We examine the near-field radiative heat transfer between finite-thickness planar fused silica slabs covered with graphene gratings, through the utilization of the Fourier modal method augmented with local basis functions (FMM-LBF), with focus on the lateral shift effect. To do so, we propose and validate a minor modification of the FMM-LBF theory to account for the lateral shift. This approach goes far beyond the effective medium approximation because this latter cannot account for the lateral shift. We show that the heat flux can exhibit significant oscillations with the lateral shift and, at short separation, it can experience up to a 60%-70% reduction compared to the aligned case. Such a lateral shift effect is found to be sensitive to the geometric factor d/D (separation distance to grating period ratio). When d/D>1 (realized through large separation or small grating period), the two graphene gratings see each other as an effective whole rather than in detail, and thus the lateral shift effect on heat transfer becomes less important. Therefore, we can clearly distinguish two asymptotic regimes for radiative heat transfer: the LSE (Lateral Shift Effect) regime, where a significant lateral shift effect is observed, and the non-LSE regime, where this effect is negligible. Furthermore, regardless of the lateral shift, the radiative heat flux shows a non-monotonic dependence on the graphene chemical potential. That is, we can get an optimal radiative heat flux (peaking at about 0.3eV chemical potential) by in situ modulating the chemical potential. This work has the potential to unveil new avenues for harnessing the lateral shift effect on radiative heat transfer in graphene-based nanodevices.

We investigate a bi-layer scheme for circularly polarized infrared thermal radiation. Our approach takes advantage of the strong anisotropy of low-symmetry materials such as β-Ga2O$_3$ and α-MoO$_3$. We numerically report narrow-band, high degree of circular polarization (over 0.85), thermal radiation at two typical emission frequencies related to the excitation of β-Ga$_2$O$_3$ optical phonons. Optimization of the degree of circular polarization is achieved by a proper relative tilt of the crystal axes between the two layers. Our simple but effective scheme could set the basis for a new class of lithography-free thermal sources for IR bio-sensing.

Time-translation symmetry breaking is a mechanism for the emergence of non-stationary many-body phases, so-called time-crystals, in Markovian open quantum systems. Dynamical aspects of time-crystals have been extensively explored over the recent years. However, much less is known about their thermodynamic properties, also due to the intrinsic nonequilibrium nature of these phases. Here, we consider the paradigmatic boundary time-crystal system, in a finite-temperature environment, and demonstrate the persistence of the time-crystalline phase at any temperature. Furthermore, we analyze thermodynamic aspects of the model investigating, in particular, heat currents, power exchange and irreversible entropy production. Our work sheds light on the thermodynamic cost of sustaining nonequilibrium time-crystalline phases and provides a framework for characterizing time-crystals as possible resources for, e.g. quantum sensing. Our results may be verified in experiments, for example with trapped ions or superconducting circuits, since we connect thermodynamic quantities with mean value and covariance of collective (magnetization) operators.