Dissipation and geometry in nonlinear quantum transports of multiband electronic systems

Nonlinear electrical response permits a unique window into effects of band structure geometry. It can be calculated either starting from a Boltzmann approach for small frequencies, or using Kubo’s formula for resonances at finite frequency. However, a precise connection between both approaches has not been established. Focusing on the second order nonlinear response, here we show how the semiclassical limit can be recovered from perturbation theory in the velocity gauge, provided that finite quasiparticle lifetimes are taken into account. We find that matrix elements related to the band geometry combine in this limit to produce the semiclassical nonlinear conductivity. We demonstrate the power of the new formalism by deriving a quantum contribution to the nonlinear conductivity which is of order \tau^{-1}τ−1 in the relaxation time \tauτ, which is principally inaccessible within the Boltzmann approach. We outline which steps can be generalized to higher orders in the applied perturbation, and comment about potential experimental signatures of our results.

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“…Finally, the space-time classification of table 3 remains meaningful even when taking into account the extrinsic mechanism (Watanabe and Yanase 2020, Ma et al 2023a); in other words, the (conventional) skew-scattering and sidejump effects of equation ( 51) vanishes by the PT symmetry, while the anomalous skew-scattering effect survives in the PT -symmetric system due to its T -odd and PTeven nature. The classification is similarly extended to cover the self-energy effect as corroborated in the Green's-function fashion (Michishita and Nagaosa 2022).…”

Section: Nonlinear Drudementioning

confidence: 99%

Magnetic parity violation and parity-time-reversal-symmetric magnets

Watanabe,

Yanase

2024

J. Phys.: Condens. Matter

1

0

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Parity-time-reversal symmetry ( PT symmetry), a symmetry for the combined operations of space inversion ( P ) and time reversal ( T ), is a fundamental concept of physics and characterizes the functionality of materials as well as P and T symmetries. In particular, the PT -symmetric systems can be found in the centrosymmetric crystals undergoing the parity-violating magnetic order which we call the odd-parity magnetic multipole order. While this spontaneous order leaves PT symmetry intact, the simultaneous violation of P and T symmetries gives rise to various emergent responses that are qualitatively different from those allowed by the nonmagnetic P -symmetry breaking or by the ferromagnetic order. In this review, we introduce candidates hosting the intriguing spontaneous order and overview the characteristic physical responses. Various off-diagonal and/or nonreciprocal responses are identified, which are closely related to the unusual electronic structures such as hidden spin-momentum locking and asymmetric band dispersion.

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“…All the formulas comprise the Fermi-surface effect ∂ ε f (ε), and hence the above intrinsic mechanisms are allowed in conductors and prohibited in insulators. The derivations have been presented in the density-matrix formalism (Kaplan et al, 2022;Matsyshyn and Sodemann, 2019;Watanabe and Yanase, 2020;Yatsushiro et al, 2022) and diagrammatic approach (João and Viana Parente Lopes, 2020;Michishita and Nagaosa, 2022;Oiwa and Kusunose, 2022). Since the intraband matrix element of the velocity operator is given as v a pp = ∂ ka ε ka in the band-electron system, only the band energy ε kp is relevant to the nonlinear Drude effect.…”

Section: Nonreciprocal Conductivitymentioning

confidence: 99%

“…The nonreciprocal conductivity shows the richer property when one goes beyond the independent-particle approximation such as by taking account of the electron-correlation and disorder-scattering effects (Isobe et al, 2020;Kappl et al, 2023;Kofuji et al, 2021;Michishita and Nagaosa, 2022;. For instance, the scattering event occurs in the presence of impurities (Du et al, 2019;Ma et al, 2023a;Nandy and Sodemann, 2019;Xiao et al, 2019), spin degree of freedom (Ishizuka and Nagaosa, 2020;Yasuda et al, 2017), and magnetic-multipolar object (Isobe and Nagaosa, 2022;Liu et al, 2022).…”

Section: Nonreciprocal Conductivitymentioning

confidence: 99%

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Photocurrent response in parity-time symmetric current-ordered states

Watanabe

¹

,

Yanase

²

2021

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Parity-time-reversal symmetry (PT symmetry), a symmetry for the combined operations of space inversion (P) and time reversal (T ), is a fundamental concept of physics and characterizes the functionality of materials as well as P and T symmetries. In particular, the PT -symmetric systems can be found in the centrosymmetric crystals undergoing the parity-violating magnetic order which we call the odd-parity magnetic multipole order. While this spontaneous order leaves PT symmetry intact, the simultaneous violation of P and T symmetries gives rise to various emergent responses that are qualitatively different from those allowed by the nonmagnetic P-symmetry breaking or by the ferromagnetic order. In this review, we introduce candidates hosting the intriguing spontaneous order and overview the characteristic physical responses. Various off-diagonal and/or nonreciprocal responses are identified, which are closely related to the unusual electronic structures such as hidden spin-momentum locking and asymmetric band dispersion. Contents I. Introduction II. Magnetic Parity Violation and Space-Time Symmetry A. Parity-time-reversal symmetry and parity violations B. Hidden Magnetic Degrees of Freedom in Crystals C. Multipolar degree of freedom of visible antiferromagnets III. Emergent Responses of PT -symmetric magnets A. Electric-Magnetic Classification of Response Function B. Magnetic Counterpart of Piezoelectric Effect C. Nonreciprocal Property of Electronic Transport and Optical Response 1. Nonreciprocal conductivity 2. Photocurrent generation IV. Availability of PT -symmetric Magnets and Physical Properties A. Switching the compensated magnets B. Control of electronic property with PT -symmetric magnetic order V.

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Dissipation and geometry in nonlinear quantum transports of multiband electronic systems

Cited by 23 publications

References 50 publications

Unifying semiclassics and quantum perturbation theory at nonlinear order

Unifying semiclassics and quantum perturbation theory at nonlinear order

Magnetic parity violation and parity-time-reversal-symmetric magnets

Photocurrent response in parity-time symmetric current-ordered states

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