Nontrivial Berry Curvature Research Articles

High spin-Chern-number insulator in α-antimonene with a hidden topological phase

For a time-reversal symmetric system, the quantum spin Hall phase is assumed to be the same as the Z2 topological insulator phase in the existing literature. The spin Chern number Cs is presumed to yield the same topological classification as the Z2 invariant. Here, by investigating the electronic structures of monolayer α-phase group V elements, we uncover the presence of a topological phase in α-Sb, which can be characterized by a spin Chern number Cs = 2, even though it is Z2 trivial. Although α-As and Sb would thus be classified as trivial insulators within the classification schemes, we demonstrate the existence of a phase transition between α-As and Sb, which is induced by band inversions at two generic k points. Without spin–orbit coupling (SOC), α-As is a trivial insulator, while α-Sb is a Dirac semimetal with four Dirac points (DPs) located away from the high-symmetry lines. Inclusion of the SOC gaps out the DPs and induces a nontrivial Berry curvature, endowing α-Sb with a high spin Chern number of Cs = 2. We further show that monolayer α-Sb exhibits either a gapless band structure or a gapless spin spectrum on its edges, as expected from topological considerations.

Atomic scale quantum anomalous hall effect in monolayer graphene/MnBi2Te4 heterostructure.

The two-dimensional quantum anomalous Hall (QAH) effect is direct evidence of non-trivial Berry curvature topology in condensed matter physics. Searching for QAH in 2D materials, particularly with simplified fabrication methods, poses a significant challenge in future applications. Despite numerous theoretical works proposed for the QAH effect with C = 2 in graphene, neglecting magnetism sources such as proper substrate effects lacks experimental evidence. In this work, we propose the QAH effect in graphene/MnBi2Te4 (MBT) heterostructure based on density-functional theory (DFT) calculations. The monolayer MBT introduces spin-orbital coupling, Zeeman exchange field, and Kekulé distortion as a substrate effect into graphene, resulting in QAH with C = 1 in the heterostructure. Our effective Hamiltonian further presents a rich phase diagram that has not been studied previously. Our work provides a new and practical way to explore the QAH effect in monolayer graphene and the magnetic topological phases by the flexibility of MBT family materials.

Role of topological charges in the nonlinear optical response from Weyl semimetals

The successful realization of the topological Weyl semimetals has revolutionized contemporary physics. In recent years, multi-Weyl semimetals, a class of topological Weyl semimetals, has attracted broad interest in condensed-matter physics. Multi-Weyl semimetals are emerging topological semimetals with nonlinear anisotropic energy dispersion, which is characterized by higher topological charges. In this study, we investigate how the topological charge affects the nonlinear optical response from multi-Weyl semimetals. It has been observed that the laser-driven electronic current is characteristic of the topological charge, and the laser polarization's direction influences the current's direction and amplitude. In addition, the anomalous current, perpendicular to the laser's polarization, carries a distinct signature of the topological charges and encodes the information about the parity and amplitude of the nontrivial Berry curvature. We show that the anomalous current associated with the anomalous Hall effect remains no longer proportional to the topological charge at higher laser intensity -- a significant deviation from the linear response theory. High-harmonic spectroscopy is employed to capture the distinct and interesting features of the currents in multi-Weyl semimetals where the topological charge drastically impacts the harmonics' yield and energy cutoff.

Temperature-induced magnonic Chern insulator in collinear antiferromagnets

Thermal fluctuation in magnets causes temperature-dependent self-energy corrections in magnons; however, its effects on the topological orders of magnons is not well explored. Here we demonstrate that such corrections can induce a Chern insulating phase in two-dimensional collinear antiferromagnets with sublattice asymmetries by increasing temperature. We present the phase diagram of the system and show that the trivial magnon bands at zero temperature exhibit Chern insulating phase above a critical temperature before the paramagnetic phase transition. The self-energy corrections close and reopen the band gap at $\mathrm{\ensuremath{\Gamma}}$ or $\mathbf{K}$ points, accompanied by a magnon chirality switch and nontrivial Berry curvature transition. The thermal Hall effect of magnons or detecting the magnon polarization can highlight the experimentally prominent signatures of the topological transitions. We include the numerical results based on the van der Waals magnet ${\mathrm{MnPS}}_{3}$, calling for experimental implementation. Our work presents a paradigm for constructing topological phases that is beyond the linear spin wave theory.

Sizable suppression of magnon Hall effect by magnon damping in Cr2Ge2Te6

Two-dimensional (2D) Heisenberg honeycomb ferromagnets are expected to have interesting topological magnon effects as their magnon dispersion can have Dirac points. The Dirac points are gapped with finite second nearest neighbor Dzyaloshinskii-Moriya interaction, providing nontrivial Berry curvature with finite magnon Hall effect. Yet, it is unknown how the topological properties are affected by magnon damping. We report the thermal Hall effect in Cr$_2$Ge$_2$Te$_6$, an insulating 2D honeycomb ferromagnet with a large Dirac magnon gap and significant magnon damping. Interestingly, the thermal Hall conductivity in Cr$_2$Ge$_2$Te$_6$ shows the coexisting phonon and magnon contributions. Using an empirical two-component model, we successfully estimate the magnon contribution separate from the phonon part, revealing that the magnon Hall conductivity was 20 times smaller than the theoretical calculation. Finally, we suggest that such considerable suppression in the magnon Hall conductivity is due to the magnon damping effect in Cr$_2$Ge$_2$Te$_6$.

Spatial symmetry modulation of planar Hall effect in Weyl semimetals

The planar Hall effect in Weyl semimetals has been proposed as a key feature of chiral anomaly and nontrivial Berry curvature, while the effect of fundamental spatial symmetry remains to be explored. Here, we show with general symmetry analysis and lattice model calculations that the planar Hall effect can be significantly modulated by a certain class of spatial symmetry operations. The odd terms of conductivity with respect to magnetic field, including the linear terms, vanish in the plane perpendicular to the axis of twofold rotation (${C}_{2}$) or the ${C}_{2}$ combined symmetry operations (mirror, twofold screw rotation, glide plane). When applying the magnetic field perpendicular to the glide plane, we find that the planar Hall conductivity in bulk forbidden by glide symmetry becomes nonzero in its quasi-two-dimensional counterpart with broken glide symmetry. It is further clarified that the nonzero planar Hall conductivity comes from surface states. This signature can be used to distinguish bulk and surface transport in Weyl semimetals.

Anomalous Nernst effect in compensated ferrimagnetic CoxGd1-x films

The anomalous Nernst effect (ANE) is one of the most intriguing thermoelectric phenomena, which has attracted growing interest both for its underlying physics and potential applications. Typically, a large ANE response is observed in magnets with pronounced magnetizations or nontrivial Berry curvature. Here, we report a significant ANE signal in compensated ferrimagnetic CoxGd1-x amorphous films, which exhibit vanishingly small magnetization. In particular, we found that the polarity of ANE signal is dominated by the magnetization orientation of the transition metal Co sublattices, rather than the net magnetization of CoxGd1-x films. This observation is not expected from the conventional understandings of ANE but is analogous to the anomalous Hall effect in compensated ferrimagnets. The joint contribution from the Berry curvature and the scattering mechanisms near the Co-dominant Fermi surface could interpret the Co-dominant property of ANE. Our work may trigger a more comprehensive understanding of ANE and may be useful for building energy-harvesting devices by employing ANE in compensated ferrimagnets.

In-plane magnetotransport phenomena in tilted Weyl semimetals

The nontrivial Berry curvature and chiral anomaly result in plenty of interesting magnetotransport and magneto-thermoelectric transport phenomena in Weyl semimetals, two of which are the planar Hall effect and planar Nernst effect. Based on the semi-classical Boltzmann theory, we theoretically study the in-plane magnetotransport coefficients (including electric conductivity, thermoelectric conductivity and Nernst thermopower) for both type-I and type-II Weyl semimetals using a linearized low-energy Hamiltonian. We find that for tilt-coplanar setup where the electric field (or temperature gradient) is applied along the tilted direction of the Weyl nodes, the planar Hall conductivity (or planar Nernst thermopower) shows a magnetic field linear dependence. And these linear responses do no obey the reported dependence on the angle θ between the magnetic and electric field for planar Hall effect. For tilt-perpendicular setup where the applied field (E or ) and magnetic field are perpendicular to the tilted direction, the planar Hall conductivity (or planar Nernst thermopower) mainly follows a magnetic field quadratic dependence, and it satisfies the characteristic. There are also anomalous Hall effect and anomalous Nernst effect in the plane perpendicular to the tilted direction of the two oppositely tilted Weyl nodes. These findings can be verified experimentally by changing the direction and magnitude of the in-plane magnetic field.

Symmetry-enforced electronic nodal straight lines in CsNb3SBr7

We propose the quaternary-compounds CsNb3SBr7 is a nodal-straight-line semimetal candidate based on the first-principles calculations and symmetry analyses. There are a pair of nodal straight lines locate in the k z = 0 plane of Brillouin zone, which is protected by the crystal symmetry. The topological properties of nodal-straight-line state are characterized by the nontrivial Berry phase and Berry curvature. On the (001) surface of CsNb3SBr7, Fermi arcs form the belt-like surface state, connecting the nodal straight lines with opposite chirality. Furthermore, the Hofstadter’s butterfly and optical conductivity are investigated using a slab sample. These results not only reveal the symmetric protection mechanism of nodal straight lines, but also pave a way for exploring the electronic and optical properties of CsNb3SBr7 in further condensed matter physics experiments.

Gate tunable anomalous Hall effect: Berry curvature probe at oxides interfaces

We present the theoretical prediction of a gate tunable anomalous Hall effect (AHE) in an oxide interface as a hallmark of spin-orbit coupling. The observed AHE at low-temperatures in the presence of an external magnetic field emerges from a complex structure of the Berry curvature of the electrons on the Fermi surface and strongly depends on the orbital character of the occupied bands. A detailed picture of the results comes from a multiband low-energy model with a generalized Rashba interaction that supports characteristic out-of-plane spin and orbital textures. We discuss strategies for optimizing the intrinsic AHE in (111) SrTiO$_3$ heterostructure interfaces.

Chern mosaic and Berry-curvature magnetism in magic-angle graphene

Charge carriers in magic angle graphene come in eight flavors described by a combination of their spin, valley, and sublattice polarizations. When the inversion and time reversal symmetries are broken by the substrate or by strong interactions, the degeneracy of the flavors can be lifted and their corresponding bands can be filled sequentially. Due to their non-trivial band topology and Berry curvature, each of the bands is classified by a topological Chern number, leading to the quantum anomalous Hall and Chern insulator states at integer fillings $\nu$ of the bands. It has been recently predicted, however, that depending on the local atomic-scale arrangements of the graphene and the encapsulating hBN lattices, rather than being a global topological invariant, the Chern number C may become position dependent, altering transport and magnetic properties of the itinerant electrons. Using a SQUID-on-tip, we directly image the nanoscale Berry-curvature-induced equilibrium orbital magnetism, the polarity of which is governed by the local Chern number, and detect its two constituent components associated with the drift and the self-rotation of the electronic wave packets. At $\nu=1$, we observe local zero-field valley-polarized Chern insulators forming a mosaic of microscopic patches of C=-1, 0, or 1, governed by the local sublattice polarization, consistent with predictions. Upon further filling, we find a first-order phase transition due to recondensation of electrons from valley K to K', which leads to irreversible flips of the local Chern number and the magnetization, and to the formation of valley domain walls giving rise to hysteretic global anomalous Hall resistance. The findings shed new light on the structure and dynamics of topological phases and call for exploration of the controllable formation of flavor domain walls and their utilization in twistronic devices.

Half-quantized Hall effect and power law decay of edge-current distribution

The half-quantized Hall conductance is characteristic of quantum systems with parity anomaly. Here we investigate topological and transport properties of a class of parity anomalous semimetals, in which massive Dirac fermions coexist with massless Dirac fermions in momentum space or real space, and uncovered a distinct bulk-edge correspondence that the half-quantized Hall effect is realized via the bulk massless Dirac fermions while the nontrivial Berry curvature is provided by the massive Dirac fermions. The spatial distribution of the edge current decays away from the boundary in a power law instead of an exponential law in integer quantum Hall effect. We further address physical relevance of parity anomalous semimetal to three-dimensional semi-magnetic topological insulators and two-dimensional photonic crystals.

Antiferromagnetic insulators with tunable magnon-polaron Chern numbers induced by in-plane optical phonons

We theoretically study magnon-phonon hybrid excitations (magnon-polarons) in two-dimensional antiferromagnets on a honeycomb lattice. With an in-plane Dzyaloshinskii-Moriya interaction (DMI) allowed from mirror symmetry breaking from phonons, we find non-trivial Berry curvature around the anti-crossing rings among magnon and both optical and acoustic phonon bands, which gives rise to finite Chern numbers. We show that the Chern numbers of the magnon-polaron bands can be manipulated by changing the magnetic field direction or strength. We evaluate the thermal Hall conductivity reflecting the non-trivial Berry curvatures of magnon-polarons and propose a valley Hall effect resulting from spin-induced chiral phonons as a possible experimental signature. Our study complements prior work on magnon-phonon hybridized systems without optical phonons and suggests possible applications in spin caloritronics with topological magnons and chiral phonons.

Boundary conductance in macroscopic bismuth crystals

The interface between a solid and vacuum can become electronically distinct from the bulk. This feature, encountered in the case of quantum Hall effect, has a manifestation in insulators with topologically protected metallic surface states. Non-trivial Berry curvature of the Bloch waves or periodically driven perturbation are known to generate it. Here, by studying the angle-dependent magnetoresistance in prismatic bismuth crystals of different shapes, we detect a robust surface contribution to electric conductivity when the magnetic field is aligned parallel to a two-dimensional boundary between the three-dimensional crystal and vacuum. The effect is absent in antimony, which has an identical crystal symmetry, a similar Fermi surface structure and equally ballistic carriers, but an inverted band symmetry and a topological invariant of opposite sign. Our observation confirms that the boundary interrupting the cyclotron orbits remains metallic in bismuth, which is in agreement with what was predicted by Azbel decades ago. However, the absence of the effect in antimony indicates an intimate link between band symmetry and this boundary conductance.

Chiral anomaly induced nonlinear Hall effect in semimetals with multiple Weyl points

After the experimental realization, the Berry curvature dipole (BCD) induced nonlinear Hall effect (NLHE) has attracted tremendous interest to the condensed matter community. Here, we investigate another family of Hall effect, namely, chiral anomaly induced nonlinear Hall effect (CNHE) in multi-Weyl semimetal (mWSM). In contrast to the BCD induced NLHE, CNHE appears because of the combination of both chiral anomaly and anomalous velocity due to non-trivial Berry curvature. Using the semiclassical Boltzmann theory within the relaxation time approximation, we show that, in contrast to the chiral anomaly induced linear Hall effect, the magnitude of CNHE decreases with the topological charge n. Interestingly, we find that unlike the case of n=1, the CNHE has different behaviors in different planes. Our prediction on the behavior of CNHE in mWSM can directly be checked in experiments.

Anisotropically large anomalous and topological Hall effect in a kagome magnet

Recently, kagome materials have become an engrossing platform to study the interplay among symmetry, magnetism, topology, and electron correlation. The latest works on $R{\mathrm{Mn}}_{6}{\mathrm{Sn}}_{6}$ ($R$ = rare-earth metal) compounds have illustrated that this family could be intriguing to investigate various physical phenomena due to large spin-orbit coupling and strong magnetic ordering. However, combined transport and spectroscopic studies in $R{\mathrm{Mn}}_{6}{\mathrm{Sn}}_{6}$ materials are still limited. Here, we report magnetic, magnetotransport, and angle-resolved photoemission spectroscopy measurements of a kagome magnet ${\mathrm{ErMn}}_{6}{\mathrm{Sn}}_{6}$ that undergoes antiferromagnetic (${T}_{N}=345\phantom{\rule{0.28em}{0ex}}\mathrm{K}$) to ferrimagnetic (${T}_{C}=68\phantom{\rule{0.16em}{0ex}}\mathrm{K}$) phase transitions in the presence of a field. We observe large anomalous and topological Hall effects serving as transport signatures of the nontrivial Berry curvature. The isothermal magnetization exhibits strong anisotropic nature and the topological Hall effect of the compound depends on the critical field of metamagnetic transition. Our spectroscopic results complemented by theoretical calculations show the multiorbital kagome fermiology. This Letter provides new insight into the tunability and interplay of topology and magnetism in a kagome magnet.

Planar Hall effect in the quasi-one-dimensional topological superconductor TaSe3

A novel planar Hall effect (PHE) is induced by the chiral anomaly or nontrivial Berry curvature, which has been predicted in nonmagnetic Weyl/Dirac semimetals. Recent theories suggest such an effect exists in three-dimensional (3D) topological insulators even in the absence of chiral anomaly. In this paper, we present a detailed analysis of the transport properties in the quasi-1D $\mathrm{Ta}{\mathrm{Se}}_{3}$, a candidate of topological superconductor (TSC) predicted by the theorist. There are some interesting observations on $\mathrm{Ta}{\mathrm{Se}}_{3}$. (1) The electron-hole compensation has been confirmed by the Hall effect measurements around ${T}_{\mathrm{com}}\ensuremath{\sim}30\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, which accounts for the extremely large magnetoresistance in $\mathrm{Ta}{\mathrm{Se}}_{3}$. (2) The remarkable PHE and anisotropic magnetoresistance (AMR) are observed in $\mathrm{Ta}{\mathrm{Se}}_{3}$. Based on the detailed analysis of the PHE and AMR curves, the origin of PHE in $\mathrm{Ta}{\mathrm{Se}}_{3}$ is suggested to originate from the resistivity anisotropy induced by the difference of field-induced anisotropic scattering in surface Dirac fermions of various spins. (3) We observed the successive Fermi surface reconstruction induced by the temperature around ${T}^{*}\ensuremath{\sim}50\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, where the amplitude of intrinsic PHE drops sharply related to the suppression of the topological surface state. Meanwhile, the $d{\ensuremath{\rho}}_{xx}(T)/dT$ curve presents a broad anomaly around ${T}_{\mathrm{peak}}\ensuremath{\sim}70\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, which can be explained as a possible charge-density wave associated with imperfect Fermi surface nesting. PHE provides an effective method to understand the relationship between the electronic transport properties and the topological structure in quasi-1D TSC $\mathrm{Ta}{\mathrm{Se}}_{3}$.

Topological Magnus responses in two- and three-dimensional systems

Recently, time-reversal symmetric but inversion broken systems with nontrivial Berry curvature in the presence of a built-in electric field have been proposed to exhibit a new type of linear Hall effect in ballistic regime, namely, the Magnus Hall effect. The transverse current here is caused by the Magnus velocity that is proportional to the built-in electric field enabling us to examine the Magnus responses, in particular, Magnus Hall conductivity and Magnus Nernst conductivity, with chemical potential. Starting with two-dimensional (2D) topological systems, we find that warping induced asymmetry in both the Fermi surface and Berry curvature can in general enhance the Magnus response for monolayer graphene and surface states of topological insulator. The strain alone is only responsible for Magnus valley responses in monolayer graphene, while warping leads to finite Magnus response there. Interestingly, on the other hand, strain can change the Fermi surface character substantially that further results in distinct behavior of Magnus transport coefficients as we observe in bilayer graphene. These responses there remain almost insensitive to warping unlike the case of monolayer graphene. Going beyond 2D systems, we also investigate the Magnus responses in three-dimensional multi-Weyl semimetals (mWSMs) to probe the effect of tilt and anisotropic nonlinear energy dispersion. Remarkably, Magnus responses can only survive for the WSMs with chiral tilt. In particular, our study indicates that the chiral (achiral) tilt engenders Magnus (Magnus valley) responses. Therefore, Magnus responses can be used as a tool to distinguish between the untilted and tilted WSMs in experiments. In addition, we find that the Magnus Hall responses get suppressed with increasing the nonlinearity associated with the band touching around the multi-Weyl node.

Photogalvanic effects in symmetry broken nodal ring materials

Nodal ring semimetals are a class of topological material characterized by a one-dimensional circular region of band crossing in momentum space. The presence of spin-orbit coupling, whether extrinsic or intrinsic, may change the parent nodal ring phase to a Weyl semimetal, Dirac semimetal, or topological insulator child phase. We investigate second harmonic generation and circular photogalvanic effect in the mid-infrared region of nodal ring materials where spin-orbit coupling produces a Weyl semimetal child phase (such as in $\mathrm{Zr}{\mathrm{Te}}_{5}$ and $\mathrm{Ca}{\mathrm{P}}_{3}$). Spin-orbit coupling breaks the symmetries protecting the nodal ring, inducing a nontrivial Berry curvature which gives rise to colossal photocurrents up to the order of ${10}^{3} \ensuremath{\mu}\mathrm{A}/{\text{V}}^{2}$ at the interband harmonic. Our results are found to be rather robust to parameters such as Fermi level, residual scattering rate, and the number of Weyl points. However, decreasing temperature tends to destroy the harmonic peaks and changing the nodal ring radius drastically alters the harmonic condition, shifting the peak frequency. Equivalent calculations and experiments have been carried out for intrinsic Weyl semimetals such as TaAs where the photocurrents calculated and observed were at least one order of magnitude smaller, highlighting that the parent nodal ring phase enhances these optical nonlinear phenomena.

Anomalous planar Hall effect in two-dimensional trigonal crystals

The planar Hall effect (PHE) is the appearance of an in-plane transverse voltage in the presence of coplanar electric and magnetic fields. Its hallmark is a characteristic $\pi$-periodic, i.e. even under a magnetic field reversal, angular dependence with the transverse voltage that exactly vanishes when the electric and magnetic fields are aligned. Here we demonstrate that in two-dimensional trigonal crystals Zeeman-induced non-trivial Berry curvature effects yield a previously unknown anomalous PHE that is odd in the magnetic field and independent of the relative angle with the driving electric field. We further show that when an additional mirror symmetry forces the transverse voltage to vanish in the linear response regime, the anomalous PHE can occur as a second-order response at both zero and twice the frequency of the applied electric field. We demonstrate that this non-linear PHE possesses an antisymmetric quantum contribution that originates from a Zeeman-induced Berry curvature dipole.