We are interested in novel quantum phenomena that are enabled by topological materials. We use analytical methods such as quantum field theory, combined with some numerical simulations. Our research interests include:

- Topological phases of matter (Topological insulators, Weyl/Dirac semimetals)
- Nonlinear optical/transport phenomena (Shift current, nonreciprocal current response)
- Nonequilibrium phenomena (Floquet theory, Keldysh formalism)

#### １. Classification of topological insulators and its applications

We formulated classification theory of topological insulators by using representation theory of Clifford algebra and applied it to various topological phases:

- Topological crystalline insulators [1]。
- Weyl/Dirac semimetals [2,3,4]。
- Strongly correlated topological insulators and superconductors [5]。

Table: Classification table of strongly correlated topological insulators and superconductors

[1] Takahiro Morimoto, and Akira Furusaki, ” Topological classification with additional symmetries from Clifford algebras ” Phys. Rev. B **88**, 125129 (2013).

[2] Takahiro Morimoto, and Akira Furusaki, ” Weyl and Dirac semimetals with Z2 topological charge ” Phys. Rev. B **89**, 235127 (2014).

[3] Bohm-Jung Yang, Takahiro Morimoto, and Akira Furusaki, ” Topological charges of three-dimensional Dirac semimetals with rotation symmetry ” Phys. Rev. B **92**, 165120 (2015).

[4] Bohm-Jung Yang, Troels Arnfred Bojesen, Takahiro Morimoto, and Akira Furusaki, ” Topological semimetals protected by off-centered symmetries in nonsymmorphic crystals ” Phys. Rev. B **95**, 075135 (2017).

[5] Takahiro Morimoto, Akira Furusaki, and Christopher Mudry, ” Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactions ” Phys. Rev. B **92**, 125104 (2015).

#### 2. Theory of shift current based on Floquet theory and its applications

The responses of materials to high intensity light, i.e., nonlinear optical responses, constitute a vast field of physics and engineering. While topology has been playing a central role in recent studies of condensed matters, topological aspects of nonlinear optical effects have not been fully explored so far. We showed there exist a few examples of nonlinear optical effects that have topological origins. First, we studied the second-order nonlinear optical effects including the shift-current, a candidate mechanism for recently discovered solar cell action in perovskite materials. We showed that shift current has a close relationship to the modern theory of polarization, and is described by the Berry connection of Bloch wave function [1].

- Shift current of excitons [2]。
- Shift spin current [3]。
- I-V characteristics and shot noise spectra of shift current photovoltaics, where we discussed its potential application to efficient energy conversion and photodetectors [4]。

Fig. Description of nonlinear optical effects based on Floquet theory

[1] Takahiro Morimoto, Naoto Nagaosa, ” Topological nature of nonlinear optical effects in solids ” Science Advances **2**, e1501524 (2016).

[2] Takahiro Morimoto, Naoto Nagaosa, ” Topological aspects of nonlinear excitonic processes in noncentrosymmetric crystals ” Phys. Rev. B **94**, 035117 (2016).

[3] Kun Woo Kim, Takahiro Morimoto, and Naoto Nagaosa, ” Shift charge and spin photocurrents in Dirac surface states of topological insulator ” Phys. Rev. B **95**, 035134 (2017).

[4] Takahiro Morimoto, Masao Nakamura, Masashi Kawasaki, and Naoto Nagaosa, ” Current-Voltage Characteristic and Shot Noise of Shift Current Photovoltaics ” Phys. Rev. Lett. **121**, 267401 (2018).

[Review] Naoto Nagaosa, Takahiro Morimoto, ” Concept of Quantum Geometry in Optoelectronic Processes in Solids: Application to Solar Cells ” Advanced Materials (2017) doi:10.1002/adma.201603345 .

[Talk slide] Takahiro Morimoto, “Topological aspects of nonlinear optical effects” APS March Meeting 2018 (Y05.00004)

#### ３．Topological nonlinear optical effects in Weyl semimetals

Weyl semimetals support stable gapless excitations that are characterized quantized Berry flux around the Weyl points. There have been efforts to find quantized responses from Weyl semimetals, but it has been difficult in linear resposnes. Here we showed that another second-order nonlinear effect, circular photogalvanic effect (CPGE), is governed by Berry curvature and measuring CPGE in Weyl semimetals allows an access to monopole physics of Weyl fermions [1]. We generalized our analysis to chiral multifold fermions which support stable gapless point where more than 2 bands are degenerate, and showed chiral multifold fermions show quantized CPGE [3].

Fig: Quantization of circular photogalvanic effect in Weyl semimetals

[1] Fernando de Juan, Adolfo G. Grushin, Takahiro Morimoto, and Joel E. Moore: ” Quantized circular photogalvanic effect in Weyl semimetals ” Nature Communications **8**, 15995 (2017).

[2] Felix Flicker, Fernando de Juan, Barry Bradlyn, Takahiro Morimoto, Maia G. Vergniory, and Adolfo G. Grushin: ” Chiral optical response of multifold fermions ” Phys. Rev. B **98**, 155145 (2018).

#### ３．Floquet topological phases

Nonequilibrium systems under periodic driving (Floquet systems) realize novel topological phases that cannot be achieved in equilibrium systems. One unique feature of periodically driven systems is that they can host a purely dynamical symmetry that involves time-translation. In this talk, we present a new class of Floquet topological phases protected by one realization of such dynamical symmetry, i.e., “time-glide symmetry” which is defined by a combination of reflection and time translation [1]. We constructed models of time-glide symmetric Floquet TI and developed a general classification theory of time-glide symmetric Floquet topological phases by using a Clifford algebra approach.

We also study strong correlation effects in Floquet topological phases. We classified Floquet topological phases of interacting bosons and constructed models of nontrivial bosonic Floquet topological phases in 1D and 2D systems [2,3].

Fig: A model of Floquet topological phase in 2D.

[1] Takahiro Morimoto, Hoi Chun Po, and Ashvin Vishwanath, ” Floquet topological phases protected by time glide symmetry ” Phys. Rev. B **95**, 195155 (2017).

[2] Andrew C. Potter, Takahiro Morimoto, Ashvin Vishwanath, ” Classification of Interacting Topological Floquet Phases in One Dimension ” Phys. Rev. X **6**, 041001 (2016).

[3] Andrew C. Potter and Takahiro Morimoto, ” Dynamically enriched topological orders in driven two-dimensional systems ” Phys. Rev. B **95**, 155126 (2017).