Microscopic theory of the linear and nonlinear optical properties of TMDCs

Since the discovery of graphene, the research interest in two-dimensional materials has drastically increased. Among them, semiconducting transition-metal dichalcogenides promise great potential for future applications in optoelectronics and photonics as they combine atomic-scale thickness with pronounced light-matter coupling and sizable band gaps in the visible to near-infrared range. In this context, a quantitative and predictive description of the optical properties is of great importance. For the results summarized in this thesis, a self-consistent scheme was established to provide such a quantitative and predictive description for various semiconducting transition-metal dichalcogenide systems in the vicinity of the K/K' points. The theoretical framework combines an anisotropic dielectric model for the Coulomb potential in layered materials with gap equations for the ground-state renormalization, Dirac-Wannier equation to determine the excitonic properties, and Dirac-Bloch equations to access linear and nonlinear optical properties. The latter are formally equivalent to the semiconductor Bloch equations, that have proven to be reliable to compute the optical properties of various semiconductor systems for many years. Detailed differences arise from the relativistic framework, the massive Dirac Fermion model, that applies to transition-metal dichalcogenides. To account for the finite out-of-plane extension of the individual layers, a form factor was introduced in the Coulomb potential. The theoretical framework described above was applied in investigations on the ground-state and excitonic properties of monolayer and homogeneous-multilayer structures. For the case of an unspecified monolayer, the dielectric tuning of the renormalized bands and excitonic resonances was simulated by variation of the Coulomb coupling showing characteristics that are observed in experiments on real monolayer systems. Encouraged by the initial results, realistic monolayers were considered, i.e. MoS2, MoSe2, WS2, WSe2, whose material parameters were taken from external density-functional-theory calculations. The procedure to determine the effective-thickness parameter, entering the form factor to account for finite-thickness effects, was illustrated for a SiO2-supported MoS2 monolayer. Once this parameter was fixed for a given material, the advantage of this approach was demonstrated for MoS2, again, by predicting the K/K'-point interband transition energies and excitonic resonances for various dielectric environments and layer numbers, including the bulk limit. Comparisons to experimental findings and similar theoretical approaches were drawn for all of the stated material systems yielding almost excellent overall agreement. In particular, the results suggest a reinterpretation of the bulk exciton series of MoS 2 as a combined two-dimensional intra- and interlayer exciton series. The results strongly indicate that the applied approach captures the essential physics around the K/K' points. Stacking two materials with different band gaps adds a new element to the band-gap engineering of transition-metal dichalcogenides. Heterostructures such as bilayers WSe2/MoS2 and WSe2 /MoSe2 display type-II band alignment enabling highly efficient charge transfer which is promising for applications in photovoltaics. In a theoretical study on the stated bilayer systems, it was demonstrated that the established theoretical framework could also be applied to investigate intra- and interlayer excitons in transition-metal dichalcogenide heterostructures. For this purpose the anisotropic dielectric model for the Coulomb potential was adjusted to the hetero-bilayer environment. Based on the material parameters provided by internal density-functional-theory calculations, linear optical absorption spectra were computed revealing tightly bound interlayer excitons with binding energies comparable to those of the intralayer excitons. Computing the oscillator strength of the respective resonances yielded relatively long ratiative lifetimes for the interlayer excitons, two orders of magnitude larger than that of the intralayer excitons. The artificial strain in WSe2/MoS2 bilayer resulted in heavily misaligned spectra which is why theory-experiment comparisons were avoided for this system. For the rather unstrained WSe2/MoSe2 bilayer, intra- and interlayer excitonic resonances as well as the ratio of the intra- and interlayer exciton lifetimes compared reasonably well to experimental and theoretical findings. Among the semiconducting transition-metal dichalcogenides, monolayer MoS2 has drawn the most attention from researchers, not least because it was the first representative that displayed experimental evidence of a direct band gap. Combining the direct band gap with pronounced light-matter coupling, monolayer systems hold promise for laser applications on the atomic scale. In this context, the optical properties of suspended and SiO2-supported MoS2 monolayers were investigated in the nonlinear excitation regime for the case of initial thermal charge carriers located in the K/K' valleys. In particular, it was demonstrated that excited carriers lead to an enormous reduction of the band gap. In the range of comparable carrier densities, the computed optical spectra, excitation-induced band-gap renormalization and exciton binding energies were found to be in good agreement with earlier theoretical investigations on MoS2 , as was the predicted Mott-density. For densities beyond the Mott-transition, broadband plasma-induced optical gain energetically below the exciton resonance was observed, which has yet to be realized in experimental setups. Besides the canonical representatives discussed so far, the optical properties of a SiO2-supported MoTe2 monolayer were studied. This material system became of particular interest since room- temperature lasing had already been observed. A numerical experiment in the nonlinear excitation regime was performed. In particular, excitation conditions for achieving plasma gain in MoTe2 monolayers were identified. Within the scope of this investigation, the theoretical framework was extended beyond the quasiequilibrium regime by including Boltzmann-like carrier- and phonon-scattering rates. Whereas a Markovian treatment was sufficient within the simulation of the K/K'-point carrier-relaxation dynamics, the excitation-induced dephasing of the microscopic polarizations was treated dynamically in order to avoid unphysical behavior within the optical spectra. It was demonstrated that pump-injected charge carriers induce a huge reduction of the band gap on the timescale of the optical pulse. This observation including the magnitude of the band-gap renormalization compared well with experimental findings on monolayer MoS2 . Probing the strongly excited system at distinct time delays yielded ultrafast gain build-up on a few-picosecond timescale as a result of efficient carrier thermalization. Allowing the carriers to equilibriate within the entire Billouin zone, even larger output was predicted. This numerical experiment represents the first study proposing monolayer MoTe2 as a promising candidate to achieve plasma-induced optical gain

Direct current superconducting quantum interferometers with asymmetric shunt resistors

We have investigated asymmetrically shunted Nb/Al-AlO$_x$/Nb direct current (dc) superconducting quantum interference devices (SQUIDs). While keeping the total resistance $R$ identical to a comparable symmetric SQUID with $R^{-1} = R_1^{-1} + R_2^{-1}$, we shunted only one of the two Josephson junctions with $R = R_{1,2}/2$. Simulations predict that the optimum energy resolution $\epsilon$ and thus also the noise performance of such an asymmetric SQUID can be 3--4 times better than that of its symmetric counterpart. Experiments at a temperature of 4.2\,K yielded $\epsilon \approx 32\,\hbar$ for an asymmetric SQUID with an inductance of $22\,\rm{pH}$. For a comparable symmetric device $\epsilon = 110\,\hbar$ was achieved, confirming our simulation results.Comment: 5 pages, 4 figure

Ultrafast band-gap renormalization and build-up of optical gain in monolayer MoTe2_2

The dynamics of band-gap renormalization and gain build-up in monolayer MoTe$_2$ is investigated by evaluating the non-equilibrium Dirac-Bloch equations with the incoherent carrier-carrier and carrier-phonon scattering treated via quantum-Boltzmann type scattering equations. For the case where an approximately $300$ fs-long high intensity optical pulse generates charge-carrier densities in the gain regime, the strong Coulomb coupling leads to a relaxation of excited carriers on a few fs time scale. The pump-pulse generation of excited carriers induces a large band-gap renormalization during the time scale of the pulse. Efficient phonon coupling leads to a subsequent carrier thermalization within a few ps, which defines the time scale for the optical gain build-up energetically close to the low-density exciton resonance.Comment: This is a post-peer-review version of an article published in Physical Review

Spectroscopy of a fractional Josephson vortex molecule

In long Josephson junctions with multiple discontinuities of the Josephson phase, fractional vortex molecules are spontaneously formed. At each discontinuity point a fractional Josephson vortex carrying a magnetic flux $|\Phi|<\Phi_0$, $\Phi_0\approx 2.07\times 10^{-15}$ Wb being the magnetic flux quantum, is pinned. Each vortex has an oscillatory eigenmode with a frequency that depends on $\Phi/\Phi_0$ and lies inside the plasma gap. We experimentally investigate the dependence of the eigenfrequencies of a two-vortex molecule on the distance between the vortices, on their topological charge $\wp=2\pi\Phi/\Phi_0$ and on the bias current $\gamma$ applied to the Josephson junction. We find that with decreasing distance between vortices, a splitting of the eigenfrequencies occurs, that corresponds to the emergence of collective oscillatory modes of both vortices. We use a resonant microwave spectroscopy technique and find good agreement between experimental results and theoretical predictions.Comment: submitted to Phys. Rev.

Superconducting Multilayer Technology for Josephson Devices : Technology, Engineering, Physics, Applications

Within this book fabrication processes for high-quality Josephson junctions based on niobium and aluminum oxide as well as niobium nitride and aluminum nitride on various substrates are discussed. Techniques for achieving a planar chip topography and sub-µm lateral dimensions, aiding the realization of sophisticated Josephson devices such as SQUIDs, flux-flow oscillators and long Josephson junctions with artificial phase discontinuities, are presented in detail

Carrier dynamics in TMDCs for optical applications

Fully microscopic many-body models based on the Dirac-Bloch equations and quantum-Boltzmann type scattering equations are used to study the carrier dynamics in monolayer transition metal dichalcogenides (TMDCs) under conditions as typical for applications as lasers, diodes or saturable absorbers. The carrier-carrier scattering is shown to be happening on an ultra-fast few-femtosecond timescale for excitations high above the bandgap. Once the carriers have relaxed into quasi-equilibrium distributions near the bandgap, the scattering is slowed dramatically by phase-space filling and screening of the Coulomb interaction. Here, the scatterings and resulting dephasing of the optical polarizations happen on a 100fs timescale and lead to similar broadenings as found in conventional III-V semiconductor materials. Also like the case in III-V materials, the carrier phonon scattering times are found to be in the picosecond range. The scatterings are shown to allow for gain spectra as needed for good lasing operation. It is shown that the weak interaction between the two bands associated with the two different sub-lattices can potentially allow for simultaneous lasing at two different frequencies. Strong absorption and ultrafast carrier relaxation could allow for TMDCs to be used in saturable absorption applications.Air Force Office of Scientific Research [FA9550-17-1-0246]This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Aluminum Hard Mask Technique for the Fabrication of High-Quality Submicron Nb/Al-AlOx/Nb Josephson Junctions

We have developed a combined photolithography and electron-beam lithography fabrication process for sub-\mum to \mum-size Nb/Al-AlOx/Nb Josephson junctions. In order to define the junction size and protect its top electrode during anodic oxidation, we developed and used the new concept of an aluminum hard mask. Josephson junctions of sizes down to 0.5 \mum2 have been fabricated and thoroughly characterized. We found that they have a very high quality, which is witnessed by the IV curves with quality parameters Vm > 50 mV and Vgap = 2.8 mV at 4.2 K, as well as IcRN products of 1.75-1.93 mV obtained at lower temperatures. In order to test the usability of our fabrication process for superconducting quantum bits, we have also designed, fabricated and experimentally investigated phase qubits made of these junctions. We found a relaxation time of T1 = 26 ns and a dephasing time of T2 = 21 ns