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DOI: 10.1016/j.jcis.2023.01.050
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Ref Arxiv: 2301.08066
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By exploiting new mathematical relations between Pandharipande-Thomas (PT) invariants, closely related to Gopakumar-Vafa (GV) invariants, and rank 0 Donaldson-Thomas (DT) invariants counting D4-D2-D0 BPS bound states, we rigorously compute the first few terms in the generating series of Abelian D4-D2-D0 indices for compact one-parameter Calabi-Yau threefolds of hypergeometric type. In all cases where GV invariants can be computed to sufficiently high genus, we find striking confirmation that the generating series is modular, and predict infinite series of Abelian D4-D2-D0 indices. Conversely, we use these results to provide new constraints for the direct integration method, which allows to compute GV invariants (and therefore the topological string partition function) to higher genus than hitherto possible. The triangle of relations between GV/PT/DT invariants is powered by a new explicit formula relating PT and rank 0 DT invariants, which is proven in an Appendix by the second named author. As a corollary, we obtain rigorous Castelnuovo-type bounds for PT and GV invariants for CY threefolds with Picard rank one.

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Ref Arxiv: 2301.00640
Ref INSPIRE: 2620237
DOI: 10.1103/PhysRevD.108.023504
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Based on a formalism introduced in our previous work, we reconstruct the phenomenological function $G_{\rm eff}(z)$ describing deviations from General Relativity (GR) in a model-independent manner. In this alternative approach, we model $\mu\equiv G_\mathrm{eff}/G$ as a Gaussian process and use forecasted growth-rate measurements from a stage-IV survey to reconstruct its shape for two different toy-models. We follow a two-step procedure: (i) we first reconstruct the background expansion history from Supernovae (SNe) and Baryon Acoustic Oscillation (BAO) measurements; (ii) we then use it to obtain the growth history $f\sigma_8$, that we fit to redshift-space distortions (RSD) measurements to reconstruct $G_\mathrm{eff}$. We find that upcoming surveys such as the Dark Energy Spectroscopic Instrument (DESI) might be capable of detecting deviations from GR, provided the dark energy behavior is accurately determined. We might even be able to constrain the transition redshift from $G\to G_\mathrm{eff}$ for some particular models. We further assess the impact of massive neutrinos on the reconstructions of $G_\mathrm{eff}$ (or $\mu$) assuming the expansion history is given, and only the neutrino mass is free to vary. Given the tight constraints on the neutrino mass, and for the profiles we considered in this work, we recover numerically that the effect of such massive neutrinos do not alter our conclusions. Finally, we stress that incorrectly assuming a $\Lambda$CDM expansion history leads to a degraded reconstruction of $\mu$, and/or a non-negligible bias in the ($\Omega_\mathrm{m0}$,$\sigma_{8,0}$)-plane.

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Ref Arxiv: 2301.05942
DOI: 10.1038/s41566-022-01129-1
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Since the emergence of graphene, we have seen several proposals for the realization of Landau lasers tunable over the terahertz frequency range. The hope was that the non-equidistance of the Landau levels from Dirac fermions would suppress the harmful non-radiative Auger recombination. Unfortunately, even with this non-equidistance, an unfavourable non-radiative process persists in Landau-quantized graphene, and so far no cyclotron emission from Dirac fermions has been reported. One way to eliminate this last non-radiative process is to sufficiently modify the dispersion of the Landau levels by opening a small gap in the linear band structure. HgTe quantum wells close to the topological phase transition are a proven example of such gapped graphene-like materials. In this work we experimentally demonstrate Landau emission from Dirac fermions in such HgTe quantum wells, where the emission is tunable by both the magnetic field and the carrier concentration. Consequently, these results represent an advance in the realization of terahertz Landau lasers tunable by a magnetic field and gate voltage.

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Ref Arxiv: 2301.05515
DOI: 10.1039/d2nr05016a
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Patchy particles have received great attention due to their ability to develop directional and selective interactions and serve as building units for the self-assembly of innovative colloidal molecules and crystalline structures. Although synthesizing particles with multiple dissimilar patches is still highly challenging and lacks efficient methods, these building blocks would open paths towards a broader range of ordered materials with inherent properties. Herein, we describe a new approach to pattern functional DNA patches at the surface of particles, by the use of colloidal stamps. DNA inks are transferred only at the contact zones between the target particles and the stamps thanks to selective strand-displacement reactions. The produced DNA-patchy particles are ideal candidates to act as advanced precision/designer building blocks to self-assemble the next generation of colloidal materials.

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Ref Arxiv: 2207.00452
DOI: 10.1088/2053-1583/acb21c
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Abstract The transport and optical properties of semiconducting transition metal dichalcogenides around room temperature are dictated by electron-phonon scattering mechanisms within a complex, spin-textured and multi-valley electronic landscape. The relative positions of the valleys are critical, yet they are sensitive to external parameters and very difficult to determine directly. We propose a first-principles model as a function of valley positions to calculate carrier mobility and Kerr rotation angles, and apply it to MoS$_2$, WS$_2$, MoSe$_2$, and WSe$_2$. The model brings valuable insights, as well as quantitative predictions of macroscopic properties for a wide range of carrier density. The doping-dependant mobility displays a characteristic peak, the height depending on the position of the valleys. In parallel, the Kerr rotation signal is enhanced when same spin-valleys are aligned, and quenched when opposite spin-valleys are populated. We provide guidelines to optimize and correlate these quantities with respect to experimental parameters, as well as the theoretical support for \emph{in situ} characterization of the valley positions.