Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time-Reversal Invariant Materials.

By I. Sodemann, Liang Fu. Physical Review Letters, 2015

814 citations recorded by the source corpus.

It is well known that a nonvanishing Hall conductivity requires broken time-reversal symmetry. However, in this work, we demonstrate that Hall-like currents can occur in second-order response to external electric fields in a wide class of time-reversal invariant and inversion breaking materials, at both zero and twice the driving frequency. This nonlinear Hall effect has a quantum origin arising from the dipole moment of the Berry curvature in momentum space, which generates a net anomalous velocity when the system is in a current-carrying state. The nonlinear Hall coefficient is a rank-two pseudotensor, whose form is determined by point group symmetry. We discus optimal conditions to observe this effect and propose candidate two- and three-dimensional materials, including topological crystalline insulators, transition metal dichalcogenides, and Weyl semimetals.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/57783e8ffe450e2d43e76a10ac6425e368c33d51

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Ashvin Vishwanath
2. N. P. Armitage
3. Hsin Lin
4. J. Moore
5. E. Mele
6. N. Nagaosa
7. Cheng Guo
8. Bo Zhao

In Materials Chemistry

1. Ashvin Vishwanath
2. J. Moore
3. Hsin Lin
4. N. P. Armitage
5. Jun-Woo Ahn
6. N. Nagaosa
7. E. Mele
8. T. Morimoto

Citations in the corpus

• Weyl and Dirac semimetals in three-dimensional solids (2017, background): “Other effects have been proposed such as a nonlinear Hall effect arising from an effective dipole moment of the Berry curvature in momentum space (Sodemann and Fu, 2015) and a photoinduced anomalous Hall effect(Chan et al., 2016) for WSMs and photogalvanic effects (Cortijo, 2016b) in DSMs.”
• Flat bands, strange metals and the Kondo effect (2023, neutral): “Twisted bilayers”
• Quantized circular photogalvanic effect in Weyl semimetals (2016, background): “[35] Inti Sodemann and Liang Fu, “Quantum nonlinear hall effect induced by berry curvature dipole in time-reversal invariant materials,” Phys.”
• Light control with Weyl semimetals (2022, background): “Nonlinear responses of topological materials have only been investigated recently [11, 182–190]; a systematic discussion is beyond the scope of this paper.”
• Direct optical detection of Weyl fermion chirality in a topological semimetal (2017, background): “Apart from the present study and the proposed anomaly related physics [13, 18, 23–26], the nontrivial Berry curvatures in WSMs can also lead to various novel optical phenomena such as photocurrents [19–21], Hall voltages [22], Kerr rotations [20], and second harmonic generations [20, 21].”
• Low-Frequency Divergence and Quantum Geometry of the Bulk Photovoltaic Effect in Topological Semimetals (2020, background): “(36) has the form of the Berry curvature dipole [61] and the quantum metric dipole [62], respectively.”
• Riemannian geometry of resonant optical responses (2021, background): “As we show in Supplementary Note 3, w 1 = w n 1 − w 1 , (63) where w 1 and w m 1 are the first Stiefel-Whitney numbers of bands n and m, or equivalently, the Berry phases of bands n and m divided by π [3, 4].”