Giant nonlinear Hall effect in strained twisted bilayer graphene

Zhang, Cheng-Ping; Xiao, Jiewen; Benjamin, Zhou; Hu, Jinxin; Xie, Ying-Ming; Yan, Binghai; Law, Kam Tuen

doi:10.48550/arxiv.2010.08333

Cited by 17 publications

(32 citation statements)

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“…Many interesting signatures of QG are revealed in transport properties and optical responses of these systems [12][13][14][15][16][17][18][19][20][21][22], and especially in the zero-magnetic field quantized anomalous linear hall effect in setups with time-reversal symmetry (TRS) [5,11,23]. The effects of QG go well beyond linear response, and can manifest themselves in nonlinear optical responses (NLOR) as shown recently [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. Furthermore, the NLOR does not require broken TRS, but rather a non-zero Berry curvature profile.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, the NLOR does not require broken TRS, but rather a non-zero Berry curvature profile. These nonlinear effects can manifest in various ways, such as nonlinear response to DC fields (induced by Berry curvature dipole [24,28,29,[35][36][37][38][39]), second-harmonic generation (SHG), and bulk-photovoltaic effects like shift-current (SC) [30,31,33,40], and circular photogalvanic effects (CPGE) [26,41,42]. Recently, there has been a lot of emphasis on the non-linear response to AC fields [25,42,43] which not only serve as a probe of non-trivial topology but also heralds promises of more efficient and robust photovoltaic devices [34].…”

Section: Introductionmentioning

confidence: 99%

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Shift-current response as a probe of quantum geometry and electron-electron interactions in twisted bilayer graphene

Chaudhary,

Lewandowski,

Refael

2021

Preprint

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Moiré materials, and in particular twisted bilayer graphene (TBG), exhibit a range of fascinating phenomena, that emerge from the interplay of band topology and interactions. We show that the non-linear second-order photoresponse is an appealing probe of this rich interplay. A dominant part of the photoresponse is the shift-current, which is determined by the geometry of the electronic wave-functions and carrier properties, and thus becomes strongly modified by electron-electron interactions. We analyze its dependence on the twist angle and doping, and investigate the role of interactions. In the absence of interactions, the response of the system is dictated by two energy scales: the mean energy of direct transitions between the hole and electron flat bands, and the gap between flat and dispersive bands. Including electron-electron interactions, both enhance the response at the non-interacting characteristic frequencies as well as produce new resonances. We attribute these changes to the filling-dependent band renormalization in TBG. Our results highlight the connection between non-trivial geometric properties of TBG and its optical response, as well as demonstrate how optical probes can access the role of interactions in moiŕe materials.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Shift-current response as a probe of quantum geometry and electron-electron interactions in twisted bilayer graphene

Chaudhary,

Lewandowski,

Refael

2021

Preprint

View full text Add to dashboard Cite

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“…Mathematically, the BCD is an integral of the product of local Berry curvature and velocity over the Fermi surface, so metals with prominent Berry curvature near the Fermi surface are ideal platforms to observe this effect. Under this guiding principle, as band degeneracies are natural sources of divergent Berry curvature, three-dimensional Weyl semimetals [21][22][23][24][25][26][27][28][29][30], two-dimensional transition-metal dichalcogenides [31][32][33][34][35][36][37][38][39][40][41], strained graphene [42][43][44] and topological insulators close to the phase boundary [45], which have either tilted gapless Weyl cones or tilted gapped Dirac cones, have been actively studied both theoretically and experimentally [46,47]. As the nonlinear Hall effect is an effect related to Fermi surface, it is noteworthy that doping is necessary for its observation in pristine gapped systems, such as topological insulators.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Hall effect in two-dimensional class AI metals

Liao,

Zhang,

Yan

2021

Preprint

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In a time-reversal invariant system, while the anomalous Hall effect identically vanishes in the linear response regime due to the constraint of time-reversal symmetry on the distribution of Berry curvature, a nonlinear Hall effect can emerge in the second-order response regime if the inversion symmetry is broken to allow a nonzero Berry curvature dipole (BCD) on the Fermi surface. In this work, we study the nonlinear Hall effect of the BCD origin in two-dimensional doped insulators and semimetals belonging to the symmetry class AI which has spinless time-reversal symmetry. Despite that the class AI does not host any strong topological insulator phase in two dimensions, we find that they can still be classified as topologically obstructed insulators and trivial insulators if putting certain constraint on the Hamiltonians. When the insulator gets closer to the phase boundary of the two distinct phases, we find that the BCDs will become more prominent if the doping level is located near the band edge. Moreover, when the insulator undergoes a phase transition between the two distinct phases, we find that the BCDs will dramatically change their signs. For the semimetals without inversion symmetry, we find that the BCDs will sharply reverse their signs when the doping level crosses the Dirac points. With the shift of the locations of Dirac points in energy, the critical doping level at which the BCDs sharply reverse their signs will accordingly change. Our study reveals that class AI materials can also have interesting geometrical and topological properties, and remarkable nonlinear Hall effect can also appear in this class of materials even though the spin-orbit coupling is negligible. Our findings broaden the scope of materials to study the nonlinear Hall effect and provide new perspectives for the application of this effect.

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“…In recent years, twisted bilayer graphene(TBG) has attracted great attention in condensed matter physics as a novel platform for studying strong correlated phenomena, 1-5 topological properties, 6,7 chiralities, 8,9 and nonlinear Hall effects. 10 The underlying physics arises from flat bands at certain "magic angles", implying strong carrier-carrier interactions. TBG is formed by the relative rotation of two monolayer graphene at a twist angle θ.…”

Section: Introductionmentioning

confidence: 99%

Optical Coherent Injection of Carrier and Current in Twisted Bilayer graphene

Zheng,

Song,

Shan

et al. 2021

Preprint

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We theoretically investigate optical injection processes, including one-and two-photon carrier injection and two-color coherent current injection, in twisted bilayer graphene with moderate angles.The electronic states are described by a continuum model, and the spectra of injection coefficients are numerically calculated for different chemical potentials and twist angles, where the transitions between different bands are understood by the electron energy resolved injection coefficients. The comparison with the injection in monolayer graphene shows the significance of the interlayer coupling in the injection processes. For undoped twisted bilayer graphene, all spectra of injection coefficients can be divided into three energy regimes, which vary with the twist angle. For very low photon energies in the linear dispersion regime, the injection is similar to graphene with a renormalized Fermi velocity determined by the twist angle; for very high photon energies where the interlayer coupling is negligible, the injection is the same as that of graphene; and in the middle regime around the transition energy of the Van Hove singularity, the injection shows fruitful fine structures. Furthermore, the two-photon carrier injection diverges for the photon energy in the middle regime due to the existence of double resonant transitions.

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Giant nonlinear Hall effect in strained twisted bilayer graphene

Cited by 17 publications

References 0 publications

Shift-current response as a probe of quantum geometry and electron-electron interactions in twisted bilayer graphene

Shift-current response as a probe of quantum geometry and electron-electron interactions in twisted bilayer graphene

Nonlinear Hall effect in two-dimensional class AI metals

Optical Coherent Injection of Carrier and Current in Twisted Bilayer graphene

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