Tunnelling and switching phenomena in superconducting quantum dots and Josephson junctions

This work is devoted to investigation of tunnelling and switching phenomena arising in Condensed Matter Physics. In the first part I investigate quantum tunnelling of a single Abrikosov vortex in a superconducting quantum dot. The escape of a vortex carrying magnetic flux leads to a switching of a quantum dot to non-magnetic state. Tunnelling of a vortex manifests itself as a spontaneous relaxation of magnetization. I showed that it is possible to use an instanton technique based on path integral formalism even in presence of forces breaking time-reversal symmetry. [Continues.

Three-particle states and brightening of intervalley excitons in a doped MoS2_2 monolayer

Optical spectra of two-dimensional transition-metal dichalcogenides (TMDC) are influenced by complex multi-particle excitonic states. Their theoretical analysis requires solving the many-body problem, which in most cases, is prohibitively complicated. In this work, we calculate the optical spectra by exact diagonalization of the three-particle Hamiltonian within the Tamm-Dancoff approximation where the doping effects are accounted for via the Pauli blocking mechanism, modelled by a discretized mesh in the momentum space. The single-particle basis is extracted from the {\it ab initio} calculations. Obtained three-particle eigenstates and the corresponding transition dipole matrix elements are used to calculate the linear absorption spectra as a function of the doping level. Results for negatively doped MoS$_2$ monolayer (ML) are in an excellent quantitative agreement with the available experimental data, validating our approach. The results predict additional spectral features due to the intervalley exciton that is optically dark in an undoped ML but is brightened by the doping. Our approach can be applied to a plethora of other atomically thin semiconductors, where the doping induced brightening of the many-particle states is also anticipated

Nonlinear gap modes and compactons in a lattice model for spin-orbit coupled exciton-polaritons in zigzag chains

We consider a system of generalized coupled Discrete Nonlinear Schr\"{o}dinger (DNLS) equations, derived as a tight-binding model from the Gross-Pitaevskii-type equations describing a zigzag chain of weakly coupled condensates of exciton-polaritons with spin-orbit (TE-TM) coupling. We focus on the simplest case when the angles for the links in the zigzag chain are $\pm \pi/4$ with respect to the chain axis, and the basis (Wannier) functions are cylindrically symmetric (zero orbital angular momenta). We analyze the properties of the fundamental nonlinear localized solutions, with particular interest in the discrete gap solitons appearing due to the simultaneous presence of spin-orbit coupling and zigzag geometry, opening a gap in the linear dispersion relation. In particular, their linear stability is analyzed. We also find that the linear dispersion relation becomes exactly flat at particular parameter values, and obtain corresponding compact solutions localized on two neighboring sites, with spin-up and spin-down parts $\pi/2$ out of phase at each site. The continuation of these compact modes into exponentially decaying gap modes for generic parameter values is studied numerically, and regions of stability are found to exist in the lower or upper half of the gap, depending on the type of gap modes.Comment: 18 pages, 11 figures. Revised version with minor additions to text and reference list. To be published in Journal of Physics Communication

Electrostatic and Environmental Control of the Trion Fine Structure in Transition Metal Dichalcogenide Monolayers

Charged excitons or trions are essential for optical spectra in low-dimensional doped monolayers (ML) of transitional metal dichalcogenides (TMDC). Using a direct diagonalization of the three-body Hamiltonian, we calculate the low-lying trion states in four types of TMDC MLs as a function of doping and dielectric environment. We show that the fine structure of the trion is the result of the interplay between the spin-valley fine structure of the single-particle bands and the exchange interaction. We demonstrate that by variations of the doping and dielectric environment, the fine structure of the trion energy can be tuned, leading to anticrossing of the bright and dark states, with substantial implications for the optical spectra of the TMDC ML

Nonlinear spectroscopy of excitonic states in transition metal dichalcogenides

Second-harmonic generation (SHG) is a well-known nonlinear spectroscopy method to probe electronic structure, specifically, in transition metal dichalcogenide (TMDC) monolayers. This work investigates the nonlinear dynamics of a strongly excited TMDC monolayer by solving the time evolution equations for the density matrix. It is shown that the presence of excitons qualitatively changes the nonlinear dynamics leading, in particular, to a huge enhancement of the nonlinear signal as a function of the dielectric environment. It is also shown that the SHG polarization angular diagram and its dependence on the driving strength are very sensitive to the type of exciton state. This sensitivity suggests that SHG spectroscopy is a convenient tool for analyzing the fine structure of excitonic states.Comment: 13 pages, 5 figure

Hybrid surface waves in two-dimensional Rashba-Dresselhaus materials

We address the electromagnetic properties of two-dimensional electron gas confined by a dielectric environment in the presence of both Rashba and Dresselhaus spin-orbit interactions. It is demonstrated that off-diagonal components of the conductivity tensor resulting from a delicate interplay between Rashba and Dresselhaus couplings lead to the hybridization of transverse electric and transverse magnetic surface electromagnetic modes localized at the interface. We show that the characteristics of these hybrid surface waves can be controlled by additional intense external off-resonant coherent pumping.MOE (Min. of Education, S’pore)Published versio