$R_{xx}$$$R_{\mathrm{xx}}$minima- the latter occurring for$$\nu = 4/3, 7/5$$$\nu =4/3,7/5$and the 10/7. The results demonstrate both size dependence and the possibility, not just of competition between different spin polarized states at the same$$\nu$$$\nu$and$$R_{xy}$$$R_{\mathrm{xy}}$, but also the tilt- or Zeeman-energy-dependent- crossover between distinct FQHE associated withmore »different Hall resistances.

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2. Low rank representations for quantum simulation of electronic structure

   https://doi.org/10.1038/s41534-021-00416-z  

   Motta, Mario ; Ye, Erika ; McClean, Jarrod R. ; Li, Zhendong ; Minnich, Austin J. ; Babbush, Ryan ; Chan, Garnet Kin-Lic ( May 2021 , npj Quantum Information)

   The quantum simulation of quantum chemistry is a promising application of quantum computers. However, forNmolecular orbitals, the$${\mathcal{O}}({N}^{4})$$$O\left(N^4\right)$gate complexity of performing Hamiltonian and unitary Coupled Cluster Trotter steps makes simulation based on such primitives challenging. We substantially reduce the gate complexity of such primitives through a two-step low-rank factorization of the Hamiltonian and cluster operator, accompanied by truncation of small terms. Using truncations that incur errors below chemical accuracy allow one to perform Trotter steps of the arbitrary basis electronic structure Hamiltonian with$${\mathcal{O}}({N}^{3})$$$O\left(N^3\right)$gate complexity in small simulations, which reduces to$${\mathcal{O}}({N}^{2})$$$O\left(N^2\right)$gate complexity in the asymptotic regime; and unitary Coupled Cluster Trotter steps with$${\mathcal{O}}({N}^{3})$$$O\left(N^3\right)$gate complexity as a function of increasing basis size for a given molecule. In the case of the Hamiltonian Trotter step, these circuits have$${\mathcal{O}}({N}^{2})$$$O\left(N^2\right)$depth on a linearly connected array, an improvement over the$${\mathcal{O}}({N}^{3})$$$O\left(N^3\right)$scaling assuming no truncation. As a practical example, we show that a chemically accurate Hamiltonian Trotter step for a 50 qubit molecular simulation can be carried out in the molecular orbital basis with as few as 4000 layers of parallel nearest-neighbor two-qubit gates, consisting of fewer than 10⁵non-Clifford rotations. We also apply our algorithm to iron–sulfur clusters relevant for elucidating the mode of action of metalloenzymes.
3. GHz Ultrasonic Chip-Scale Device Induces Ion Channel Stimulation in Human Neural Cells

   https://doi.org/10.1038/s41598-020-58133-0  

   Balasubramanian, Priya S. ; Singh, Ankur ; Xu, Chris ; Lal, Amit ( February 2020 , Scientific Reports)

   Emergent trends in the device development for neural prosthetics have focused on establishing stimulus localization, improving longevity through immune compatibility, reducing energy re-quirements, and embedding active control in the devices. Ultrasound stimulation can single-handedly address several of these challenges. Ultrasonic stimulus of neurons has been studied extensively from 100 kHz to 10 MHz, with high penetration but less localization. In this paper, a chip-scale device consisting of piezoelectric Aluminum Nitride ultrasonic transducers was engineered to deliver gigahertz (GHz) ultrasonic stimulus to the human neural cells. These devices provide a path towards complementary metal oxide semiconductor (CMOS) integration towards fully controllable neural devices. At GHz frequencies, ultrasonic wavelengths in water are a few microns and have an absorption depth of 10–20 µm. This confinement of energy can be used to control stimulation volume within a single neuron. This paper is the first proof-of-concept study to demonstrate that GHz ultrasound can stimulate neuronsin vitro. By utilizing optical calcium imaging, which records calcium ion flux indicating occurrence of an action potential, this paper demonstrates that an application of a nontoxic dosage of GHz ultrasonic waves$$(\ge 0.05\frac{W}{c{m}^{2}})$$$\left(\ge 0.05\frac{W}{c{m}^2}\right)$caused an average normalized fluorescence intensity recordings >1.40 for the calcium transients. Electrical effects due to chip-scale ultrasound delivery wasmore »discounted as the sole mechanism in stimulation, with effects tested atα = 0.01 statistical significance amongst all intensities and con-trol groups. Ionic transients recorded optically were confirmed to be mediated by ion channels and experimental data suggests an insignificant thermal contributions to stimulation, with a predicted increase of 0.03^oCfor$$1.2\frac{W}{c{m}^{2}}\cdot $$$1.2\frac{W}{c{m}^2}\cdot$This paper paves the experimental framework to further explore chip-scale axon and neuron specific neural stimulation, with future applications in neural prosthetics, chip scale neural engineering, and extensions to different tissue and cell types.

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4. Stabilization of three-dimensional charge order through interplanar orbital hybridization in PrxY1−xBa2Cu3O6+δ

   https://doi.org/10.1038/s41467-022-33607-z  

   Ruiz, Alejandro ; Gunn, Brandon ; Lu, Yi ; Sasmal, Kalyan ; Moir, Camilla M. ; Basak, Rourav ; Huang, Hai ; Lee, Jun-Sik ; Rodolakis, Fanny ; Boyle, Timothy J. ; et al ( October 2022 , Nature Communications)

   The shape of 3d-orbitals often governs the electronic and magnetic properties of correlated transition metal oxides. In the superconducting cuprates, the planar confinement of the$${d}_{{x}^{2}-{y}^{2}}$$$d_{x^2-y^2}$orbital dictates the two-dimensional nature of the unconventional superconductivity and a competing charge order. Achieving orbital-specific control of the electronic structure to allow coupling pathways across adjacent planes would enable direct assessment of the role of dimensionality in the intertwined orders. Using CuL₃and PrM₅resonant x-ray scattering and first-principles calculations, we report a highly correlated three-dimensional charge order in Pr-substituted YBa₂Cu₃O₇, where the Prf-electrons create a direct orbital bridge between CuO₂planes. With this we demonstrate that interplanar orbital engineering can be used to surgically control electronic phases in correlated oxides and other layered materials.
5. Microphysics of Relativistic Collisionless Electron-ion-positron Shocks

   https://doi.org/10.3847/1538-4357/ac713e  

   Grošelj, Daniel ; Sironi, Lorenzo ; Beloborodov, Andrei M. ( July 2022 , The Astrophysical Journal)

   We perform particle-in-cell simulations to elucidate the microphysics of relativistic weakly magnetized shocks loaded with electron-positron pairs. Various external magnetizationsσ≲ 10⁻⁴and pair-loading factorsZ_±≲ 10 are studied, whereZ_±is the number of loaded electrons and positrons per ion. We find the following: (1) The shock becomes mediated by the ion Larmor gyration in the mean field whenσexceeds a critical valueσ_Lthat decreases withZ_±. Atσ≲σ_Lthe shock is mediated by particle scattering in the self-generated microturbulent fields, the strength and scale of which decrease withZ_±, leading to lowerσ_L. (2) The energy fraction carried by the post-shock pairs is robustly in the range between 20% and 50% of the upstream ion energy. The mean energy per post-shock electron scales as${\overline{E}}_{\mathrm{e}}\propto {\left(Z_{\pm }+1\right)}^{-1}$. (3) Pair loading suppresses nonthermal ion acceleration at magnetizations as low asσ≈ 5 × 10⁻⁶. The ions then become essentially thermal with mean energy${\overline{E}}_{\mathrm{i}}$, while electrons form a nonthermal tail, extending from$E\sim {\left(Z_{\pm }+1\right)}^{-1}{\overline{E}}_{\mathrm{i}}$to${\overline{E}}_{\mathrm{i}}$. Whenσ= 0, particle acceleration is enhanced by the formation of intense magnetic cavities that populate the precursor during the late stages of shock evolution. Here,more »the maximum energy of the nonthermal ions and electrons keeps growing over the duration of the simulation. Alongside the simulations, we develop theoretical estimates consistent with the numerical results. Our findings have important implications for models of early gamma-ray burst afterglows.

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