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Developing low-power, high-sensitivity photodetectors for the terahertz (THz) band that operate at room temperature is an important challenge in optoelectronics. In this study, we introduce a photo-thermal-electric (PTE) effect detector based on quasi-free standing bilayer graphene (BLG) on a silicon carbide (SiC) substrate, designed for the THz frequency range. Our detector's performance hinges on a quasi-optical coupling scheme, which integrates an aspherical silicon lens, to optimize impedance matching between the THz antenna and the graphene p-n junction. At room temperature, we achieved a noise equivalent power (NEP) of less than 300 $pW/\sqrt{Hz}$. Through an impedance matching analysis, we coupled a planar antenna with a graphene p-n junction, inserted in parallel to the nano-gap of the antenna, via two coupling capacitors. By adjusting the capacitors and the antenna arm length, we tailored the antenna's maximum infrared power absorption to specific frequencies. The sensitivity, spectral properties, and scalability of our material make it an ideal candidate for future development of far-infrared detectors operating at room temperature., Comment: 21 pages, 4 figures

Using ultrafast pump-probe reflectivity with 3.1 eV pump and coherent white light probe (1.1 to 2.6 eV), we show that graphene on gold nanostructures exhibits a strong coupling to the plasmonic resonances of the ordered lattice hole array, thus injecting a high density of hot carriers in graphene through plasmons. The system being studied is single-layer graphene on ultrathin film of gold with periodic arrangements of holes showing anomalous transmission. A comparison is made with gold film with and without hole array. By selectively probing transient carrier dynamics in the spectral regions corresponding to plasmonic resonances, we show efficient plasmon-induced hot carrier generation in graphene. We also show that due to high electromagnetic field intensities at the edge of the sub-micron holes, fast decay time (10-100 fs) and short decay length (1 nm) of plasmons, a highly confined density of hot carriers (very close to edge of the holes) is generated by Landau damping of plasmons within the holey gold film. A contribution to transient decay dynamics due to diffusion of initial non-uniform distribution of hot carriers away from the hole edges is observed. Our results are important for future applications of novel hot carrier device concepts where hot carriers with tunable energy can be generated in different graphene regions connected seamlessly., Comment: 19 pages, 4 figures

The class of layered 3D-topological insulators have shown intriguingly anomalous temperature dependence in their thermal expansion coefficients. It was proposed that stacking faults are the origin of the observed anomalous thermal expansion. Here, using femtosecond pump-probe differential reflectivity measurements we probe the carrier and coherently generated totally symmetric A1g1 optical phonons in Bi2Se3. Transient signals also show a low frequency (~GHz) oscillations due to coherent longitudinal acoustic phonons. We extract temperature dependence of optical constants, sound velocity and Young's modulus of Bi2Se3 using the strain pulse propagation model. A remarkable anomalous behavior around ~180 K is observed in the temperature dependence of optical and acoustic phonons as well as the optical constants. First-principles density functional theory (DFT) reveals that thermally activated formation of stacking faults is responsible for the anomalies observed in Bi2Se3, similar to case of Sb2Te3. We also show that inclusion of spin-orbit coupling plays an important role in reducing the total energy difference between the pristine and the faulted structures., Comment: 18 pages, 6 figures

Carrier dynamics in metallic nanostructures is strongly influenced by their confining dimensions. Gold nanoparticles of size $\sim 2$ nm lie at the boundary separating metallic and non-metallic behavior. In this work, we report carrier dynamics in high aspect ratio ultrathin gold nanowires (Au-UNWs) of average diameter $\sim$2 nm using pump (3.1 eV) and coherent white light continuum as probe in the spectral range of 1.15 eV to 2.75 eV. The transient carrier dynamics in Au-UNWs under extreme excitation regime is slower than predicted by the often used two temperature model. We identify Auger-assisted carrier heating process which slows down the hot carrier cooling dynamics. The rate equation model fitted to the data yields an estimate of Auger coefficient for gold nanostructures., Comment: 15 pages, 4 figures

Besides various asymptotic results on the concept of sum-product bases in $\mathbb{N}_0$, we consider by probabilistic arguments the existence of thin sets $A,A'$ of integers such that $AA+A=\mathbb{N}_0$ and $A'A'+A'A'=\mathbb{N}_0$.

When the sequences of squares of primes is coloured with $K$ colours, where $K \geq 1$ is an integer, let $s(K)$ be the smallest integer such that each sufficiently large integer can be written as a sum of no more than $s(K)$ squares of primes, all of the same colour. We show that $s(K) \ll K \exp\left(\frac{(3\log 2 + {\rm o}(1))\log K}{\log \log K}\right)$ for $K \geq 2$. This improves on $s(K) \ll_{\epsilon} K^{2 +\epsilon}$, which is the best available upper bound for $s(K)$., Comment: 22 pages