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In quantum mechanics, supersymmetry (SUSY) posits an equivalence between two elementary degrees of freedom, bosons and fermions. Here we show how this fundamental concept can be applied to connect bosonic and fermionic lattice models in the realm of condensed matter physics, e.g., to identify a variety of (bosonic) phonon and magnon lattice models which admit topologically nontrivial free fermion models as superpartners. At the single-particle level, the bosonic and the fermionic models that are generated by the SUSY are isospectral except for zero modes, such as flat bands, whose existence is undergirded by the Witten index of the SUSY theory. We develop a unifying framework to formulate these SUSY connections in terms of general lattice graph correspondences and discuss further ramifications such as the definition of supersymmetric topological invariants for generic bosonic systems. Notably, a Hermitian form of the supercharge operator, the generator of the SUSY, can itself be interpreted as a hopping Hamiltonian on a bipartite lattice. This allows us to identify a wide class of interconnected lattices whose tight-binding Hamiltonians are superpartners of one another or can be derived via squaring or square-rooting their energy spectra all the while preserving band topology features. We introduce a five-fold way symmetry classification scheme of these SUSY lattice correspondences, including cases with a non-zero Witten index, based on a topological classification of the underlying Hermitian supercharge operator. These concepts are illustrated for various explicit examples including frustrated magnets, Kitaev spin liquids, and topological superconductors. 

We present an overview of four challenging research areas in multiscale physics and engineering as well as four data science topics that may be developed for addressing these challenges. We focus on multiscale spatiotemporal problems in light of the importance of understanding the accompanying scientific processes and engineering ideas, where “multiscale” refers to concurrent, non-trivial and coupled models over scales separated by orders of magnitude in either space, time, energy, momenta, or any other relevant parameter. Specifically, we consider problems where the data may be obtained at various resolutions; analyzing such data and constructing coupled models led to open research questions in various applications of data science. Numeric studies are reported for one of the data science techniques discussed here for illustration, namely, on approximate Bayesian computations. 

The remote central Arctic during summertime has a pristine atmosphere with very low aerosol particle concentrations. As the region becomes increasingly ice-free during summer, enhanced ocean-atmosphere fluxes of aerosol particles and precursor gases may therefore have impacts on the climate. However, large knowledge gaps remain regarding the sources and physicochemical properties of aerosols in this region. Here, we present insights into the molecular composition of semi-volatile aerosol components collected in September 2018 during the MOCCHA (Microbiology-Ocean-Cloud-Coupling in the High Arctic) campaign as part of the Arctic Ocean 2018 expedition with the Swedish Icebreaker Oden . Analysis was performed offline in the laboratory using an iodide High Resolution Time-of-Flight Chemical Ionization Mass Spectrometer with a Filter Inlet for Gases and AEROsols (FIGAERO-HRToF-CIMS). Our analysis revealed significant signal from organic and sulfur-containing compounds, indicative of marine aerosol sources, with a wide range of carbon numbers and O : C ratios. Several of the sulfur-containing compounds are oxidation products of dimethyl sulfide (DMS), a gas released by phytoplankton and ice algae. Comparison of the time series of particulate and gas-phase DMS oxidation products did not reveal a significant correlation, indicative of the different lifetimes of precursor and oxidation products in the different phases. This is the first time the FIGAERO-HRToF-CIMS was used to investigate the composition of aerosols in the central Arctic. The detailed information on the molecular composition of Arctic aerosols presented here can be used for the assessment of aerosol solubility and volatility, which is relevant for understanding aerosol–cloud interactions. 

Magnetic fluctuations induced by geometric frustration of local Ir-spins disturb the formation of long-range magnetic order in the family of pyrochlore iridates. As a consequence, Pr2Ir2O7 lies at a tuning-free antiferromagnetic-to-paramagnetic quantum critical point and exhibits an array of complex phenomena including the Kondo effect, biquadratic band structure, and metallic spin liquid. Using spectroscopic imaging with the scanning tunneling microscope, complemented with machine learning, density functional theory and theoretical modeling, we probe the local electronic states in Pr2Ir2O7 and find an electronic phase separation. Nanoscale regions with a well-defined Kondo resonance are interweaved with a non-magnetic metallic phase with Kondo-destruction. These spatial nanoscale patterns display a fractal geometry with power-law behavior extended over two decades, consistent with being in proximity to a critical point. Our discovery reveals a nanoscale tuning route, viz. using a spatial variation of the electronic potential as a means of adjusting the balance between Kondo entanglement and geometric frustration.