arXiv subjects

Hiroki Isobe

Publications and source records attributed to Hiroki Isobe.

34 records · Page 2Linked to original sources

arXiv2019

Magic of high order van Hove singularity

We introduce a new type of van Hove singularity in two dimensions, where a saddle point in momentum space is changed from second-order to high-order. Correspondingly, the density of states near such ``high-order van Hove singularity'' is significantly enhanced from logarithmic to power-law divergence, which promises stronger electron correlation effects. High-order van Hove singularity can be generally achieved by tuning the band structure with a single parameter in moiré superlattices, such as twisted bilayer graphene by tuning twist angle or applying pressure, and trilayer graphene by applying vertical electric field.

cond-mat.str-el↗

arXiv2019

Nematic superconductivity stabilized by density wave fluctuations: Possible application to twisted bilayer graphene

Nematic superconductors possess unconventional superconducting order parameters that spontaneously break rotational symmetry of the underlying crystal. In this work we propose a mechanism for nematic superconductivity stabilized by strong density wave fluctuations in two dimensions. While the weak-coupling theory finds the fully gapped chiral state to be energetically stable, we show that strong density wave fluctuations result in an additional contribution to the free energy of a superconductor with multicomponent order parameters, which generally favors nematic superconductivity. Our theory shades light on the recent observation of rotational symmetry breaking in the superconducting state of twisted bilayer graphene.

cond-mat.supr-con↗

arXiv2019

Observation of half-integer level shift of vortex bound states in an iron-based superconductor

Vortices in topological superconductors host Majorana zero modes (MZMs), which are proposed to be building blocks of fault-tolerant topological quantum computers. Recently, a new single-material platform for realizing MZM has been discovered in iron-based superconductors, without involving hybrid semiconductor-superconductor structures. Here we report on a detailed scanning tunneling spectroscopy study of a FeTe0.55Se0.45 single crystal, revealing two distinct classes of vortices present in this system which differ by a half-integer level shift in the energy spectra of the vortex bound states. This level shift is directly tied with the presence or absence of zero-bias peak and also alters the ratios of higher energy levels from integer to half-odd-integer. Our model calculations fully reproduce the spectra of these two types of vortex bound states, suggesting the presence of topological and conventional superconducting regions that coexist within the same crystal. Our findings provide strong evidence for the topological nature of superconductivity in FeTe0.55Se0.45 and establish it as an excellent platform for further studies on MZMs.

cond-mat.supr-con↗

arXiv2018

Nodal Arc in Disordered Dirac Fermions: Connection to Non-Hermitian Band Theory

We show that Dirac fermion systems in two dimensions generally exhibit disorder-induced nodal arc replacing the nodal point and tilted Dirac cone, provided that the two components of the Dirac fermion correspond to two distinct orbitals unrelated by symmetry. This result is explicitly demonstrated using renormalization group analysis in a disordered Dirac model that we introduce, where the disorder potential acts differently on the two orbitals. As we show by numerical simulations and self-consistent Born approximation calculation, this drives the system into a new strongly disordered phase.

cond-mat.dis-nn↗

arXiv2018

Unconventional Superconductivity and Density Waves in Twisted Bilayer Graphene

We study electronic ordering instabilities of twisted bilayer graphene with $n=2$ electrons per supercell, where correlated insulator state and superconductivity are recently observed. Motivated by the Fermi surface nesting and the proximity to Van Hove singularity, we introduce a hot-spot model to study the effect of various electron interactions systematically. Using renormalization group method, we find $d$/$p$-wave superconductivity and charge/spin density wave emerge as the two types of leading instabilities driven by Coulomb repulsion. The density wave state has a gapped energy spectrum at $n=2$ and yields a single doubly-degenerate pocket upon doping to $n>2$. The intertwinement of density wave and superconductivity and the quasiparticle spectrum in the density wave state are consistent with experimental observations.

cond-mat.str-el↗

arXiv2017

Interlayer Pairing Symmetry of Composite Fermions in Quantum Hall Bilayers

We study the pairing symmetry of the interlayer paired state of composite fermions in quantum Hall bilayers. Based on the Halperin-Lee-Read (HLR) theory, the effect of the long-range Coulomb interaction and the internal Chern-Simons gauge fluctuation is analyzed with the random-phase approximation beyond the leading order contribution in small momentum expansion, and we observe that the interlayer paired states with a relative angular momentum $l=+1$ are energetically favored for filling $ν=\frac{1}{2}+\frac{1}{2}$ and $\frac{1}{4}+\frac{1}{4}$. The degeneracy between states with $\pm l$ is lifted by the interlayer density-current interaction arising from the interplay of the long-range Coulomb interaction and the Chern-Simons term in the HLR theory.

cond-mat.str-el↗

arXiv2016

New quantum critical points of $j=3/2$ Dirac electrons in antiperovskite topological crystalline insulators

We study the effect of the long-range Coulomb interaction in $j=3/2$ Dirac electrons in cubic crystals with the $O_h$ symmetry, which serves as an effective model for antiperovskite topological crystalline insulators. The renormalization group analysis reveals three fixed points that are Lorentz invariant, rotationally invariant, and $O_h$ invariant. Among them, the Lorentz- and $O_h$-invariant fixed points are stable in the low-energy limit while the rotationally invariant fixed point is unstable. The existence of a stable $O_h$-invariant fixed point of Dirac fermions with finite velocity anisotropy presents an interesting counterexample to emergent Lorentz invariance in solids.

cond-mat.str-el↗

arXiv2016

Coulomb interaction effect in tilted Weyl fermion in two dimensions

Weyl fermions with tilted linear dispersions characterized by several different velocities appear in some systems including the quasi-two-dimensional organic semiconductor $α$-(BEDT-TTF)$_2$I$_3$ and three-dimensional WTe$_2$. The Coulomb interaction between electrons modifies the velocities in an essential way in the low-energy limit, where the logarithmic corrections dominate. Taking into account the coupling to both the transverse and longitudinal electromagnetic fields, we derive the renormalization group equations for the velocities of the tilted Weyl fermions in two dimensions, and found that they increase as the energy decreases and eventually hit the speed of light $c$ to result in the Cherenkov radiation. Especially, the system restores the isotropic Weyl cone even when the bare Weyl cone is strongly tilted and the velocity of electrons becomes negative in certain directions.

cond-mat.str-el↗

arXiv2015

Emergent non-Fermi liquid at the quantum critical point of a topological phase transition in two dimensions

We study the effects of Coulomb interaction between 2D Weyl fermions with anisotropic dispersion which displays relativistic dynamics along one direction and Newtonian dynamics along the other. Such a dispersion can be realized in phosphorene under electric field or strain, in TiO$_2$/VO$_2$ superlattices, and, more generally, at the quantum critical point between a nodal semimetal and an insulator in systems with a chiral symmetry. Using the one-loop renormalization group approach in combination with the large-$N$ expansion, we find that the system displays interaction-driven non-Fermi liquid behavior in a wide range of intermediate frequencies and marginal Fermi liquid behavior at the smallest frequencies. In the non-Fermi liquid regime, the quasiparticle residue $Z$ at energy $E$ scales as $Z \propto E^a$ with $a >0$, and the parameters of the fermionic dispersion acquire anomalous dimensions. In the marginal Fermi-liquid regime, $Z \propto (|\log E|)^{-b}$ with universal $b = 3/2$.

cond-mat.str-el↗

arXiv2015

Theory of interacting topological crystalline insulators

We study the effect of electron interactions in topological crystalline insulators (TCIs) protected by mirror symmetry, which are realized in the SnTe material class and host multi-valley Dirac fermion surface states. We find that interactions reduce the integer classification of noninteracting TCIs in three dimensions, indexed by the mirror Chern number, to a finite group $Z_8$. In particular, we explicitly construct a microscopic interaction Hamiltonian to gap 8 flavors of Dirac fermions on the TCI surface, while preserving the mirror symmetry. Our construction builds on interacting edge states of $U(1)\times Z_2$ symmetry-protected topological (SPT) phases of fermions in two dimensions, which we classify. Our work reveals a deep connection between 3D topological phases protected by spatial symmetries and 2D topological phases protected by internal symmetries.

cond-mat.str-el↗

arXiv2015

Renormalization group analysis of multi-Dirac-node materials

We theoretically study the electromagnetic interaction in Dirac systems with $N$ nodes by using the renormalization group, which is relevant to the quantum critical phenomena of topological phase transition ($N=1$) and Weyl semimetals ($N=4$ or $N=12$). Compared with the previous work for $N=1$ [H. Isobe and N. Nagaosa, Phys. Rev. B 86, 165127 (2012); arXiv:1205.2427], we obtained the analytic solution for the large $N$ limit, which differs qualitatively for the scaling of the speed of light $c$ and that of electron $v$, i.e., $v$ does notchange while $c$ is reduced to $v$. We also found a reasonably accurate approximate analytic solution for generic $N$, which well interpolates between $N=1$ and large $N$ limit, and it concludes that $c^2 v^N$ is almost unrenormalized. The temperature dependence of the physical properties, the dielectric constant, magnetic susceptibility, spectral function, DC conductivity, and mass gap are discussed based on these results.

cond-mat.str-el↗

arXiv2014

Generalized Hund's rule for two-atom systems

Hund's rule is one of the fundamentals of the correlation physics at the atomic level, determining the ground state multiplet of the electrons. It consists of three laws: (i) maximum $S$ (total spin), (ii) maximum $L$ (total orbital angular momentum) under the constraint of (i), and (iii) the total angular momentum $J$ is $|L-S|$ for electron number less than half, while $J=L+S$ for more than half due to the relativistic spin-orbit interaction (SOI). In real systems, the electrons hop between the atoms and gain the itinerancy, which is usually described by the band theory. The whole content of theories on correlation is to provide a reliable way to describe the intermediate situation between the two limits. Here we propose an approach toward this goal, i.e., we study the two-atom systems of three $t_{2g}$ orbitals and see how the Hund's rule is modified by the transfer integral $t$ between them. It is found that the competition between $t$ and the Hund's coupling $J$ at each atom determines the crossover from the molecular orbital limit to the strong correlation limit. Especially, the focus is on the generalization of the third rule, i.e., the inter-and intra-atomic SOI's in the presence of the correlation. We have found that there are cases where the effective SOI's are appreciably enhanced by the Hund's coupling. The conditions for the enhancement are the intermediate Hund's coupling and the filling of four or five electrons.

cond-mat.str-el↗

arXiv2014

Quantum Criticality of Topological Phase Transitions in 3D Interacting Electronic Systems

Topological phase transitions in condensed matters accompany emerging singularities of the electronic wave function, often manifested by gap-closing points in the momentum space. In conventional topological insulators in three dimensions (3D), the low energy theory near the gap-closing point can be described by relativistic Dirac fermions coupled to the long range Coulomb interaction, hence the quantum critical point of topological phase transitions provides a promising platform to test the novel predictions of quantum electrodynamics. Here we show that a new class of quantum critical phenomena emanates in topological materials breaking either the inversion symmetry or the time-reversal symmetry. At the quantum critical point, the theory is described by the emerging low energy fermions, dubbed the anisotropic Weyl fermions, which show both the relativistic and Newtonian dynamics simultaneously. The interplay between the anisotropic dispersion and the Coulomb interaction brings about a new screening phenomena distinct from the conventional Thomas-Fermi screening in metals and logarithmic screening in Dirac fermions.

cond-mat.str-el↗

arXiv2013

Theory of topological quantum phase transitions in 3D noncentrosymmetric systems

We have constructed a general theory describing the topological quantum phase transitions in 3D systems with broken inversion symmetry. While the consideration of the system's codimension generally predicts the appearance of a stable metallic phase between the normal and topological insulators, it is shown that a direct topological phase transition between two insulators is also possible when an accidental band crossing (ABC) occurs along directions with high crystalline symmetry. At the quantum critical point (QCP), the energy dispersion becomes quadratic along one direction while the dispersions along the other two orthogonal directions are linear, which manifests the zero chirality of the band touching point (BTP). Due to the anisotropic dispersion at QCP, various thermodynamic and transport properties show unusual temperature dependence and anisotropic behaviors.

cond-mat.str-el↗

arXiv2012

Theory of a quantum critical phenomenon in a topological insulator: (3+1)-dimensional quantum electrodynamics in solids

We study theoretically the quantum critical phenomenon of the phase transition between the trivial insulator and the topological insulator in (3+1) dimensions, which is described by a Dirac fermion coupled to the electromagnetic field. The renormalization group (RG) equations for the running coupling constant α, the speed of light c and electron v are derived. The almost exact analytic solutions to these RG equations are obtained to reveal that (i) c and v approach to the common value with combination c^2v being almost unrenormalized, (ii) the RG flow of αis the same as that of usual QED with c^3 being replaced by c^2v, and (iii) there are two crossover momentum/energy scales separating three regions of different scaling behaviors. The dielectric and magnetic susceptibilities, angle-resolved photoemission spectroscopy (ARPES), and the behavior of the gap are discussed from this viewpoint.

cond-mat.mes-hall↗

arXiv2012

Renormalization Effects on Quasi-Two-Dimensional Organic Conductor α-(BEDT-TTF)2I3

The quasi-two-dimensional organic semiconductor α-(BEDT-TTF)2I3 [BEDT-TTF=bis(ethylenedithio)tetrathiafulvalene] has an anisotropic linear dispersion with a zero energy gap near the Fermi level. Owing to the vanishing density of states at the Fermi level, the Coulomb interaction is unscreened in this material. We theoretically study the effect of the long-range Coulomb interaction and the low-energy/long-wavelength behavior of α-(BEDT-TTF)2I3 using the renormalization group analysis. The nearly logarithmic enhancement of the velocity reshapes tilted Dirac cones, and changes the low-temperature behavior. We also show the theoretical calculation for the site-selective spin susceptibility, which can be measured in an NMR experiment.

cond-mat.str-el↗