First-principle study of various quantum states in two-dimensional electron systems

Abstract

In the low-dimensional electron system, interesting quantum states such as charge density wave, superconductivity, magnetism, and Mott insulator appear due to the spatial confinement of electrons. In particular, the semiconductor surfaces have been representative examples for studying various quantum states occurring in a low-dimensional electron systems because various exotic phenomena can be realized by controlling the adsorbed substances and the type of the surfaces. In addition, the transition metal dichalcogenides having layered structure can be easily peeled into a mono- or multi-layer structure due to very weak interaction between layers, and many studies have been conducted as a platform to realize a two-dimensional electron system. Moreover, recently discovered two-dimensional electrides have attracted much attention having the potential to be used as new electronic materials.

Firstly, I studied the origin of insulating ground state of triangular Sn atomic lattice on silicon carbide (SiC) (0001) surface. It is known that this system exhibits an insulating ground state at low temperature. In general, the Mott insulating mechanism has been adopted in which dangling bond electrons are localized to the Sn atoms and feel strong on-site Coulomb interaction between electrons to become an insulator. However, through the systematic density functional theory study, it is confirmed that the dangling bond electrons are not localized only to the Sn atoms and they are highly hybridized with the SiC surface, which is different from the previously proposed Mott insulator model. Due to the hybridization between the Sn atom and the surface, super-exchange interaction between neighboring Sn atom can be facilitated. In this study, using density functional theory, it is found that this system with a narrow half-filled band has an antiferromagnetic insulating phase, which give results similar to the band gap observed in experiment without on-site Coulomb interaction $U$. In addition, according to the Mott insulating mechanism, the spin moment should be localized to the Sn atom, but the density functional theory calculation represents that the spin moment is spread not only on the Sn atom but also on the SiC surface. Consequently, it is found that the ground state of this system can be interpreted as a Slater insulator in which a band gap is formed by long-range antiferromagnetic order.

Secondly, I studied the origin of the charge density wave and metal-insulator transition of monolayer TaS$_2$. The charge density wave refers to the periodic modulation of electron density, the origin of such phenomenon has been controversial in modern condensed matter physics. The formation of charge density waves has been interpreted as a result of the Peierls instability caused by Fermi surface nesting in electronic structure. However, in a real material such as a transition metal dichalcogenide, which is a typical low-dimensional material, there is no perfect Fermi surface nesting. To explain this, a strong momentum dependent electron-phonon interaction mechanism has been proposed as an alternative description of formation of charge density waves. However, strong momentum dependent electron-phonon interaction mechanism is a phenomenological interpretation, and the detailed mechanism has not been established. Interestingly, the transition metal dichalcogenide TaS$_2$ has charge density wave so-called David star and insulating ground state simultaneously. As a result of this study, it is found that spontaneous lattice distortion in TaS$_2$ is due to the formation of quasi-molecular orbitals. Also, due to the formation of quasi-molecular orbitals, the electron exists around the David star, and these localized electron has a flat band in electronic structure. In this case, the Stoner instability occurs and the ferromagnetic state becomes stable. To confirm the origin of insulating ground state, I estimate the exchange interaction between the David stars. It is confirm that the exchange interaction is very small, and as a result, this charge density wave and ferromagnetic insulating state of TaS$_2$ can be interpreted as a Mott insulator.

Finally, it is found that a stacking-sequence independent electronic structures in the two-dimensional electride Ca$_2$N bilayer and bulk structure. The electride is a compound which has electrons, named as interstitial electrons, in a space between the ions inside the crystal. The electride has a low electron binding energy, so it shows a low work function and high electron transfer characteristics. The electronic structure without change by stacking-sequence shows that the interstitial electrons uniformly distributed between the [Ca$_2$N]$^+$ cation layers completely screening the electrostatic interaction between cationic layers. In addition, I also find that the energy barrier required for the lateral layer shift in the bilayer Ca$_2$N is very low, comparable with bilayer graphene, due to the perfect screening of interstitial electrons. In order to confirm the change in the interlayer interaction by the additional electrons, the binding energy of the bulk Ca$_2$N is calculated as function of the additional electrons. As a result, it is found that the binding energy of the bulk decreases linearly with the additional electron doping concentration, which can be easily made into a mono-, bi-, or multi-layer film through the shear exfoliation process with additional electron doping.