arXiv subjects
Publications and source records attributed to Hideo Aoki.
Peculiarity in the cyclotron radiation and emission in graphene is theoretically examined in terms of the optical conductivity and relaxation rates to propose that graphene in magnetic fields can be a candidate to realize the Landau level laser, proposed decades ago [H. Aoki, Appl. Phys. Lett. {\bf 48}, 559 (1986)].
Phase diagram of the Hubbard-Holstein model in the coexistence of electron-electron and electron-phonon interactions has been theoretically obtained with the density-matrix renormalization group method for one-dimensional (1D) systems, where an improved warm-up (the recursive sweep) procedure has enabled us to calculate various correlation functions. We have examined the cases of (i) the systems half-filled by electrons for the full parameter space spanned by the electron-electron and electron-phonon coupling constants and the phonon frequency, (ii) non-half-filled system, and (iii) trestle lattice. For (i), we have detected a region where both the charge and on-site pairing correlations decay with power-laws in real space, which suggests a metallic behavior. While pairing correlations are not dominant in (i), we have found that they become dominant as the system is doped in (ii), or as the electronic band structure is modified (with a broken electron-hole symmetry) in (iii) in certain parameter regions.
In order to resolve the long-standing issue of how the itinerant ferromagnetism is affected by the lattice structure and Hund's coupling, we have compared various three-dimensional lattice structures in the single- and multiorbital Hubbard models with the dynamical mean-field theory with an improved quantum Monte Carlo algorithm that preserves the spin-SU(2) symmetry. The result indicates that {\it both} the lattice structure and the d-orbital degeneracy are essential for the ferromagnetism in the parameter region representing a transition metal. Specifically, (a) Hund's coupling, despite the common belief, is important, which is here identified to come from particle-hole scatterings, and (b) the ferromagnetism is a correlation effect (outside the Stoner picture) as indicated from the band-filling dependence.
The nonequilibrium Green's function method is used to study the ballistic transport in metallic carbon nanotubes when a current is injected from the electrodes with finite bias voltages. We reveal, both analytically and numerically, that large loop currents circulating around the tube are induced, which come from a quantum mechanical interference and are much larger than the current along the tube axis when the injected electron is resonant with a time-reversed pair of degenerate states, which are, in fact, inherent in the zigzag and chiral nanotubes. This results in large orbital magnetic moments, making the nanotube a molecular solenoid.
We propose to combine the Trotter decomposition and a series expansion of the partition function for Hund's exchange coupling in a quantum Monte Carlo (QMC) algorithm for multiorbital systems that preserves spin and orbital rotational symmetries. This enables us to treat the Hund's (spin-flip and pair-hopping) terms, which is difficult in the conventional QMC method. To demonstrate this, we first apply the algorithm to study ferromagnetism in the two-orbital Hubbard model within the dynamical mean-field theory (DMFT). The result reveals that the preservation of the SU(2) symmetry in Hund's exchange is important, where the Curie temperature is grossly overestimated when the symmetry is degraded, as is often done, to Ising (Z$_2$). We then calculate the $t_{2g}$ spectral functions of Sr$_2$RuO$_4$ by a three-band DMFT calculation with tight-binding parameters taken from the local density approximation with proper rotational symmetry.
Density-matrix renormalization group is used to study the pairing when both of electron-electron and electron-phonon interactions are strong in the Holstein-Hubbard model at half-filling in a region intermediate between the adiabatic (Migdal's) and antiadiabatic limits. We have found: (i) the pairing correlation obtained for a one-dimensional system is nearly degenerate with the CDW correlation in a region where the phonon-induced attraction is comparable with the electron-electron repulsion, but (ii) pairing becomes dominant when we destroy the electron-hole symmetry in a trestle lattice. This provides an instance in which pairing can arise, in a lattice-structure dependent manner, from coexisting electron-electron and electron-phonon interactions.
Non-linear transport of electrons in strong electric fields, as typified by dielectric breakdown, is re-formulated in terms of the ground-state decay rate originally studied by Schwinger in non-linear QED. We discuss the effect of electron interaction on Zener tunneling by comparing the dielectric breakdown of the band insulator and the Mott insulator, where the latter is studied by the time-dependent density-matrix renormalization group (DMRG). The relation with the Berry's phase theory of polarization is also established.
We explore how the superconductivity arising from the on-site electron-electron repulsion will change when the repulsion is changed to a long-ranged, 1/r-like one by introducing an extended Hubbard model with the repulsion extending to distant (12th) neighbors. With a simplified fluctuation-exchange approximation, we have found for the square lattice that (i) as the band filling becomes dilute enough, the charge susceptibility becomes comparable with the spin susceptibility, where p and then s pairings become dominant, in agreement with the result for the electron gas by Takada, while (ii) the d-wave, which reflects the lattice structure, dominates well away from the half filling. All these can be understood in terms of the spin and charge structures along with the shape and size of the Fermi surface.
The pairing symmetry in the electron mechanism for superconductivity is explored when charge fluctuations coexist with spin fluctuations. The extended Hubbard model is adopted to obtain, with the fluctuation exchange approximation, a phase diagram against the on-site Coulomb repulsion U and the off-site repulsion V for the square lattice with second-neighbor hopping t'. We have found that (i) for large U(>9) a triplet superconductivity with a sin(kx+ky) symmetry can appear just below the charge density wave phase. The pairing is degenerate with sin(kx-ky), so a chiral sin(kx+ky)+isin(kx-ky) that breaks the time reversal symmetry should result, which is a candidate for the gap function on the gamma band of Sr2RuO4 and is consistent with a recent measurement of the specific heat. (ii) By systematically deforming the Fermi surface with varied t', we have identified the region where the triplet pairing is most favored to be the region where the Fermi surface traverses the van Hove singularity with the charge susceptibility strongly enhanced.
Time-dependent Schroedinger's equation is integrated for a one-dimensional strongly-correlated electron system driven by large electric fields. For larger electric fields, many-body Landau-Zener tunneling takes place at anti-crossings of the many-body energy levels. The nonlinear $I$-$V$ characteristics as well as the time dependence of the energy expectation value are obtained. The energy of the Mott insulator in electric fields shows a saturation, which suggests a dynamical localization in energy space of many-body wave functions.
Quantum transport properties of electron systems driven by strong electric fields are studied by mapping the Landau-Zener transition dynamics to a quantum walk on a semi-infinite one-dimensional lattice with a reflecting boundary, where the sites correspond to energy levels and the boundary the ground state. Quantum interference induces a distribution localized around the ground state, and when the electric field is strengthened, a delocalization transition occurs describing breakdown of the original electron system.
A Dirac particle in general dimensions moving in a 1/r potential is shown to have an exact N = 2 supersymmetry, for which the two supercharge operators are obtained in terms of (a D-dimensional generalization of) the Johnson-Lippmann operator, an extension of the Runge-Lenz-Pauli vector that relativistically incorporates spin degrees of freedom. So the extra symmetry (S(2))in the quantum Kepler problem, which determines the degeneracy of the levels, is so robust as to accommodate the relativistic case in arbitrary dimensions.
In order to explore how superconductivity arises when charge fluctuations and spin fluctuations coexist, we have obtained a phase diagram against the off-site repulsion V and band filling n for the extended, repulsive Hubbard model on the square lattice with the fluctuation exchange approximation. We have found the existence of (i) a transition between dxy and dx2-y2 pairing symmetries, (ii) f-pairing in between the dx2-y2 and CDW phases for intermediate 0.5 f -> s when V (hence the charge fluctuations) are increased. All these are consequences of the structure in the charge and spin susceptibilities, which have peaks habitating at the common or segregated positions in k space.
We have shown, both experimentally and theoretically, that the metal-induced gap states (MIGS) can exist in epitaxially grown organic insulator/metal interfaces. The experiment is done for alkane/Cu(001) with an element-selective near edge x-ray absorption fine structure (NEXAFS), which exhibits a pre-peak indicative of MIGS. An {\it ab initio} electronic structure calculation supports the existence of the MIGS. When the Cu substrate is replaced with Ni, an interface magnetism (spin-polarized organic crystal at the interface) is predicted to be possible with a carrier doping.
In order to numerically study electron correlation effects in multi-orbital systems, we propose a new type of discrete transformation for the exchange (Hund's coupling) and pair-hopping interactions to be used in the dynamical mean field theory + quantum Monte Carlo method. The transformation, which is real and exact, turns out to suppress the sign problem in a wide parameter region including non-half-filled bands. This enables us to obtain the dominant pairing symmetry in the double-orbital Hubbard model, which shows that the spin-triplet, orbital-antisymmetric pairing that exploits Hund's coupling is stable in a wide region of the band filling.
In order to probe the effect of charge fluctuations on triplet pairing, we study the pairing symmetry in the one-band Hubbard model having the off-site Coulomb repulsion ($V$) on top of the on-site repulsion as a model for the $γ$ band of Sr$_2$RuO$_4$, a strong candidate for triplet pairing superconductor. The result, obtained with the dynamical cluster approximation combined with the quantum Monte-Carlo method, and confirmed from the fluctuation exchange approximation, shows that while $d_{x^2-y^2}$-pairing dominates over $p$ in the absence of $V$, introduction of $V$ makes $p_{x+y}$ and $d_{xy}$ dominant. The gap function for the chiral $p_{x+y}$+i$p_{x-y}$ has nodes that are consistent with the recent measurement of specific heat in rotated magnetic fields in the ruthenate. This suggests that the off-site repulsion may play an essential role in triplet superconductivity in this material.
We propose that one of the best grounds for the materials design from the viewpoint of {\it electron correlation} such as ferromagnetism, superconductivity is the atomically controlled nanostructures and heterointerfaces, as theoretically demonstrated here from three examples with first-principles calculations: (i) Band ferromagnetism in a purely organic polymer of five-membered rings, where the flat-band ferromagnetism due to the electron-electron repulsion is proposed. (ii) Metal-induced gap states (MIGS) of about one atomic monolayer thick at insulator/metal heterointerfaces, recently detected experimentally, for which an exciton-mechanism superconductivity is considered. (iii) Alkali-metal doped zeolite, a class of nanostructured host-guest systems, where ferromagnetism has been experimentally discovered, for which a picture of the "supercrystal" composed of "superatoms" is proposed and Mott-insulator properties are considered. These indicate that design of electron correlation is indeed a promising avenue for nanostructures and heterointerfaces.
A recent report [Kiguchi {\it et al.}, Phys. Rev. B {\bf 68}, 115402 (2003)] that the (111) surface of 5 MgO layers grown epitaxially on Ag(111) becomes metallic to reduce the electric dipole moment raises a question of what will happen when we have fewer MgO layers. Here we have revealed, first experimentally with electron energy-loss spectroscopy, that MgO(111) remains metallic even when one-layer thick, and theoretically with the density functional theory that the metallization should depend on the nature of the substrate. We further show, with a spin-density functional calculation, that a ferromagnetic instability may be expected for thicker films.