arXiv subjects

C. M. Wang

Publications and source records attributed to C. M. Wang.

At least 19 recordsLinked to original sources

arXiv2026

Nonlinear Ohmic electromagnetic response

We systematically investigate nonlinear Ohmic responses in second-harmonic generation and bilinear magnetoelectric effects within the Matsubara Green's function formalism. The optical nonlinear Ohmic conductivity is shown to consist of a nonlinear Drude-like part and an intrinsic term determined by the fully symmetrized normalized quantum metric dipole. Notably, we predict a previously unrecognized intrinsic Ohmic conductivity arising from band geometry in the bilinear magnetoelectric response, which exhibits transverse behavior similar to its optical counterpart. Using a two-dimensional Dirac model, we demonstrate that this geometrically induced nonlinear Ohmic response is observable in materials with high Fermi velocity and narrow band gaps. Our work provides a systematic quantum field-theoretic framework for describing nonlinear Ohmic transport in condensed matter systems.

cond-mat.mes-hall↗

arXiv2025

Quantum theory of nonlinear electromagnetic response

In recent years, the investigation of nonlinear electromagnetic responses has received significant attention due to its potential for elucidating the quantum properties of matter. Although remarkable progress has been achieved in developing quantum theories of nonlinear responses to electric field, a comprehensive quantum theory framework that systematically addresses nonlinear responses to both electric and magnetic fields has yet to be thoroughly discussed. Here, we present a systematic quantum theory of nonlinear electromagnetic response using the Matsubara Green's function approach, which explicitly incorporates the wave vector dependence of external electromagnetic fields. We provide diagrammatic representation and reveal the general properties of transport coefficients. We apply our theory to second-order responses, deriving the nonlinear Hall effects and magneto-nonlinear Hall effects in both time-reversal symmetric and time-reversal breaking systems. These effects stem from diverse quantum geometric quantities. Additionally, we analyze the contributions arising from the Zeeman interaction. Our work presents a unified quantum theory of nonlinear electromagnetic response, paving the way for further exploration of novel phenomena in this field.

cond-mat.mes-hall↗

arXiv2025

Quantum oscillation in Hopf-link semimetals

Since the discovery of the relation between the Chern number and quantum Hall effect, searching for observables of topological invariants has been an intriguing topic. Topological Hopf-link semimetals have attracted tremendous interest, in which the conduction and valence energy bands touch at linked nodal lines. However, it is challenging to identify this sophisticated topology. We propose to use the quantum oscillation in strong magnetic fields to probe the Hopf links. For a generic model of Hopf-link semimetal that captures the linked-trivial phase transition, we figure out the phase shifts of oscillation for all Fermi pockets in all magnetic-field directions, by presenting self-consistent results from the Fermi surface tomography, Landau fan diagram, and electrical resistivity. As the magnetic field is rotated, the phase shifts exhibit a unique pattern, which could help to identify Hopf links in real materials, such as those in Li$_2$NaN.

cond-mat.mes-hall↗

arXiv2024

Thermoelectric transport of the coexistence topological semimetal in the quantum limit

We explore the thermoelectric transport properties of a coexistence topological semimetal, characterized by the presence of both a pair of Weyl points and a nodal ring in the quantum limit. This system gives rise to complex Landau bands when subjected to a magnetic field aligned with the direction connecting two Weyl points. In the longitudinal configuration, where the magnetic field is parallel to the electric field or the temperature gradient, the thermoelectric conductivity indicates a plateau independent of the magnetic field and the Fermi energy at $δ$-form short-range scattering. This platform structure should also exist in pure two-node Weyl semimetals. However, the thermoelectric conductivity and the Seebeck coefficient are significantly influenced by the parameters of long-ranged Gaussian or screened Coulomb scattering potentials for both fixed carrier density and Fermi energy scenarios. In the transverse configuration, both Gaussian and screened Coulomb scatterings yield substantial positive magnetoresistance and thermoelectric conductance. Since the Hall conductivity is larger than the longitudinal one, the Seebeck coefficient, exhibiting a quadratic increase with the magnetic field, is close to the dissipationless limit irrespective of scatterings, while the Nernst response is notably dependent on the scattering mechanism. Additionally, the model parameter, distinct from the two-node Weyl model, influences the thermoelectric transport properties. The magnetic field response of the thermoelectric coefficients to different scattering potentials can be used as a basis for distinguishing scattering mechanisms in materials.

cond-mat.mes-hall↗

arXiv2024

Quantized Hall conductance in 3D topological nodal-line semimetals without chiral symmetry

A quantized Hall conductance (not conductivity) in three dimensions has been searched for more than 30 years. Here we explore it in 3D topological nodal-line semimetals, by using a model capable of describing all essential physics of a semimetal, in particular the drumhead surface states protected by a momentum-dependent winding number. We develop a microscopic theory to demonstrate that the drumhead surface states can host quantized Hall conductance in this 3D material. We stress that breaking chiral symmetry is necessary for the quantum Hall effect of the drumhead surface states. The analytic theory can be verified numerically by the Kubo formula. There may also be trivial quantum Hall effects from the bulk states. We propose an experimental setup to distinguish the surface and bulk quantum Hall effects. The theory will be useful for ongoing explorations on nodal-line semimetals.

cond-mat.mes-hall↗

arXiv2023

Absence of the anomalous Hall effect in planar Hall experiments

Recently, the planar Hall effect has attracted tremendous interest. In particular, an in-plane magnetization can induce an anomalous planar Hall effect with a $2π/3$ period for hexagon-warped energy bands. This effect is similar to the anomalous Hall effect resulting from an out-of-plane magnetization. However, this anomalous planar Hall effect is absent in the planar Hall experiments. Here, we explain its absence, by performing a calculation that includes not only the Berry curvature mechanism as those in the previous theories, but also the disorder contributions. The conventional $π$-period planar Hall effect will occur if the mirror reflection symmetry is broken, which buries the anomalous one. We show that an in-plane strain can enhance the anomalous Hall conductivity and changes the period from $2π/3$ to $2π$. We propose a scheme to extract the hidden anomalous planar Hall conductivity from the experimental data. Our work will be helpful in detecting the anomalous planar Hall effect and could be generalized to understand mechanisms of the planar Hall effects in a wide range of materials.

cond-mat.mes-hall↗

arXiv2021

Quantum theory of the nonlinear Hall effect

The nonlinear Hall effect is an unconventional response, in which a voltage can be driven by two perpendicular currents in the Hall-bar measurement. Unprecedented in the family of the Hall effects, it can survive time-reversal symmetry but is sensitive to the breaking of discrete and crystal symmetries. It is a quantum transport phenomenon that has deep connection with the Berry curvature. However, a full quantum description is still absent. Here we construct a quantum theory of the nonlinear Hall effect by using the diagrammatic technique. Quite different from nonlinear optics, nearly all the diagrams account for the disorder effects, which play decisive role in the electronic transport. After including the disorder contributions in terms of the Feynman diagrams, the total nonlinear Hall conductivity is enhanced but its sign remains unchanged for the 2D tilted Dirac model, compared to the one with only the Berry curvature contribution. We discuss the symmetry of the nonlinear conductivity tensor and predict a pure disorder-induced nonlinear Hall effect for point groups $C_{3}$, $C_{3h}$, $C_{3v}$, $D_{3h}$, $D_{3}$ in 2D, and $T$, $T_{d}$, $C_{3h}$, $D_{3h}$ in 3D. This work will be helpful for explorations of the topological physics beyond the linear regime.

cond-mat.mes-hall↗

arXiv2021

Field-Tunable One-Sided Higher-Order Topological Hinge States in Dirac Semimetals

Recently, higher-order topological matter and 3D quantum Hall effects have attracted great attention. The Fermi-arc mechanism of the 3D quantum Hall effect proposed in Weyl semimetals is characterized by the one-sided hinge states, which do not exist in all the previous quantum Hall systems and more importantly pose a realistic example of the higher-order topological matter. The experimental effort so far is in the Dirac semimetal Cd$_3$As$_2$, where however time-reversal symmetry leads to hinge states on both sides of the top/bottom surfaces, instead of the aspired one-sided hinge states. We propose that under a tilted magnetic field, the hinge states in Cd$_3$As$_2$-like Dirac semimetals can be one-sided, highly tunable by field direction and Fermi energy, and robust against weak disorder. Furthermore, we propose a scanning tunneling Hall measurement to detect the one-sided hinge states. Our results will be insightful for exploring not only the quantum Hall effects beyond two dimensions, but also other higher-order topological insulators in the future.

cond-mat.mes-hall↗

arXiv2021

Quantum Hall effect originated from helical edge states in Cd$_3$As$_2$

The recent experimental observations of the quantum Hall effect in 3D topological semimetals have attracted great attention, but there are still debates on its origin. We systematically study the dependence of the quantum Hall effect in topological semimetals on the thickness, Fermi energy, and growth direction, taking into account the contributions from the Fermi-arc surface states, confinement-induced bulk subbands, and helical side-surface edge states. In particular, we focus on the intensively studied Dirac semimetal Cd$_{3}$As$_{2}$ and its slabs grown along experimentally accessible directions, including [001], [110], and [112]. We reveal an ignored mechanism from the Zeeman splitting of the helical edge states, which along with Fermi-arc 3D quantum Hall effect, may give a non-monotonic dependence of the Hall conductance plateaus on the magnetic field in the most experimentally studied [112] direction slab. Our results will be insightful for exploring the quantum Hall effects beyond two dimensions.

cond-mat.mes-hall↗

arXiv2020

Analytical solution for the surface states of antiferromagnetic topological insulator MnBi$_2$Te$_4$

Recently, the intrinsic magnetic topological insulator MnBi$_2$Te$_4$ has attracted great attention. It has an out-of-plane antiferromagnetic order, which is believed to open a sizable energy gap in the surface states. This gap, however, was not always observable in the latest angle-resolved photoemission spectroscopy (ARPES) experiments. To address this issue, we analytically derive an effective model for the two-dimensional (2D) surface states by starting from a three-dimensional (3D) Hamiltonian for bulk MnBi$_2$Te$_4$ and taking into account the spatial profile of the bulk magnetization. Our calculations suggest that the diminished surface gap may be caused by a much smaller and more localized intralayer ferromagnetic order. In addition, we calculate the spatial distribution and penetration depth of the surface states, which indicates that the surface states are mainly embedded in the first two septuple layers from the terminating surface. From our analytical results, the influence of the bulk parameters on the surface states can be found explicitly. Furthermore, we derive a $\bf{k}\cdot \bf{p}$ model for MnBi$_2$Te$_4$ thin films and show the oscillation of the Chern number between odd and even septuple layers. Our results will be helpful for the ongoing explorations of the MnBi$_x$Te$_y$ family.

cond-mat.mes-hall↗

arXiv2020

Theory for the Charge-Density-Wave Mechanism of 3D Quantum Hall Effect

The charge-density-wave (CDW) mechanism of the 3D quantum Hall effect has been observed recently in ZrTe$_5$ [Tang et al., Nature 569, 537 (2019)]. Different from previous cases, the CDW forms on a one-dimensional (1D) band of Landau levels, which strongly depends on the magnetic field. However, its theory is still lacking. We develop a theory for the CDW mechanism of 3D quantum Hall effect. The theory can capture the main features in the experiments. We find a magnetic field induced second-order phase transition to the CDW phase. We find that electron-phonon interactions, rather than electron-electron interactions, dominate the order parameter. We extract the electron-phonon coupling constant from the non-Ohmic I-V relation. We point out a commensurate-incommensurate CDW crossover in the experiment. More importantly, our theory explores a rare case, in which a magnetic field can induce an order-parameter phase transition in one direction but a topological phase transition in other two directions, both depend on one magnetic field.

cond-mat.mes-hall↗

arXiv2020

Quantum oscillation beyond the quantum limit in pseudospin Dirac materials

Recently, many unexpected fine structures in electric, magnetic, and thermoelectric responses at extremely magnetic fields in topological materials have attracted tremendous interest. We propose a new mechanism of quantum oscillation beyond the strong-field quantum limit for Dirac fermions. The amplitude of the oscillation is far larger than the usual Shubnikov--de Haas oscillation. The oscillation tends to be periodic in the magnetic field B, instead of 1/B. The period of the oscillation does not depend on the Fermi energy. These behaviors cannot be described by the famous Lifshitz-Kosevich formula. The oscillation arises from a mechanism that we refer to as the inversion of the lowest Landau level, resulted from the competition between the pseudospin Dirac-type Landau levels and real-spin Zeeman spitting beyond the quantum limit. This inversion gives rise to the oscillation of the Fermi energy and conductivity at extremely large magnetic fields. This mechanism will be useful for understanding the unexpected fine structures observed in the strong-field quantum limit in Dirac materials.

cond-mat.mes-hall↗

arXiv2019

Anomalous thermoelectric effects of ZrTe$_{5}$ in and beyond the quantum limit

Thermoelectric effects are more sensitive and promising probes to topological properties of emergent materials, but much less addressed compared to other physical properties. Zirconium pentatelluride (ZrTe$_{5}$) has inspired active investigations recently because of its multiple topological nature. We study the thermoelectric effects of ZrTe$_{5}$ in a magnetic field and find several anomalous behaviors. The Nernst response has a steplike profile near zero field when the charge carriers are electrons only, suggesting the anomalous Nernst effect arising from a nontrivial profile of Berry curvature. Both the thermopower and Nernst signal exhibit exotic peaks in the strong-field quantum limit. At higher magnetic fields, the Nernst signal has a sign reversal at a critical field where the thermopower approaches to zero. We propose that these anomalous behaviors can be attributed to the Landau index inversion, which is resulted from the competition of the $\sqrt{B}$ dependence of the Dirac-type Landau bands and linear-$B$ dependence of the Zeeman energy ($B$ is the magnetic field). Our understanding to the anomalous thermoelectric properties in ZrTe$_{5}$ opens a new avenue for exploring Dirac physics in topological materials.

cond-mat.mtrl-sci↗

arXiv2019

Disorder-induced nonlinear Hall effect with time-reversal symmetry

The nonlinear Hall effect has opened the door towards deeper understanding of topological states of matter. It can be observed as the double-frequency Hall voltage response to an ac longitudinal current in the presence of time-reversal symmetry. Disorder plays indispensable roles in various linear Hall effects, such as the localization in the quantized Hall effects and the extrinsic mechanisms of the anomalous, spin, and valley Hall effects. Unlike in the linear Hall effects, disorder enters the nonlinear Hall effect even in the leading order. However, the disorder-induced contribution to the nonlinear Hall effect has not been addressed. Here, we derive the formulas of the nonlinear Hall conductivity in the presence of disorder scattering. We apply the formulas to calculate the nonlinear Hall response of the tilted 2D Dirac model, which is the symmetry-allowed minimal model for the nonlinear Hall effect and can serve as a building block in realistic band structures. More importantly, we construct the general scaling law of the nonlinear Hall effect, which may help in experiments to distinguish disorder-induced contributions to the nonlinear Hall effect. This work will be instructive for exploring unconventional responses upon breaking discrete or crystal symmetries in emergent physical systems and materials.

cond-mat.mes-hall↗

arXiv2018

Band signatures for strong nonlinear Hall effect in bilayer WTe$_2$

Unconventional responses upon breaking discrete or crystal symmetries open avenues for exploring emergent physical systems and materials. By breaking inversion symmetry, a nonlinear Hall signal can be observed, even in the presence of time-reversal symmetry, quite different from the conventional Hall effects. Low-symmetry two-dimensional materials are promising candidates for the nonlinear Hall effect, but it is less known when a strong nonlinear Hall signal can be measured, in particular, its connections with the band-structure properties. By using model analysis, we find prominent nonlinear Hall signals near tilted band anticrossings and band inversions. These band signatures can be used to explain the strong nonlinear Hall effect in the recent experiments on two-dimensional WTe$_{2}$. This Letter will be instructive not only for analyzing the transport signatures of the nonlinear Hall effect but also for exploring unconventional responses in emergent materials.

cond-mat.mes-hall↗

arXiv2018

Rules for Phase Shifts of Quantum Oscillations in Topological Nodal-line Semimetals

Nodal-line semimetals are topological semimetals in which band touchings form nodal lines or rings. Around a loop that encloses a nodal line, an electron can accumulate a nontrivial $π$ Berry phase, so the phase shift in the Shubnikov-de Haas (SdH) oscillation may give a transport signature for the nodal-line semimetals. However, different experiments have reported contradictory phase shifts, in particular, in the WHM nodal-line semimetals (W=Zr/Hf, H=Si/Ge, M=S/Se/Te). For a generic model of nodal-line semimetals, we present a systematic calculation for the SdH oscillation of resistivity under a magnetic field normal to the nodal-line plane. From the analytical result of the resistivity, we extract general rules to determine the phase shifts for arbitrary cases and apply them to ZrSiS and Cu$_3$PdN systems. Depending on the magnetic field directions, carrier types, and cross sections of the Fermi surface, the phase shift shows rich results, quite different from those for normal electrons and Weyl fermions. Our results may help exploring transport signatures of topological nodal-line semimetals and can be generalized to other topological phases of matter.

cond-mat.mes-hall↗

arXiv2018

Non-saturating Quantum Magnetization in Weyl semimetal TaAs

Detecting the spectroscopic signatures of Dirac-like quasiparticles in emergent topological materials is crucial for searching their potential applications. Magnetometry is a powerful tool for fathoming electrons in solids, yet its ability for discerning Dirac-like quasiparticles has not been recognized. Adopting the probes of magnetic torque and parallel magnetization for the archetype Weyl semimetal TaAs in strong magnetic field, we observed a quasi-linear field dependent effective transverse magnetization and a strongly enhanced parallel magnetization when the system is in the quantum limit. Distinct from the saturating magnetic responses for massive carriers, the non-saturating signals of TaAs in strong field is consistent with our newly developed magnetization calculation for a Weyl fermion system in an arbitrary angle. Our results for the first time establish a thermodynamic criterion for detecting the unique magnetic response of 3D massless Weyl fermions in the quantum limit.

cond-mat.mes-hall↗

arXiv2017

3D quantum Hall effect of Fermi arcs in topological semimetals

The quantum Hall effect is usually observed in 2D systems. We show that the Fermi arcs can give rise to a distinctive 3D quantum Hall effect in topological semimetals. Because of the topological constraint, the Fermi arc at a single surface has an open Fermi surface, which cannot host the quantum Hall effect. Via a "wormhole" tunneling assisted by the Weyl nodes, the Fermi arcs at opposite surfaces can form a complete Fermi loop and support the quantum Hall effect. The edge states of the Fermi arcs show a unique 3D distribution, giving an example of (d-2)-dimensional boundary states. This is distinctly different from the surface-state quantum Hall effect from a single surface of topological insulator. As the Fermi energy sweeps through the Weyl nodes, the sheet Hall conductivity evolves from the 1/B dependence to quantized plateaus at the Weyl nodes. This behavior can be realized by tuning gate voltages in a slab of topological semimetal, such as the TaAs family, Cd$_3$As$_2$, or Na$_3$Bi. This work will be instructive not only for searching transport signatures of the Fermi arcs but also for exploring novel electron gases in other topological phases of matter.

cond-mat.mes-hall↗