Molecular-Orbital Superconductivity In Alkali Chromium Arsenides

Correlated electron systems is among the most exciting area in condensed matter physics since they tend to exhibit a plenty of interesting phenomena and novel quantum states at low temperatures. The delicate interplay between elec-tron correlation and dimensionality, however, has remaind as a long-standing the-oretical challenge in understanding the basic physics in those correlated systems with low dimensionality and complicated crystalline structures. In this thesis, we develop a theoretical framework for the description of electron correlation and low-dimensionality in a complex molecular orbital system, the newly discovered alkali chromium arsenides A2Cr3As3(A=K,Rb,Cs) showing unconventional super-conductivity and various correlation effects. We shall investigate the influence of various electron correlations on the unconventional superconductivity and other possible candidate quantum groundstates in this class of quasi-one-dimensional (Q1D) inorganic crystals of superconducting materials.The materials.A2Cr3As3 have a double-wall nanotube structure [Cr3As3]2∞ in common. Electron correlation effect arises mainly due to the 3d orbitals of Cr atoms. In this Q1D structure, each unit cell-the [Cr6As6] molecular- contains six Cr atoms, and, each Cr atom has five local 3d electron orbitals which may be partially filled and thus contribute to the electronic band structure near the Fermi energy. Hence as far as various correlation effects are concerned, there are totally thirty molecular orbitals involved in each unit cell, or thirty molecular or-bital bands for the crystalline materials. While only those across the Fermi energy are relevant to the low temperature physics, the characterization of the relevant molecular orbital bands, decisive to the correlation effect but not as straightfor-ward as atomic 3d-orbitals, is of crucial importance for a microscopic theory. As a comparison, there is only Cu atom in the unit cell of the well-known super-conducting copper oxides. For the iron-based superconducting materials such as iron pnictides. although there are two Fe atoms in a conventional unite cell, the further simplified primary unit cell has still one Fe atom owing to the underlying crystalline symmetry. This means that in distinct to the atomic orbital super-conductors, including the copper oxides and iron pnictides, the newly discovered alkali chromium arsenides are genuine molecular orbital superconductors. In this sense, the applicability of the conventional theoretical approach to the atomic or-bital systems is in question to the molecular orbital systems represented by the alkali chromium arsenides.In order to study the electron correlation effect in the alkali chromium ar-senides A2Cr3As3, we propose to study the electronic structure of the genuine Q1D CrAs tube from the microscopic framework instead of the phenomenological one. The CrAs tube is then modeled by a twisted Hubbard lattice model involving various short-range electron interactions of the 3d electrons. The model is able to faithfully depict all the thirty molecular orbitals of the CrAs tube. For con-creteness, we shall focus on the superconducting compound K2Cr3As3. Based on a combinational use of the exact diagonalization of non-interacting tight-binding model, the first principle calculations of band strctures, as well as the renormaliza-tion and bosonization techniques, we shall eventually establish an universal theory of the Luttinger liquid for the low-energy elementary excitations of the relevant molecular orbital bands cross the Fermi energy. Our main results are summarized as follows:(1) Under the assumption of quasi-degenerate atomic orbitals in the CrAs tubes, the tight-binding part of the Hubbard model can be exactly solved based on the symmetry argument, resulting in all thirty molecular orbital bands in the non-interacting limit. Each molecular orbital band is characterized by a set of conserved quantum numbers and the corresponding band energy is obtained ex-plicitly;(2) By fitting the band structures of K2Cr3As3 obtained by first-principles calculations based on the density-functional theory (DFT), the conserved quan-tum numbers of the three molecular orbital bands intersecting the Fermi surface are successfully identified. This allows to further deduce various short-ranged Coulomb interactions and Hund’s coupling among these molecules orbital bands. Compared to the original atomic interactions, the deduced local interactions are significantly suppressed due to the formation of the molecular orbital bands;(3) By utilizing the perturbative renormalization group and bosonization technique, the effective three channel Luttinger liquid Hamiltonian capturing the low-energy excitations of the relevant molecular orbital bands is derived. The three diagonal channels involved in this Luttinger theory are the superpositions of the original three DFT molecular orbital bands;(4) The ground state phase diagram of the three-channel Luttinger liquid Hamiltonian is figured out, exhibiting various interaction-induced instabilities such as spin-triplet superconductivity, spin-density-wave, and charge-density-wave in-stabilities. In particular, when the Hund’s coupling is weaker than the Coulomb interaction in the original atomic 3d orbitals, the spin excitations of all three Lut-tinger channels are gapless and the spin-triplet superconducting instability will be dominanting.Our results presented above imply that the spin triplet superconducting in-stability can emerge out even in a single Q1D CrAs nanotube owing to the deli-cate interplay of various local interactions. Then, the existing intertube couplings in realistic materials, though much weaker than the intratube interactions, can further stabilize the spin-triplet long-range superconducting order. Our theory successfully explains the concurrence of the possible spin triplet pairing in the superconducting state and the Luttinger liquid behavior in the normal state, and is so far consistent with most experiments on K2Cr3As3. In addition, several straightforward extensions and inferences for the material Rb2Cr3As3, the Q1D-3D dimensional crossover, etc., are also briefly discussed. To our best knowledge, the present theory provides the first successful route to the correlation effect of molecular orbital bands from the microscopic local atomic orbitals. Our approach shall be applicable to a wide class of more complicated molecular crystalline mate-rials with moderately strong electron correlations due to the Coulomb interaction and Hund’s coupling of the local atomic orbitals.Remark:The main results presented in this thesis come from a published work in the group of my superadvisor:Hanting Zhong, Xiao-Yong Feng, Hua Chen, and Jianhui Dai, "Formation of Molecular-Orbital Bands in a Twisted Hubbard Tube: Implications for Unconventional Superconductivity in K2Cr3As3", Phys. Rev. Lett.115.227001 (2015).