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Nodal line semimetals, a class of topological quantum materials, exhibit a variety of novel phenomena due to their properties, such as bands touching on a one-dimensional line or a ring in the Brillouin zone and drumheadlike surface states. In addition, these semimetals are protected by the combined space-inversion and time-reversal (𝒫𝒯) symmetries. In this study, we investigate the longitudinal dc conductivity of the Dirac nodal line semimetals for the broken 𝒫𝒯-symmetric system by the mass term. Here, using the quantum kinetic technique, we find the intrinsic (field-driven) and extrinsic (scattering-driven) contributions to the total dc conductivity due to interband effects. Interestingly, the resulting intrinsic conductivity is the Fermi-sea contribution, while the extrinsic stems from the Fermi-surface contribution. We show that at low chemical potential, the extrinsic part contributes more and dominates over the traditional Drude intraband term, while at the high chemical potential, the intrinsic conductivity contributes. Furthermore, the total dc response due to interband effects saturates at high chemical potential and its strength decreases with increasing mass value. Our findings suggest that the extrinsic contributions are rich enough to understand the overall feature of the response for the three-dimensional system.
Nodal line semimetals, a class of topological quantum materials, exhibit a variety of novel phenomena due to their properties, such as bands touching on a one-dimensional line or a ring in the Brillouin zone and drumheadlike surface states. In addition, these semimetals are protected by the combined space-inversion and time-reversal (𝒫𝒯) symmetries. In this study, we investigate the longitudinal dc conductivity of the Dirac nodal line semimetals for the broken 𝒫𝒯-symmetric system by the mass term. Here, using the quantum kinetic technique, we find the intrinsic (field-driven) and extrinsic (scattering-driven) contributions to the total dc conductivity due to interband effects. Interestingly, the resulting intrinsic conductivity is the Fermi-sea contribution, while the extrinsic stems from the Fermi-surface contribution. We show that at low chemical potential, the extrinsic part contributes more and dominates over the traditional Drude intraband term, while at the high chemical potential, the intrinsic conductivity contributes. Furthermore, the total dc response due to interband effects saturates at high chemical potential and its strength decreases with increasing mass value. Our findings suggest that the extrinsic contributions are rich enough to understand the overall feature of the response for the three-dimensional system.
We investigate the intrinsic linear and nonlinear ac orbital Hall (OH) conductivity in a two-dimensional system, arising from the transverse motion of electrons with finite orbital angular momentum in an applied electric field. Using the quantum kinetic approach, we show that the total OH conductivity comprises both interband and intraband contributions. However, the interband contribution dominates over the intraband in the high frequency regime. Our analysis predicts that the interband part of the linear OH conductivity is governed by the Fermi sea contribution. Meanwhile the nonlinear responses, including second harmonic and rectification effects, stem from the interplay between the Fermi sea and Fermi surface contributions. We find that the broken inversion symmetry in the system yields nonzero orbital angular momentum and consequently the orbital Hall response. In addition, the linear OH conductivity exhibits a resonant peak and a sign transition depending on the gap and Fermi energy values relative to the incident energy. Unlike the linear, the second harmonic OH conductivity shows two sign conversions as the incident energy approaches to the gap value and twice its value. These findings shed light on the modulation of field-driven orbital Hall conductivity with frequency, Fermi energy, and band gap.
We investigate the intrinsic linear and nonlinear ac orbital Hall (OH) conductivity in a two-dimensional system, arising from the transverse motion of electrons with finite orbital angular momentum in an applied electric field. Using the quantum kinetic approach, we show that the total OH conductivity comprises both interband and intraband contributions. However, the interband contribution dominates over the intraband in the high frequency regime. Our analysis predicts that the interband part of the linear OH conductivity is governed by the Fermi sea contribution. Meanwhile the nonlinear responses, including second harmonic and rectification effects, stem from the interplay between the Fermi sea and Fermi surface contributions. We find that the broken inversion symmetry in the system yields nonzero orbital angular momentum and consequently the orbital Hall response. In addition, the linear OH conductivity exhibits a resonant peak and a sign transition depending on the gap and Fermi energy values relative to the incident energy. Unlike the linear, the second harmonic OH conductivity shows two sign conversions as the incident energy approaches to the gap value and twice its value. These findings shed light on the modulation of field-driven orbital Hall conductivity with frequency, Fermi energy, and band gap.
In this theoretical investigation, we analyze light-induced nonlinear spin Hall currents in a gated single-layer 1T-WTe2, flowing transversely to the incident laser polarization direction. Our study encompasses the exploration of the second and third-order rectified spin Hall currents using an effective low-energy Hamiltonian and employing the Kubo’s formalism. We extend our analysis to a wide frequency range spanning both transparent and absorbing regimes, investigating the influence of light frequency below and above the optical band gap. Additionally, we investigate the influence of an out-of-plane gate potential on the system, disrupting inversion symmetry and effectively manipulating both the strength and sign of nonlinear spin Hall responses. We predict a pronounced third-order spin Hall current relative to its second-order counterpart. The predicted nonlinear spin currents show strong anisotropic dependence on the laser polarization angle. The outcomes of our study contribute to a generalized framework for nonlinear response theory within the spin channel will impact the development of emerging field of opto-spintronic.
In this theoretical investigation, we analyze light-induced nonlinear spin Hall currents in a gated single-layer 1T-WTe2, flowing transversely to the incident laser polarization direction. Our study encompasses the exploration of the second and third-order rectified spin Hall currents using an effective low-energy Hamiltonian and employing the Kubo’s formalism. We extend our analysis to a wide frequency range spanning both transparent and absorbing regimes, investigating the influence of light frequency below and above the optical band gap. Additionally, we investigate the influence of an out-of-plane gate potential on the system, disrupting inversion symmetry and effectively manipulating both the strength and sign of nonlinear spin Hall responses. We predict a pronounced third-order spin Hall current relative to its second-order counterpart. The predicted nonlinear spin currents show strong anisotropic dependence on the laser polarization angle. The outcomes of our study contribute to a generalized framework for nonlinear response theory within the spin channel will impact the development of emerging field of opto-spintronic.
The quantum kinetic framework provides a versatile method for investigating the dynamical optical and transport currents of crystalline solids. In this paper, starting from the density-matrix equations of motion, we present a general theoretical path to obtain the nonlinear optical response in an elegant and transparent manner. We devise an extensive kinetic theory that can be applied to materials with arbitrary band structures and captures intraband and interband coherence effects, finite Fermi surfaces, and disorder effects. We present a classification of the nonlinear optical currents arising from the interference of the interband and intraband components of the density matrix with distinct symmetry and quantum geometrical origin for each contribution. In this context, we report the following four primary findings: (i) The Fermi golden rule approach is insufficient to derive the correct expression for the injection current, a shortcoming that we remedy in our theory while associating the injection current with the intraband-interband contribution to the second-order density matrix. (ii) The interband-intraband contribution yields a resonant current that survives irrespective of any symmetry constraint in addition to the well-known anomalous nonlinear current (nonresonant), which requires time-reversal symmetry. (iii) Quite generally, the nonlinear current is significantly enhanced by contributions arising from the finite Fermi surface. (iv) The finite Fermi surface and Fermi sea additionally lead to sizable novel nonlinear effects via contributions we term double resonant and higher-order pole. We investigate such effects in sum frequency and difference frequency generation. As an illustration, we compute the nonlinear response of the topological antiferromagnet CuMnAs and thin film tilted Weyl semimetals as model systems dominated by interband coherence contributions. We find that the nonlinear response of CuMnAs is responsive to the direction of the finite magnetization field and the response of Weyl semimetal to the tilt. In addition, the choice of the polarization angle of the beam is crucial to have a nonlinear current in CuMnAs, while it is not the case for Weyl semimetals.
The quantum kinetic framework provides a versatile method for investigating the dynamical optical and transport currents of crystalline solids. In this paper, starting from the density-matrix equations of motion, we present a general theoretical path to obtain the nonlinear optical response in an elegant and transparent manner. We devise an extensive kinetic theory that can be applied to materials with arbitrary band structures and captures intraband and interband coherence effects, finite Fermi surfaces, and disorder effects. We present a classification of the nonlinear optical currents arising from the interference of the interband and intraband components of the density matrix with distinct symmetry and quantum geometrical origin for each contribution. In this context, we report the following four primary findings: (i) The Fermi golden rule approach is insufficient to derive the correct expression for the injection current, a shortcoming that we remedy in our theory while associating the injection current with the intraband-interband contribution to the second-order density matrix. (ii) The interband-intraband contribution yields a resonant current that survives irrespective of any symmetry constraint in addition to the well-known anomalous nonlinear current (nonresonant), which requires time-reversal symmetry. (iii) Quite generally, the nonlinear current is significantly enhanced by contributions arising from the finite Fermi surface. (iv) The finite Fermi surface and Fermi sea additionally lead to sizable novel nonlinear effects via contributions we term double resonant and higher-order pole. We investigate such effects in sum frequency and difference frequency generation. As an illustration, we compute the nonlinear response of the topological antiferromagnet CuMnAs and thin film tilted Weyl semimetals as model systems dominated by interband coherence contributions. We find that the nonlinear response of CuMnAs is responsive to the direction of the finite magnetization field and the response of Weyl semimetal to the tilt. In addition, the choice of the polarization angle of the beam is crucial to have a nonlinear current in CuMnAs, while it is not the case for Weyl semimetals.
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