arXiv subjects

Hideo Aoki

Publications and source records attributed to Hideo Aoki.

At least 19 recordsLinked to original sources

arXiv2026

Integer quantum Hall effect

Integer quantum Hall effect, which is the Hall effect quantized into integer times $e^2/h$ ($e$: elementary charge, $h$: Planck's constant) observed first in two-dimensional electron gases in strong magnetic fields, is reviewed from both theoretical and experimental standpoints. Basic physics underlying the phenomenon is explained. Specifically in this new edition we have a fresh look at how the quantum Hall effect is captured in a perspective of topological systems, since, while the quantum Hall effect is historically the first realization of the topological systems, the field has been delved into a much wider realm of physics of topological systems. We also mention diverse advances such as the quantum Hall effect (QHE) in various materials and contexts that include graphene, oxides and narrow-gap semiconductors, a relation with the fractional quantum Hall effect, and the quantum Hall effect as the resistance standard and further roles in the new SI system. We also expound the Floquet topological insulator (a light-matter coupled system) as a new paradigm in nonequilibrium topological systems, where an anomalous quantum Hall effect in zero magnetic field is realized as theoretically predicted to occur in graphene illuminated by a circularly-polarized laser and experimentally verified recently.

cond-mat.mes-hall↗

arXiv2025

Flat bands in condensed-matter systems -- perspective for magnetism and superconductivity

There is a recent upsurge of interests in flat bands in condensed-matter systems and the consequences for magnetism and superconductivity. This article highlights the physics, where peculiar quantum-mechanical mechanisms for the physical properties such as flatband ferromagnetism and flatband superconductivity that arise when the band is not trivially flat but has a strange Hilbert space with non-orthogonalisable Wannier states, which goes far beyond just the diverging density of states. Peculiar wavefunctions come from a quantum-mechanical interference and entanglement. Interesting phenomena become even remarkable when many-body interactions are introduced, culminating in flatband superconductivity as well as flatband ferromagnetism. Flatband physics harbours a very wide range physics indeed, extending to non-equilibrium physics in laser illumination, where Floquet states for topologcial superconductivity is promoted in flatbands. While these are theoretically curious, possible candidates for the flatband materials are beginning to emerge, which is also described. These provide a wide and promising outlook.

cond-mat.supr-con↗

arXiv2024

Emergent Fano-Feshbach resonance in two-band superconductors with an incipient quasi-flat band: Enhanced critical temperature evading particle-hole fluctuations

In superconductivity, a surge of interests in enhancing $T_{\rm c}$ is ever mounting, where a recent focus is toward multi-band superconductivity. In $T_{\rm c}$ enhancements specific to two-band cases, especially around the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover considered here, we have to be careful about how quantum fluctuations affect the many-body states, i.e., particle-hole fluctuations suppressing the pairing for attractive interactions. Here we explore how to circumvent the suppression by examining multichannel pairing interactions in two-band systems. With the Gor'kov-Melik-Barkhudarov (GMB) formalism for particle-hole fluctuations in a continuous space, we look into the case of a deep dispersive band accompanied by an incipient heavy-mass (i.e., quasi-flat) band. We find that, while the GMB corrections usually suppress $T_{\rm c}$ significantly, this in fact competes with the enhanced pairing arising from the heavy band, with the trade-off leading to a peaked structure in $T_{\rm c}$ against the band-mass ratio when the heavy band is incipient. The system then plunges into a strong-coupling regime with the GMB screening vastly suppressed. This occurs prominently when the chemical potential approaches the bound state lurking just below the heavy band, which can be viewed as a Fano-Feshbach resonance, with its width governed by the pair-exchange interaction. The diagrammatic structure comprising particle-particle and particle-hole channels is heavily entangled, so that the emergent Fano-Feshbach resonance dominates all the channels, suggesting a universal feature in multiband superconductivity.

cond-mat.supr-con↗

arXiv2023

Nematicity-enhanced superconductivity in systems with a non-Fermi liquid behavior

We explore the interplay between nematicity~(spontaneous breaking of the sixfold rotational symmetry), superconductivity, and non-Fermi liquid behavior in partially flat-band models on the triangular lattice. A key result is that the nematicity (Pomeranchuk instability), which is driven by many-body effect and stronger in flat-band systems, enhances superconducting transition temperature in a systematic manner on the $T_{\rm c}$ dome. There, a $s_{x^2+y^2} - d_{x^2-y^2} - d_{xy}$-wave symmetry, in place of the conventional $d_{x^2-y^2}$-wave, governs the nematicity-enhanced pairing with a sharp rise in the $T_{\rm c}$ dome on the filling axis. When the sixfold symmetry is spontaneously broken, the pairing becomes more compact in real space than in the case when the symmetry is enforced. These are accompanied by a non-Fermi character of electrons in the partially flat bands with many-body interactions.

cond-mat.supr-con↗

arXiv2022

Superconductivity enhanced by pair fluctuations between wide and narrow bands

Full or empty narrow bands near the Fermi level are known to enhance superconductivity by promoting scattering processes and spin fluctuations. Here, we demonstrate that doublon-holon fluctuations in systems with half-filled narrow bands can similarly boost the superconducting $T_c$. We study the half-filled attractive bilayer Hubbard model on the square lattice using dynamical mean-field theory. The band structure of the noninteracting system contains a wide band formed by bonding orbitals and a narrow band formed by antibonding orbitals, with bandwidths tunable by the inter-layer hopping. The shrinking of the narrow band can lead to a substantial increase in the superconducting order parameter and phase stiffness in the wide band. At the same time, the coupling to the wide band allows the narrow band to remain superconducting -- and to reach the largest order parameter -- in the flat band limit. We develop an anomalous worm sampling method to study superconductivity in the limit of vanishing effective hopping. By analyzing the histogram of the local eigenstates, we clarify how the interplay between different interaction terms in the bonding/antibonding basis promotes pair fluctuations and superconductivity.

cond-mat.supr-con↗

arXiv2022

Floquet topological $d+id$ superconductivity induced by chiral many-body interactions

We study how a $d$-wave superconductivity is changed when illuminated by circularly-polarised light (CPL) in the repulsive Hubbard model in the strong-coupling regime. We adopt the Floquet formalism for the Gutzwiller-projected effective Hamiltonian with the time-periodic Schrieffer-Wolff transformation. We find that CPL induces a topological superconductivity with a $d+id$ pairing, which arises from the chiral spin coupling and the three-site term generated by the CPL. The latter term remains significant even for low frequencies and low intensities of the CPL. This is clearly reflected in the obtained phase diagram against the laser intensity and temperature for various frequencies red-detuned from the Hubbard $U$, with the transient dynamics also examined. The phenomenon revealed here can open a novel, dynamical way to induce a topological superconductivity.

cond-mat.str-el↗

arXiv2021

Resonant pair-exchange scattering and BCS-BEC crossover in a system composed of dispersive and heavy incipient bands: a Feshbach analogy

We theoretically show that a two-band system with very different masses harbors a resonant pair scattering that leads to novel pairing properties, as highlighted by the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover. Most importantly, the interband pair-exchange coupling induces an effective intraband attraction in each band, enhancing the superfluidity/superconductivity. The effect, a kind of Suhl-Kondo mechanism, is specifically enhanced when the second band has a heavy mass and is incipient (lying close to, but just above, the chemical potential, $μ$), which we call a resonant pair scattering. By elucidating the dependence of the effective interactions and gap functions on $μ$, we can draw an analogy between the resonant pair scattering and the Feshbach resonance.

cond-mat.supr-con↗

arXiv2021

Robust Zero Modes in Disordered Two-Dimensional Honeycomb Lattice with Kekulé Bond Ordering

Robustness of zero-modes of two-dimensional Dirac fermions is examined numerically for the honeycomb lattice in the presence of Kekulé bond ordering. The split $n=0$ Landau levels in a magnetic field as well as the zero-modes generated by topological defects in the Kekulé ordering are shown to exhibit anomalous robustness against disorder when the chiral symmetry is respected.

cond-mat.dis-nn↗

arXiv2020

Optical imprinting of superlattices in two-dimensional materials

We propose an optical method of shining circularly polarized and spatially periodic laser fields to imprint superlattice structures in two-dimensional electronic systems. By changing the configuration of the optical field, we synthesize various lattice structures with different spatial symmetry, periodicity, and strength. We find that the wide optical tunability allows one to tune different properties of the effective band structure, including Chern number, energy bandwidths, and band gaps. The in situ tunability of the superlattice gives rise to unique physics ranging from the topological transitions to the creation of the flat bands through the kagome superlattice, which can allow a realization of strongly correlated phenomena in Floquet systems. We consider the high-frequency regime where the electronic system can remain in the quasiequilibrium phase for an extended amount of time. The spatiotemporal reconfigurability of the present scheme opens up possibilities to control light-matter interaction to generate novel electronic states and optoelectronic devices.

cond-mat.mes-hall↗

arXiv2020

Superconducting mechanism for the cuprate Ba$_2$CuO$_{3+δ}$ based on a multiorbital Lieb lattice model

For the recently discovered cuprate superconductor $\mathrm{Ba_{2}CuO_{3+δ}}$, we propose a lattice structure which resembles the model considered by Lieb to represent the vastly oxygen-deficient material. We first investigate the stability of the Lieb-lattice structure, and then construct a multiorbital Hubbard model based on first-principles calculation. By applying the fluctuation-exchange approximation to the model and solving the linearized Eliashberg equation, we show that $s$-wave and $d$-wave pairings closely compete with each other, and, more interestingly, that the intra-orbital and inter-orbital pairings coexist. We further show that, if the energy of the $d_{3z^2-r^2}$ band is raised to make it "incipient" with the lower edge of the band close to the Fermi level within a realistic band filling regime, $s\pm$-wave superconductivity is strongly enhanced. We reveal an intriguing relation between the Lieb model and the two-orbital model for the usual K$_2$NiF$_4$ structure where a close competition between $s-$ and $d-$wave pairings is known to occur. The enhanced superconductivity in the present model is further shown to be related to an enhancement found previously in the bilayer Hubbard model with an incipient band.

cond-mat.supr-con↗

arXiv2020

Theoretical possibilities for flat-band superconductivity

One novel arena for designing superconductors with high $T_C$ is the flat-band systems. A basic idea is that flat bands, arising from quantum mechanical interference, give unique opportunities for enhancing $T_C$ with (i) many pair-scattering channels between the dispersive and flat bands, and (ii) an even more interesting situation when the flat band is topological and highly entangled. Here we compare two routes, which comprise a multi-band system with a flat band coexisting with dispersive ones, and a one-band case with a portion of the band being flat. Superconductivity can be induced in both cases when the flat band or portion is "incipient" (close to, but away from, the Fermi energy). Differences are, for the multi-band case, we can exploit large entanglement associated with topological states, while for the one-band case a transition between different (d and p) wave pairings can arise. These hint at some future directions.

cond-mat.supr-con↗

arXiv2019

Pairing and non-Fermi liquid behavior in partially flat-band systems

While multiband systems are usually considered for flat-band physics, here we study one-band models that have flat portions in the dispersion to explore correlation effects in the 2D repulsive Hubbard model in an intermediate coupling regime. The FLEX+DMFT~(the dynamical mean-field theory combined with the fluctuation exchange approximation) is used to show that we have a crossover from ferromagnetic to antiferromagnetic spin fluctuations as the band filling is varied, which triggers a crossover from triplet to singlet pairings with a peculiar filling dependence that is dominated by the size of the flat region in the dispersion. A curious manifestation of the flat part appears as larger numbers of nodal lines associated with pairs extended in real space. We further detect non-Fermi liquid behavior in the momentum distribution function, frequency dependence of the self-energy and spectral function. These indicate correlation physics peculiar to flat-band systems.

cond-mat.supr-con↗

arXiv2019

Model construction and a possibility of cuprate-like pairing in a new d9 nickelate superconductor (Nd,Sr)NiO2

Effective models are constructed for a newly discovered superconductor (Nd,Sr)NiO2, which has been considered as a possible nickelate analogue of the cuprates owing to the d9 electron configuration. Estimation of the effective interaction, which turns out to require a multiorbital model that takes account of all the orbitals involved on the Fermi surface, shows that the effective interactions are significantly larger than in the cuprates. A fluctuation exchange study for the model indicates that dx2-y2-wave superconductivity is likely to occur as in the cuprates, where the transition temperature in the nickelate can be lower from the cuprates due to the larger interaction and narrower bandwidth.

cond-mat.supr-con↗

arXiv2019

Topologically Protected Doubling of Tilted Dirac Fermions in Two Dimensions

The doubling of massless Dirac fermions on two-dimensional lattices is theoretically studied. It has been shown that the doubling of massless Dirac fermions on a lattice with broken chiral symmetry is topologically protected even when the Dirac cone is tilted. This is due to the generalized chiral symmetry defined for lattice systems, where such models can be generated by a deformation of the chiral-symmetric lattice models. The present paper shows for two-band lattice models that this is a general way to produce systems with the generalized chiral symmetry in that such systems can always be transformed back to a lattice model with the conventional chiral symmetry. We specifically show that the number of zero modes is an invariant of the transformation, leading to the topological protection à la Nielsen-Ninomiya of the doubling of tilted and massless Dirac fermions in two dimensions.

cond-mat.mes-hall↗

arXiv2019

SO(4) FLEX+DMFT formalism with SU(2)$\otimes$SU(2)-symmetric impurity solver for superconductivity in the repulsive Hubbard model

Here we have developed a FLEX+DMFT formalism, where the symmetry properties of the system are incorporated by constructing a SO(4) generalization of the conventional fluctuation-exchange approximation (FLEX) coupled self-consistently to the dynamical mean-field theory (DMFT). Along with this line, we emphasize that the SO(4) symmetry is the lowest group-symmetry that enables us to investigate superconductivity and antiferromagnetism on an equal footing. We have imposed this by decomposing the electron operator into auxiliary fermionic and slave-boson constituents that respect SU(2)$_{\rm spin}\otimes$SU(2)$_{η{\rm spin}}$. This is used not in a mean-field treatment as in the usual slave-boson formalisms, but instead in the DMFT impurity solver with an SU(2)$_{\rm spin}\otimes$SU(2)$_{η{\rm spin}}$ hybridization function to incorporate the FLEX-generated bath information into DMFT iterations. While there have been attempts such as the doublon-less SU(2) slave-boson formalism, the present "full-SU(2)" slave-boson formalism is expected to provide a new platform for addressing the underlying physics for various quantum orders, which compete with each other and can coexist.

cond-mat.supr-con↗

arXiv2019

Why the critical temperature of high-$T_{\rm c}$ cuprate superconductors is so low: The importance of the dynamical vertex structure

To fathom the mechanism of high-temperature ($T_{\rm c}$) superconductivity, the dynamical vertex approximation (D$Γ$A) is evoked for the two-dimensional repulsive Hubbard model. After showing that our results well reproduce the cuprate phase diagram with a reasonable $T_{\rm c}$ and dome structure, we keep track of the scattering processes that primarily affect $T_{\rm c}$. We find that local particle-particle diagrams significantly screen the bare interaction at low frequencies, which in turn suppresses antiferromagnetic spin fluctuations and hence the pairing interaction. Thus we identify dynamical vertex corrections as one of the main oppressors of $T_{\rm c}$, which may provide a hint toward higher $T_{\rm c}$'s.

cond-mat.supr-con↗

arXiv2018

Momentum-dependent relaxation dynamics of the doped repulsive Hubbard model

We study the dynamical behavior of doped electronic systems subject to a global ramp of the repulsive Hubbard interaction. We start with formulating a real-time generalization of the fluctuation-exchange approximation. Implementing this numerically, we investigate the weak-coupling regime of the Hubbard model both in the electron-doped and hole-doped regimes. The results show that both local and nonlocal (momentum-dependent) observables evolve toward a thermal state, although the temperature of the final state depends on the ramp duration and the chemical doping. We further reveal a momentum-dependent relaxation rate of the distribution function in doped systems, and trace back its physical origin to the anisotropic self-energies in the momentum space.

cond-mat.str-el↗

arXiv2018

Superconductivity arising from layer-differentiation in multi-layer cuprates

In order to theoretically identify the factors governing superconductivity in multi-layer cuprates, a three-layer Hubbard model is studied with the two-particle self-consistent (TPSC) approach so as to incorporate electron correlations. The linearized Eliashberg equation is then solved for the gap function in a matrix form to resolve the role of outer CuO$_2$ planes (OPs) and inner plane (IP). We show that OPs dominate IP in the $d_{x^{2}-y^{2}}$-wave superconductivity, while IP dominates in the antiferromagnetism. This comes from an electron correlation effect in that the correlation makes the doping rates different between OPs and IP (i.e., a self-doping effect), which occurs in intermediate and strong correlation regimes. Namely, the antiferromagnetic fluctuations in IP are stronger due to a stronger electron correlation, which simultaneously reduces the quasiparticle density of states in IP with a suppressed $d_{x^{2}-y^{2}}$-wave superconductivity. Intriguingly, while the off-diagonal (inter-layer) elements in the gap function matrix are tiny, {\it inter-layer pair scattering} processes are in fact at work in enhancing the superconducting transition temperature $T_{\text{c}}$ through the inter-layer Green's functions. This actually causes the trilayer system to have higher $T_{\text{c}}$ than the single-layer in a weak- and intermediate-coupling regimes. This picture holds for a range of the on-site Hubbard repulsion $U$ that contains those estimated for the cuprates. The present result is qualitatively consistent with nuclear magnetic resonance experiments in multi-layer cuprates superconductors.

cond-mat.supr-con↗