Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals

Morimoto, Takahiro; Zhong, Shudan; Orenstein, Joseph; Moore, Joel E.

doi:10.1103/physrevb.94.245121

Cited by 186 publications

(162 citation statements)

References 39 publications

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“…Semiclassical theory -We first overview previous theoretical work on the nonlinear optical response described by the Berry curvature [22,25,35,36]. For the CPGE, the oscillating electric field E c (t) = Re{E c e iωt } of circularly polarized light induces a dc photocurrent j (0) as a second-order nonlinear optical effect:…”

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confidence: 99%

“…For a material with TRS, the nonlinear response tensor σ has been theoretically obtained as a Berry phase effect [35,36] and very recently further described by the BCD [22] as follows: [25].…”

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confidence: 99%

“…Because Weyl points are monopole sources or drains of the Berry curvature of Bloch wave functions in momentum space, a WSM can exhibit an anomalous Hall effect when breaking the time-reversal symmetry (TRS) [17][18][19] or a spin Hall effect [20], as a linear response to an external electric field. Recent theoretical [21][22][23][24][25][26][27][28][29][30] and experimental [31][32][33][34] studies have revealed giant nonlinear optical responses in inversion-symmetry-breaking WSMs, such as the photocurrent from the circular photogalvanic effect (CPGE), second harmonic generation (SHG), and nonlinear Hall effect. These nonlinear effects can be much stronger in WSMs than traditional electro-optic materials owing to the large Berry curvature [22,35,36].…”

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Berry curvature dipole in Weyl semimetal materials: An ab initio study

2018

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Noncentrosymmetric metals are anticipated to exhibit a dc photocurrent in the nonlinear optical response caused by the Berry curvature dipole in momentum space. Weyl semimetals (WSMs) are expected to be excellent candidates for observing these nonlinear effects because they carry a large Berry curvature concentrated in small regions, i.e., near the Weyl points. We have implemented the semiclassical Berry curvature dipole formalism into an ab initio scheme and investigated the second-order nonlinear response for two representative groups of materials: the TaAs-family type-I WSMs and MoTe2-family type-II WSMs. Both types of WSMs exhibited a Berry curvature dipole, in which type-II Weyl points are usually superior to the type-I because of the strong tilt. Corresponding nonlinear susceptibilities in several materials promise a nonlinear Hall effect in the dc field limit, which is within the experimentally detectable range. [31][32][33][34] studies have revealed giant nonlinear optical responses in inversion-symmetry-breaking WSMs, such as the photocurrent from the circular photogalvanic effect (CPGE), second harmonic generation (SHG), and nonlinear Hall effect. These nonlinear effects can be much stronger in WSMs than traditional electro-optic materials owing to the large Berry curvature [22,35,36]. Introduction -

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Berry curvature dipole in Weyl semimetal materials: An ab initio study

2018

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“…1a and Box 1) are explicit products of coherent interaction between light and matter 4-6 . Alternatively, the properties of quantum materials can be pre-programmed by directly manipulating the electronic wavefunction and the attendant Berry phase that give rise to the anomalous velocity of electrons in a solid [7][8][9] . These complementary avenues of controls mean that investigations no longer need to be reduced to merely observing (in contrast, for example, to astrophysics).…”

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Towards properties on demand in quantum materials

2017

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Q uantum materials are on the ascent. This term embodies a vast portfolio of compounds and phenomena where ramifications of quantum mechanics are demonstrably real. Quantum materials are in the vanguard of contemporary physics in part because these systems afford an exceptional venue to uncover the many roles of symmetry, topology, dimensionality and strong correlations in macroscopic observables. Here we set out to explore the ways and means of creating new states of matter in quantum materials and manipulating their phases via external stimuli. Practical control of these properties is a precondition for exploiting quantum advantages in new photonic, electronic and energy technologies, a task of significant societal impact 1 . We will primarily focus on the following classes of quantum materials: transition metal oxides, Fe-and Cu-based high-T c superconductors, van der Waals semiconductors, topological insulators and Weyl semimetals, and, finally, graphene.The properties of quantum materials are anomalously sensitive to external stimuli. In these systems, interactions associated with spin, charge, lattice and orbital degrees of freedom are commonly on par with the electronic kinetic energy. A rather fragile balance between coexisting and competing ground states can be readily shifted via external stimuli, leading to a raft of quantum phases and transitions between them 2,3 . Furthermore, certain classes of driven quantum states (Fig. 1a and Box 1) are explicit products of coherent interaction between light and matter 4-6 . Alternatively, the properties of quantum materials can be pre-programmed by directly manipulating the electronic wavefunction and the attendant Berry phase that give rise to the anomalous velocity of electrons in a solid [7][8][9] . These complementary avenues of controls mean that investigations no longer need to be reduced to merely observing (in contrast, for example, to astrophysics). Instead, it is now feasible to attain, in a predictable fashion, 'properties on demand' by steering a quantum material towards a desirable ground, metastable or transient state. The past decade has witnessed an explosion in the field of quantum materials, headlined by the predictions and discoveries of novel Landau-symmetry-broken phases in correlated electron systems, topological phases in systems with strong spin-orbit coupling, and ultra-manipulable materials platforms based on two-dimensional van der Waals crystals. Discovering pathways to experimentally realize quantum phases of matter and exert control over their properties is a central goal of modern condensed-matter physics, which holds promise for a new generation of electronic/photonic devices with currently inaccessible and likely unimaginable functionalities. In this Review, we describe emerging strategies for selectively perturbing microscopic interaction parameters, which can be used to transform materials into a desired quantum state. Particular emphasis will be placed on recent successes to tailor electronic interaction parameters through th...

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“…Their unique topological properties are predicted to give rise to a wide range of exotic transport and optical phenomena [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. By considering various rotational and mirror symmetries in both symmorphic and non-symmorphic contexts, researchers have predicted nodal-line semimetals [38] [48][49][50].…”

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Topological Hopf and Chain Link Semimetal States and Their Application to Co2MnGa

et al. 2017

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Topological semimetals can be classified by the connectivity and dimensionality of the band crossing in momentum space. The band crossings of a Dirac, Weyl, or an unconventional fermion semimetal are zero-dimensional (0D) points, whereas the band crossings of a nodal-line semimetal are one-dimensional (1D) closed loops. Here we propose that the presence of perpendicular crystalline mirror planes can protect three-dimensional (3D) band crossings characterized by nontrivial links such as a Hopf link or a coupled-chain, giving rise to a variety of new types of topological semimetals. We show that the nontrivial winding number protects topological surface states distinct from those in previously known topological semimetals with a vanishing spin-orbit interaction. We also show that these nontrivial links can be engineered by tuning the mirror eigenvalues associated with the perpendicular mirror planes. Using first-principles band structure calculations, we predict the ferromagnetic full Heusler compound Co2MnGa as a candidate. Both Hopf link and chain-like bulk band crossings and unconventional topological surface states are identified.Since the discovery of Dirac and Weyl semimetals [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], topological semimetals have emerged as an active frontier in condensed matter physics. Their unique topological properties are predicted to give rise to a wide range of exotic transport and optical phenomena [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. By considering various rotational and mirror symmetries in both symmorphic and non-symmorphic contexts, researchers have predicted nodal-line semimetals [38] [48][49][50]. Despite this diversity, topological semimetals can be further classified and characterized by the dimensionality of their band crossings in the bulk Brillouin zone (BZ). In a Dirac/Weyl semimetal or an unconventional (higher-fold degenerate) fermion semimetal [41,[43][44][45][46], the conduction and valence bands cross at discrete points in the BZ. Therefore, the dimension of their band crossings is 0D. In a nodal-line semimetal [38], the conduction and valence bands touch along a closed loop, thus the dimension of its band crossing is 1D. In this letter, we propose a number of previously unidentified topological semimetals and identify a candidate material class for the experimental realization. They feature 3D band crossings characterized by nontrivial links such as a Hopf link or a coupled-chain enabled by perpendicular mirror planes. The Hopf link, which consists of two rings that pass through the center of each other, represents the simplest topologically nontrivial link. While originally studied in mathematics and other areas, recently, researchers have applied this concept into topological physics in order to construct novel topological insulators and superconductors [52][53][54], although the role of Hopf link is distinctly different from what is considered here. Here we apply this idea in metals and show that the c...

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Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals

Cited by 186 publications

References 39 publications

Berry curvature dipole in Weyl semimetal materials: An ab initio study

Berry curvature dipole in Weyl semimetal materials: An ab initio study

Towards properties on demand in quantum materials

Topological Hopf and Chain Link Semimetal States and Their Application to Co2MnGa

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