arXiv subjects

Takahiro Morimoto

Publications and source records attributed to Takahiro Morimoto.

At least 91 records · Page 5Linked to original sources

arXiv2016

Chiral Floquet Phases of Many-body Localized Bosons

We construct and classify chiral topological phases in driven (Floquet) systems of strongly interacting bosons, with finite-dimensional site Hilbert spaces, in two spatial dimensions. The construction proceeds by introducing exactly soluble models with chiral edges, which in the presence of many-body localization (MBL) in the bulk are argued to lead to stable chiral phases. These chiral phases do not require any symmetry, and in fact owe their existence to the absence of energy conservation in driven systems. Surprisingly, we show that they are classified by a quantized many-body index, which is well defined for any MBL Floquet system. The value of this index, which is always the logarithm of a positive rational number, can be interpreted as the entropy per Floquet cycle pumped along the edge, formalizing the notion of quantum-information flow. We explicitly compute this index for specific models, and show that the nontrivial topology leads to edge thermalization, which provides an interesting link between bulk topology and chaos at the edge. We also discuss chiral Floquet phases in interacting fermionic systems and their relation to chiral bosonic phases.

cond-mat.dis-nn↗

arXiv2016

Chiral anomaly and giant magnetochiral anisotropy in noncentrosymmetric Weyl semimetals

We theoretically propose that giant magnetochiral anisotropy is achieved in Weyl semimetals in noncentrosymmetric crystals as a consequence of the chiral anomaly. The magnetochiral anisotropy is the nonlinearity of the resistivity $ρ$ that depends on the current $\boldsymbol{I}$ and the magnetic field $\boldsymbol{B}$ as $ρ=ρ_0 (1 + γ\boldsymbol{I} \cdot \boldsymbol{B})$, and can be applied to rectifier devices controlled by $\boldsymbol{B}$. We derive the formula for the coefficient $γ$ in noncentrosymmetric Weyl semimetals. The obtained formula for $γ$ shows that the magnetochiral anisotropy is strongly enhanced when the chemical potential is tuned to Weyl points, and that noncentrosymmetric Weyl semimetals such as TaAs can exhibit much larger magnetochiral anisotropy than that observed in other materials so far.

cond-mat.mes-hall↗

arXiv2016

Shift charge and spin photocurrents in Dirac surface states of topological insulator

The generation of photocurrent in condensed matter is of main interest for photovoltaic and optoelectronic applications. Shift current, a nonlinear photoresponse, has attracted recent intensive attention as a dominant player of bulk photovoltaic effect in ferroelectric materials. In three dimensional topological insulators $\text{Bi}_2\text{X}_3$ (X: Te, Se), we find that Dirac surface states with a hexagonal warping term carry shift current by linearly polarized light. In addition, shift spin-current is introduced with the time-reversal symmetry breaking perturbation. The estimate for the magnitudes of the shift charge- and spin-currents are 0.13$I_0$ and 0.21$I_0$(nA/m) with the intensity of light $I_0$ measured in $(\text{W}/\text{m}^2)$, respectively, which can offer a useful method to generate these currents efficiently.

cond-mat.mes-hall↗

arXiv2016

Topological aspects of nonlinear excitonic processes in noncentrosymmetric crystals

We study excitonic processes second order in the electric fields in noncentrosymmetric crystals. We derive formulas for shift current and second harmonic generation produced by exciton creation, by using the Floquet formalism combined with the Keldysh Green's function method. It is shown that (i) the steady dc shift current flows by exciton creation without dissociation into free carriers and (ii) second harmonic generation is enhanced at the exciton resonance. The obtained formulas clarify topological aspects of these second order excitonic processes which are described by Berry connections of the relevant valence and conduction bands.

cond-mat.mes-hall↗

arXiv2016

Topological nature of nonlinear optical effects in solids

There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by the strong light irradiation to materials that results in nonlinear polarizations in the electric field. These are of great importance in studying the physics of excited states of the system as well as for applications to optical devices and solar cells. Nonlinear properties of materials are usually described by the nonlinear susceptibilities $χ$'s, which have complex expressions including many matrix elements and energy denominators. On the other hand, a nonequilibrium steady state under a electric field periodic in time has a concise description in terms of the Floquet bands of electrons dressed by photons. Here, we theoretically show by using the Floquet formalism that various nonlinear optical effects, such as the shift current in noncentrosymmetric materials, photovoltaic Hall response, and photo-induced change of order parameters under the continuous irradiation of monochromatic light, can be described in a unified fashion by topological quantities involving the Berry connection and Berry curvature. It is found that vector fields defined with the Berry connections in the space of momentum and/or parameters govern the nonlinear responses. This topological view offers a new route to design the nonlinear optical materials.

cond-mat.mes-hall↗

arXiv2016

Scaling laws for nonlinear electromagnetic responses of Dirac fermions

We theoretically propose that the Dirac fermion in two-dimensions shows the giant nonlinear responses to electromagnetic fields in terahertz region. A scaling form is obtained for the current and magnetization as functions of the normalized electromagnetic fields $E/E_ω$ and $B/B_ω$, where the characteristic electric (magnetic) field $E_ω$ ($B_ω$) depends on the frequency $ω$ as $\hbarω^2/ev_F$ ($\hbarω^2/ev_F^2$), and is typically of the order of 80 V/cm ( 8 mT) in the terahertz region. Applications of the present theory to graphene and surface state of a topological insulator are discussed.

cond-mat.mes-hall↗

arXiv2016

Weyl Mott Insulator

Relativistic Weyl fermion (WF) often appears in the band structure of three dimensional magnetic materials and acts as a source or sink of the Berry curvature, i.e., the (anti-)monopole. It has been believed that the WFs are stable due to their topological indices except when two Weyl fermions of opposite chiralities annihilate pairwise. Here, we theoretically show for a model including the electron-electron interaction that the Mott gap opens for each WF without violating the topological stability, leading to a topological Mott insulator dubbed {\it Weyl Mott insulator } (WMI). This WMI is characterized by several novel features such as (i) energy gaps in the angle-resolved photo-emission spectroscopy (ARPES) and the optical conductivity, (ii) the nonvanishing Hall conductance, and (iii) the Fermi arc on the surface with the penetration depth diverging as approaching to the momentum at which the Weyl point is projected. Experimental detection of the WMI by distinguishing from conventional Mott insulators is discussed with possible relevance to pyrochlore iridates.

cond-mat.str-el↗

arXiv2015

Bosonic symmetry protected topological phases with reflection symmetry

We study two-dimensional bosonic symmetry protected topological (SPT) phases which are protected by reflection symmetry and local symmetry [$Z_N\rtimes R$, $Z_N\times R$, U(1)$\rtimes R$, or U(1)$\times R$], in the search for two-dimensional bosonic analogs of topological crystalline insulators in integer-$S$ spin systems with reflection and spin-rotation symmetries. To classify them, we employ a Chern-Simons approach and examine the stability of edge states against perturbations that preserve the assumed symmetries. We find that SPT phases protected by $Z_N\rtimes R$ symmetry are classified as $\mathbb{Z}_2\times\mathbb{Z}_2$ for even $N$ and 0 (no SPT phase) for odd $N$ while those protected by U(1)$\rtimes R$ symmetry are $\mathbb{Z}_2$. We point out that the two-dimensional Affleck-Kennedy-Lieb-Tasaki state of $S=2$ spins on the square lattice is a $\mathbb{Z}_2$ SPT phase protected by reflection and $π$-rotation symmetries.

cond-mat.str-el↗

arXiv2015

Topological charges of three-dimensional Dirac semimetals with rotation symmetry

In general, the stability of a band crossing point indicates the presence of a quantized topological number associated with it. In particular, the recent discovery of three-dimensional Dirac semimetals in Na$_{3}$Bi and Cd$_{3}$As$_{2}$ demonstrates that a Dirac point with four-fold degeneracy can be stable as long as certain crystalline symmetries are supplemented in addition to the time-reversal and inversion symmetries. However, the topological charges associated with Na$_{3}$Bi and Cd$_{3}$As$_{2}$ are not clarified yet. In this work, we identify the topological charge of three-dimensional Dirac points. It is found that although the simultaneous presence of the time-reversal and inversion symmetries forces the net chiral charge to vanish, a Dirac point can carry another quantized topological charge when an additional rotation symmetry is considered. Two different classes of Dirac semimetals are identified depending on the nature of the rotation symmetries. First, the conventional symmorphic rotational symmetry which commutes with the inversion gives rise to the class I Dirac semimetals having a pair of Dirac points on the rotation axes. Since the topological charges of each pair of Dirac points have the opposite sign, a pair-creation or a pair-annihilation is required to change the number of Dirac points in the momentum space. On the other hand, the class II Dirac semimetals possess a single isolated Dirac point at a time-reversal invariant momentum, which is protected by a screw rotation. The non-symmorphic nature of screw rotations allows the anti-commutation relation between the rotation and inversion symmetries, which enables to circumvent the doubling of the number of Dirac points and create a single Dirac point at the Brillouin zone boundary.

cond-mat.mes-hall↗

arXiv2015

Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactions

The conditions for both the stability and the breakdown of the topological classification of gapped ground states of noninteracting fermions, the tenfold way, in the presence of quartic fermion-fermion interactions are given for any dimension of space. This is achieved by encoding the effects of interactions on the boundary gapless modes in terms of boundary dynamical masses. Breakdown of the noninteracting topological classification occurs when the quantum nonlinear sigma models for the boundary dynamical masses favor quantum disordered phases. For the tenfold way, we find that (i) the noninteracting topological classification $\mathbb{Z}^{\,}_{2}$ is always stable, (ii) the noninteracting topological classification $\mathbb{Z}$ in even dimensions is always stable, (iii) the noninteracting topological classification $\mathbb{Z}$ in odd dimensions is unstable and reduces to $\mathbb{Z}^{\,}_{N}$ that can be identified explicitly for any dimension and any defining symmetries. We also apply our method to the three-dimensional topological crystalline insulator SnTe from the symmetry class AII$+R$, for which we establish the reduction $\mathbb{Z}\to\mathbb{Z}^{\,}_{8}$ of the noninteracting topological classification.

cond-mat.str-el↗

arXiv2015

Topological magneto-electric effects in thin films of topological insulators

We propose that the topological magneto-electric (ME) effect, a hallmark of topological insulators (TIs), can be realized in thin films of TIs in the $ν=0$ quantum Hall state under magnetic field or by doping two magnetic ions with opposite signs of exchange coupling. These setups have the advantage compared to previously proposed setups that a uniform configuration of magnetic field or magnetization is sufficient for the realization of the topological ME effect. To verify our proposal, we numerically calculate ME response of TI thin films in the cylinder geometry and that of effective 2D models of surface Dirac fermions. The ME response is shown to converge to the quantized value corresponding to the axion angle $θ=\pm π$ in the limit of the large top and bottom surface area of TI films, where non-topological contributions from the bulk and the side surface are negligible.

cond-mat.mes-hall↗

arXiv2015

Anderson localization and the topology of classifying spaces

We construct the generic phase diagrams encoding the topologically distinct localized and delocalized phases of noninteracting fermionic quasiparticles for any symmetry class from the tenfold way in one, two, and three dimensions. To this end, we start from a massive Dirac Hamiltonian perturbed by a generic disorder for any dimension of space and for any one of the ten symmetry classes from the tenfold way. The physics of Anderson localization is then encoded by a two-dimensional phase diagram that we deduce from the topology of the space of normalized Dirac masses. This approach agrees with previously known results and gives an alternative explanation for the even-odd effect in the one-dimensional chiral symmetry classes. We also give a qualitative explanation for the Gade singularity and Griffiths effects in the density of states using the first homotopy group of the normalized Dirac masses in two dimensions. Finally, this approach is used to analyze the stability of massless Dirac fermions on the surface of three-dimensional topological crystalline insulators.

cond-mat.mes-hall↗

arXiv2015

Topological Phases Protected By Reflection Symmetry and Cross-cap States

Twisting symmetries provides an efficient method to diagnose symmetry-protected topological (SPT) phases. In this paper, edge theories of (2+1)-dimensional topological phases protected by reflection as well as other symmetries are studied by twisting reflection symmetry, which effectively puts the edge theories on an unoriented spacetime, such as the Klein bottle. A key technical step taken in this paper is the use of the so-called cross-cap states, which encode entirely the unoriented nature of spacetime, and can be obtained by rearranging the spacetime geometry and exchanging the role of space and time coordinates. When the system is in a non-trivial SPT phase, we find that the corresponding cross-cap state is non-invariant under the action of the symmetries of the SPT phase, but acquires an anomalous phase. This anomalous phase, with a proper definition of a reference state, on which symmetry acts trivially, reproduces the known classification of (2+1)-dimensional bosonic and fermionic SPT phases protected by reflection symmetry, including in particular the Z_8 classification of topological crystalline superconductors protected by reflection and time-reversal symmetries.

cond-mat.str-el↗

arXiv2015

Charge and spin transport in edge channels of a $ν=0$ quantum Hall system on the surface of topological insulators

Three-dimensional topological insulators of finite thickness can show the quantum Hall effect (QHE) at the filling factor $ν=0$ under an external magnetic field if there is a finite potential difference between the top and bottom surfaces. We calculate energy spectra of surface Weyl fermions in the $ν=0$ QHE and find that gapped edge states with helical spin structure are formed from Weyl fermions on the side surfaces under certain conditions. These edge channels account for the nonlocal charge transport in the $ν=0$ QHE which is observed in a recent experiment on (Bi$_{1-x}$Sb$_x$)$_2$Te$_3$ films. The edge channels also support spin transport due to the spin-momentum locking. We propose an experimental setup to observe various spintronics functions such as spin transport and spin conversion.

cond-mat.mes-hall↗

arXiv2014

Z_3 symmetry-protected topological phases in the SU(3) AKLT model

We study $\mathbb{Z}_3$ symmetry-protected topological (SPT) phases in one-dimensional spin systems with $Z_3 \times Z_3$ symmetry. We construct ground-state wave functions of the matrix product form for nontrivial $\mathbb{Z}_3$ phases and their parent Hamiltonian from a cocycle of the group cohomology $H^2(Z_3\times Z_3,U(1))$. The Hamiltonian is an SU(3) version of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model, consisting of bilinear and biquadratic terms of su(3) generators in the adjoint representation. A generalization to the SU($N$) case, the SU($N$) AKLT Hamiltonian, is also presented which realizes nontrivial $\mathbb{Z}_N$ SPT phases. We use the infinite-size variant of the density matrix renormalization group (iDMRG) method to determine the ground-state phase diagram of the SU(3) bilinear-biquadratic model as a function of the parameter $θ$ controlling the ratio of the bilinear and biquadratic coupling constants. The nontrivial $\mathbb{Z}_3$ SPT phase is found for a range of the parameter $θ$ including the point of vanishing biquadratic term ($θ=0$) as well as the SU(3) AKLT point [$θ=\arctan(2/9)$]. A continuous phase transition to the SU(3) dimer phase takes place at $θ\approx -0.027π$, with a central charge $c\approx3.2$. For SU(3) symmetric cases we define string order parameters for the $\mathbb{Z}_3$ SPT phases in a similar way to the conventional Haldane phase. We propose simple spin models that effectively realize the SU(3) and SU(4) AKLT models.

cond-mat.str-el↗

arXiv2014

Weyl and Dirac semimetals with Z_2 topological charge

We study the stability of gap-closing (Weyl or Dirac) points in the three-dimensional Brillouin zone of semimetals using Clifford algebras and their representation theory. We show that a pair of Weyl points with $\mathbb{Z}_2$ topological charge are stable in a semimetal with time-reversal and reflection symmetries when the square of the product of the two symmetry transformations equals minus identity. We present toy models of $\mathbb{Z}_2$ Weyl semimetals which have surface modes forming helical Fermi arcs. We also show that Dirac points with $\mathbb{Z}_2$ topological charge are stable in a semimetal with time-reversal, inversion, and SU(2) spin rotation symmetries when the square of the product of time-reversal and inversion equals plus identity. Furthermore, we briefly discuss the topological stability of point nodes in superconductors using Clifford algebras.

cond-mat.mes-hall↗

arXiv2014

Topological zero modes and Dirac points protected by spatial symmetry and chiral symmetry

We explore a new class of topologically stable zero energy modes which are protected by coexisting chiral and spatial symmetries. If a chiral symmetric Hamiltonian has an additional spatial symmetry such as reflection, inversion and rotation, the Hamiltonian can be separated into independent chiral-symmetric subsystems by the eigenvalue of the space symmetry operator. Each subsystem supports chiral zero energy modes when a topological index assigned to the block is nonzero. By applying the argument to Bloch electron systems, we detect band touching at symmetric points in the Brillouin zone. In particular, we show that Dirac nodes appearing in honeycomb lattice (e.g. graphene) and in half-flux square lattice are protected by three-fold and two-fold rotation symmetry, respectively. We also present several examples of Dirac semimetal with isolated band-touching points in three-dimensional $k$-space, which are protected by combined symmetry of rotation and reflection. The zero mode protection by spatial symmetry is distinct from that by the conventional winding number. We demonstrate that symmetry-protected band touching points emerge even though the winding number is zero. Finally, we identify relevant topological charges assigned to the gapless points.

cond-mat.mes-hall↗

arXiv2014

CPT theorem and classification of topological insulators and superconductors

We present a systematic topological classification of fermionic and bosonic topological phases protected by time-reversal, particle-hole, parity, and combination of these symmetries. We use two complementary approaches: one in terms of K-theory classification of gapped quadratic fermion theories with symmetries, and the other in terms of the K-matrix theory description of the edge theory of (2+1)-dimensional bulk theories. The first approach is specific to free fermion theories in general spatial dimensions while the second approach is limited to two spatial dimensions but incorporates effects of interactions. We also clarify the role of CPT theorem in classification of symmetry-protected topological phases, and show, in particular, topological superconductors dis- cussed before are related by CPT theorem.

cond-mat.str-el↗