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Using first-principles calculations and group-theory based models, we study the stabilization of ferrielectricity (FiE) in CuInP$_2$Se$_6$. We find that the FiE ground state is stabilized by a large anharmonic coupling between the polar mode and a fully symmetric Raman-active mode. Our results open possibilities for controlling the single-step switching barrier for polarization by tuning the Raman-active mode. We discuss the implications of our findings in the context of designing next-generation optoelectronic devices that can overcome the voltage-time dilemma.

Transition-metal dichalcogenides containing tellurium anions show remarkable charge-lattice modulated structures and prominent interlayer character. Using cryogenic scanning transmission electron microscopy (STEM), we map the atomic-scale structures of the high temperature (HT) and low temperature (LT) modulated phases in 1T'-TaTe$_{2}$. At HT, we directly show in-plane metal distortions which form trimerized clusters and staggered, three-layer stacking. In the LT phase at 93 K, we visualize an additional trimerization of Ta sites and subtle distortions of Te sites by extracting structural information from contrast modulations in plan-view STEM data. Coupled with density functional theory calculations and image simulations, this approach opens the door for atomic-scale visualizations of low temperature phase transitions and complex displacements in a variety of layered systems.

One of the goals in making better devices is to achieve the desired functionality in materials that enable a given application. The strong link between the functional behavior and the physical properties of materials is key to making better devices. This thesis focuses on applications of density functional theory (DFT), a powerful computational tool, for understanding the electronic, magnetic, magneto-optic, topological and thermodynamic properties of two-dimensional electronic systems (2DES). Why are 2DES interesting? Firstly, the reduced dimensionality renders these materials with properties which could be absent in the bulk form. Secondly, from a technological point of view, the desired functionality can be easily controlled externally in these 2DES by the application of a gate voltage or strain. The 2DES considered here could be crucial in beyond-CMOS electronic technologies. The materials considered in this thesis can be broadly categorized into two different classes of systems. The first one is the two-dimensional electron gas observed at the complex oxide interfaces. The discussion will go into the details of the formation of 2DEG in oxides resulting both from polar catastrophe and also due to the presence of vacancies. The second class of materials is two-dimensional (2D) atomic crystals, more specifically, 2D magnets. We not only predict a class of compounds, transition metal trichalcogenides (TMTC), that can exhibit magnetism in the 2D limit, but also demonstrate control of these magnetic degrees of freedom. Finally, we also demonstrate both using symmetry based tight-binding models and first-principles calculations a new way to detect magnetism in the 2D limit, which is applicable to compounds other than TMTC as well.

The electronic structure of SrTiO3(001) surfaces was studied using scanning tunneling spectroscopy and density-functional theory. With high dynamic range measurements, an in-gap transition level was observed on SrO-terminated surfaces, at 2.7 eV above the valence band maximum. The density of centers responsible for this level was found to increase with surface segregation of oxygen vacancies and decrease with exposure to molecular oxygen. Based on these finding, the level is attributed to surface O vacancies. A level at a similar energy is predicted theoretically on SrO-terminated surfaces. For TiO2-terminated surfaces, no discrete ingap state was observed, although one is predicted theoretically. This lack of signal is believed to be due to the nature of defect wavefunction involved, as well as the possible influence of transport limitations in the tunneling spectroscopy measurements.

The electronic structure of SrTiO3(001) surfaces was studied using scanning tunneling spectroscopy and density-functional theory. With high dynamic range measurements, an in-gap transition level was observed on SrO-terminated surfaces, at 2.7 eV above the valence band maximum. The density of centers responsible for this level was found to increase with surface segregation of oxygen vacancies and decrease with exposure to molecular oxygen. Based on these finding, the level is attributed to surface O vacancies. A level at a similar energy is predicted theoretically on SrO-terminated surfaces. For TiO2-terminated surfaces, no discrete in-gap state was observed, although one is predicted theoretically. This lack of signal is believed to be due to the nature of defect wavefunction involved, as well as the possible influence of transport limitations in the tunneling spectroscopy measurements., Comment: 17 pages, 8 figures

Layered transition-metal trichalcogenides with the chemical formula ABX3have attracted recent interest as potential candidates for two-dimensional magnets. Using first-principles calculations within density functional theory, we investigate the magnetic ground states of monolayers of Mn- and Cr-based semiconducting trichalcogenides. We show that the second and third nearest-neighbor exchange interactions (J2 and J3) between magnetic ions, which have been largely overlooked in previous theoretical studies, are crucial in determining the magnetic ground state. Specifically, we find that monolayer CrSiTe3 is an antiferromagnet with a zigzag spin texture due to significant contribution from J3, whereas CrGeTe3 is a ferromagnet with a Curie temperature of 106 K. Monolayers of Mn compounds (MnPS3 and MnPSe3) always show antiferromagnetic Néel order. We identify the physical origin of various exchange interactions, and demonstrate that strain can be an effective knob for tuning the magnetic properties. Possible magnetic ordering in the bulk is also discussed. Our study suggests that ABX3 can be a promising platform to explore two-dimensional magnetic phenomena.

Layered transition-metal trichalcogenides with the chemical formula ABX3have attracted recent interest as potential candidates for two-dimensional magnets. Using first-principles calculations within density functional theory, we investigate the magnetic ground states of monolayers of Mn- and Cr-based semiconducting trichalcogenides. We show that the second and third nearest-neighbor exchange interactions (J2 and J3) between magnetic ions, which have been largely overlooked in previous theoretical studies, are crucial in determining the magnetic ground state. Specifically, we find that monolayer CrSiTe3 is an antiferromagnet with a zigzag spin texture due to significant contribution from J3, whereas CrGeTe3 is a ferromagnet with a Curie temperature of 106 K. Monolayers of Mn compounds (MnPS3 and MnPSe3) always show antiferromagnetic Néel order. We identify the physical origin of various exchange interactions, and demonstrate that strain can be an effective knob for tuning the magnetic properties. Possible magnetic ordering in the bulk is also discussed. Our study suggests that ABX3 can be a promising platform to explore two-dimensional magnetic phenomena.