Intrinsic planar Hall effect in time-reversal-broken Weyl semimetals

The exotic responses of topological Weyl semimetals (WSMs) probed by electric ($\vec{E}$) and magnetic ($\vec{B}$) fields have been intensively explored recently. In this work, we predict that the intrinsic planar Hall effect (IPHE), in which the $\vec{E}$, $\vec{B}$, and the Hall current share the same plane can emerge in time-reversal-broken WSMs. We reveal that the (field-induced) Berry curvature, arising from the nontrivial band geometry of the WSMs, is responsible for this effect, associated with the energy correction under $\vec{E}$ and $\vec{B}$ up to the second order. Importantly, dictated by the $\vec{k}$-space Lorentz force provided by this (field-induced) Berry curvature, the IPHE conductivity tensor features the anti-symmetric form, quite distinct from its extrinsic counterpart with a symmetric form reported in [\textcolor{blue}{Phys. Rev. Lett. 119, 176804 (2017)}]. Particularly, employing a linearly tilted effective model, the dependence of the IPHE on the tilt direction and the angle formed by $\vec{E}$ and $\vec{B}$ are illuminated. Interestingly, by studying angular dependence, we find that the IPHE responses exist even when $\vec{E}\cdot\vec{B}=0$, indicating that the Berry curvature plays a more fundamental role than the \textit{chiral anomaly} in WSMs. Finally, the candidate materials to detect IPHE and the experimental strategy to distinguish the IPHE response of the WSMs from its extrinsic counterpart is discussed. Our work offers a novel intrinsic topological response function to detect magnetic WSMs and opens a new window to understanding the experimental results observed in magnetic WSMs.Comment: 2 figur

Intrinsic spin Hall effect from spin quantum metric

The intrinsic spin Hall effect (ISHE) proposed in [\href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.92.126603} {Sinova \textit{et al.} Phys. Rev. Lett. \textbf{92}, 126603 (2004)}] is driven by the spin Berry curvature. Herein, we establish the concept of \textit{spin quantum metric}, which is the counterpart of the spin Berry curvature in the \textit{spin quantum geometric tensor} defined in a similar way to the quantum geometric tensor. Dual to the $\mathcal{T}$-even ($\mathcal{T}$, time reversal) spin Berry curvature, the spin quantum metric features a $\mathcal{T}$-odd characteristic. Notably, we show that the $\mathcal{T}$-odd spin quantum metric can also drive an ISHE ($\mathcal{T}$-odd ISHE) under a high-frequency electric field. Guided by symmetry, we evaluate this $\mathcal{T}$-odd ISHE in the magnetically tilted surface Dirac cone and in ferromagnetic monolayer MnBi$_2$Te$_4$. We find that this $\mathcal{T}$-odd ISHE dominates when the Fermi level is close to the band (anti)crossing point, where its magnitude can be as large as the $\mathcal{T}$-even ISHE when an infrared driving field is applied. Our work not only uncovers an indispensable ingredient in the emergent community of quantum geometric physics but also offers a novel mechanism for ultrafast spintronics.Comment: Three figure

Quantifying the photocurrent fluctuation in quantum materials by shot noise

The DC photocurrent can detect the topology and geometry of quantum materials without inversion symmetry. Herein, we propose that the DC shot noise (DSN), as the fluctuation of photocurrent operator, can also be a diagnostic of quantum materials. Particularly, we develop the quantum theory for DSNs in gapped systems and identify the shift and injection DSNs by dividing the second-order photocurrent operator into off-diagonal and diagonal contributions, respectively. Remarkably, we find that the DSNs can not be forbidden by inversion symmetry, while the constraint from time-reversal symmetry depends on the polarization of light. Furthermore, we show that the DSNs also encode the geometrical information of Bloch electrons, such as the Berry curvature and the quantum metric. Finally, guided by symmetry, we apply our theory to evaluate the DSNs in monolayer GeS and bilayer MoS$_2$ with and without inversion symmetry and find that the DSNs can be larger in centrosymmetric phase.Comment: two figure

Classification of spin Hall effect in two-dimensional systems

Physical properties such as the conductivity are usually classified according to the symmetry of the underlying system using Neumann's principle, which gives an upper bound for the number of independent components of the corresponding property tensor. However, for a given Hamiltonian, this global approach usually can not give a definite answer on whether a physical effect such as spin Hall effect (SHE) exists or not. It is found that the parity and types of spin-orbit interactions (SOIs) are good indicators that can further reduce the number of independent components of the spin Hall conductivity for a specific system. In terms of the parity as well as various Rashba-like and Dresselhaus-like SOIs, we propose a local approach to classify SHE in two-dimensional (2D) two-band models, where sufficient conditions for identifying the existence or absence of SHE in all 2D magnetic point groups are presented

Third-order intrinsic anomalous Hall effect with generalized semiclassical theory

The linear intrinsic anomalous Hall effect (IAHE) and second-order IAHE have been intensively investigated in time-reversal broken systems. However, as one of the important members of the nonlinear Hall family, the investigation of third-order IAHE remains absent due to the lack of an appropriate theoretical approach, although the third-order extrinsic AHE has been studied within the framework of first- and second-order semiclassical theory. Herein, we generalize the semiclassical theory for Bloch electrons under the uniform electric field up to the third-order using wavepacket method and based on which we predict that the third-order IAHE can also occur in time-reversal broken systems. Same as the second-order IAHE, we find the band geometric quantity, the second-order field-dependent Berry curvature arising from the second-order field-induced positional shift, plays a pivotal role to observe this effect. Moreover, with symmetry analysis, we find that the third-order IAHE, as the leading contribution, is supported by 15 time-reversal broken 3D magnetic point groups (MPGs), corresponding to a wide class of antiferromagnetic (AFM) materials. Guided by the symmetry arguments, a two-band model is chosen to demonstrate the generalized theory. Furthermore, the generalized third-order semiclassical theory depends only on the properties of Bloch bands, implying that it can also be employed to explore the IAHE in realistic AFM materials, by combining with first-principles calculations.Comment: 1 figur

On the equivalence of the semiclassical theory and the response theory

It is commonly believed that the response theory can give quantum correction (or interband coherent effects) to the semiclassical theory, while both formulations essentially are perturbatively solving the time-dependent Sch\"odinger equation in a periodic potential probed by the electric field within the independent-particle approximation. Herein, by extending the semiclassical theory under an AC uniform electric field to the nonlinear regime, we show that up to the second order of the electric field, the AC semiclassical theory is equivalent to the response theory in the absence of relaxation. Remarkably, this equivalence can be inherited when the relaxation is incorporated into the response theory, particularly by taking the semiclassical results with a finite relaxation time obtained by solving the Boltzmann equation as a benchmark. ......Comment: add a section for the nonlinear AC responses and reshape the main conclusion

Intrinsic time-reversal-even linear displacement Hall effect

Ruled by the time-reversal-odd ($\mathcal{T}$-odd) nature of linear DC conductivity, the intrinsic linear Hall effect is forbidden by $\mathcal{T}$-symmetry. Herein, inspired by the intimate connection between displacement current and electric polarization, we predict the intrinsic $\mathcal{T}$-even linear displacement Hall effect (LDHE), which refers to an intrinsic transverse displacement current response in $\mathcal{T}$-invariant systems by applying a longitudinal AC electric field. Particularly, we develop the quantum theory for displacement current under an AC electric field. We find that the displacement current conductivity (DCC), arising from the AC polarization, contains both the $\mathcal{T}$-even and $\mathcal{T}$-odd contributions, which are closely related to the quantum metric and Berry curvature of Bloch electrons, respectively. Furthermore, by symmetry analysis, we find that the $\mathcal{T}$-even DCC can favor a transverse component and hence allows the intrinsic LDHE in $\mathcal{T}$-invariant systems. We also confirm that our formulation recovers the result of semiclassical theory in the adiabatic limit. Additionally, guided by symmetry, two models are used to illustrate our theory. Finally, the candidate materials to capture the intrinsic LDHE in $\mathcal{T}$-invariant systems are proposed.Comment: 2 figure

Dissipationless gyrotropic magnetic Hall effect

A dissipationless longitudinal current can be generated by a pure magnetic field through the chiral magnetic effect. Herein, we propose that a pure oscillating magnetic field through Zeeman coupling can further drive an AC magnetic Hall current in two-dimensional systems without inversion symmetry. We dub this effect the "gyrotropic magnetic Hall effect" (GMHE), in analogy with the gyrotropic current achieved by rectifying the optical fields. Importantly, we find that the GMHE conductivity is a reactive or dissipationless transport coefficient, which is even under time-reversal symmetry. We reveal the "Zeeman Berry curvature" as the quantum origin of the GMHE, whose integral over all states below the Fermi energy gives the GMHE conductivity. Furthermore, by symmetry analysis, we show that the GMHE can appear in a wide range of two-dimensional materials. To demonstrate our proposal, we evaluate the GMHE current in two-dimensional Rashba system and in the surface of topological insulator, where a low-frequency magnetic field with a small amplitude can be converted into a detectable Hall voltage

Gapless superconducting state and mirage gap in altermagnets

The interplay between spin-orbit interaction (SOI) and magnetism produces interesting phenomena in superconductors. When a two-dimensional (2D) system with strong SOI is coupled to an $s$-wave superconductor, an in-plane magnetic field can drive the system into a gapless superconducting state and induce a mirage gap at finite energies for an Ising superconductor. In this work, we demonstrate that when an $s$-wave superconductor is proximitized to an altermagnet, the intrinsic anisotropic spin splitting of the altermagnet can result in a gapless superconducting state and a pair of mirage gaps at finite energy. The gapless superconductivity exhibits spin-polarized segmented Fermi surfaces, with coexisting spin-singlet and spin-triplet pairings that have a $d$-wave character. Importantly, the gapless superconducting and mirage gap features are quantified through quantum transport. Our results suggest that altermagnet is an ideal platform for studying gapless superconducting states and mirage gap physics.Comment: This work has been accepted by PRB Lette