arXiv subjects

Banasree Sadhukhan

Publications and source records attributed to Banasree Sadhukhan.

At least 19 recordsLinked to original sources

arXiv2026

Topological Hall plateau in quasi-2D kagome magnet YMn$_6$Sn$_6$

We examine the impact of the Dzyaloshinskii--Moriya interaction (DMI) in kagome magnets and show that a predominantly planar DMI together with ferromagnetic exchange stabilizes a disordered skyrmion phase in quasi-two-dimensional (2D) YMn$_6$Sn$_6$. Within an {\it{ab initio}} framework combining density functional theory and spin-dynamics simulations, we generate realistic spin textures of disordered skyrmion and find that this phase persists for $B_{\rm ext} \leq 0.5$~T, with a decreasing skyrmion size as magnetic field increases. We demonstrate the emergence of topological Hall plateau in the range $-0.5 \leq B_{\mathrm{ext}} \leq 0.5$~T, driven by nearly uniform scalar spin chirality and the resulting constant real-space Berry curvature. This response is anti-symmetric with magnetic field while magnitude and sign of these plateau are determined by a complex interplay between Hund's coupling strength and chemical potential signifying the role of Dirac points and van Hove singularities. In addition, we reveal topological magnon excitations in the disordered skyrmion phase of quasi-2D YMn$_6$Sn$_6$.

cond-mat.mtrl-sci↗

arXiv2026

Correlation enhanced altermagnetism mediated by spin-lattice coupling in CrSb

Altermagnets (AMs) exhibit momentum-dependent spin splitting without net magnetization, making them promising platforms for spintronic applications. While the symmetry and multipolar origins of nonrelativistic altermagnetic spin splitting (NRASS) are well established, the role of electronic correlations and spin-lattice coupling (SLC) in controlling NRASS remain unexplored. In particular, SLC provides a direct pathway for tuning altermagnetism through lattice degrees of freedom. Here we first investigate the role of electronic correlations on altermagnetic strength in NiAs-type material CrSb using density functional theory (DFT), DFT+$U$, and dynamical mean-field theory (DMFT). We find that increasing electronic correlations substantially enhance NRASS and drive the stabilization of an incommensurate spin-spiral (SS) state, while dynamical correlations further amplify the spin splitting through quasiparticle renormalization of the Cr-$3d$ states. We find that the NRASS remains 12.5\% larger in DFT+DMFT than in DFT. By evaluating SLC in next step, we establish its direct connection to the evolution of NRASS and identify SLC as a microscopic descriptor between electronic correlation and enhanced altermagnetism in CrSb. Investigating it in another NiAs-type compound MnTe, we show that the SLC-NRASS correlation is generic across AMs and establish SLC as a microscopic descriptor of altermagnetic strength. Our results provide a unified framework for tuning altermagnetism through the interplay between the electronic correlations and lattice degrees of freedom.

cond-mat.mtrl-sci↗

arXiv2026

Quantized orbital and spin Hall transport: interplay between $sp$-hybridization, altermagnetism and spin-orbit coupling

We here explore the emergence of orbital and spin Hall effects, originating beyond the $L$-$S$ coupling, and investigate the interplay between inter-orbit hybridization, relativistic Rashba spin-orbit coupling (SOC), and non-relativistic SOC, namely altermagnetic (AM) order, in a two-dimensional model Hamiltonian. The orbital (spin) Hall responses are remarkably found to be quantized within a window of Fermi energy when the strength of AM order (Rashba SOC) exceeds (falls below) the scale set by $sp$-hybridization. Importantly, orbital and spin Hall quantizations are independent of Rashba SOC and AM order, respectively, while the uniform profiles of finite orbital and vanishingly small spin moments of bands around the Fermi energy. The microscopic origin of such quantization comes from the Fermi surface-activated orbital and spin Berry curvatures. The extent of the quantized regime is strongly controlled by the intra-orbital coupling strength. As the temperature increases, the quantization is significantly compromised in the spin Hall case. We extend our analysis to the orbital and spin Nernst coefficients where the pronounced dip-peak structures signal the existence of the quantization leading to experimental relevance.

cond-mat.mes-hall↗

arXiv2026

The orbital-driven topological phase transition and planar Hall responses in ternary tellurides Weyl semi-metals

We study electronic properties of the ternary tellurides TaXTe$_4$ (X=Rh, Ir) using density functional theory and investigate chiral anomaly mediated planar Hall response from ab initio calculations. We show that TaRhTe$_4$ is a hybrid Weyl semimetal (WSM), hosting Weyl points (WPs) of both type-I, type-II, and TaIrTe$_4$ is a type-I WSM in absence of spin-orbit coupling (SOC). TaRhTe$_4$ continues to remain a hybrid WSM while TaIrTe$_4$ converts into a type-II WSM under the application of SOC. We observe long Fermi arcs connecting WPs of opposite chirality. We report orbital-driven topological phase transition in ternary tellurides. The WSM phases in TaXTe$_4$ are controlled by the orbital character of the $d_{xz}$ and $d_{z^2}$ states of X=Ir/Rh atoms. Replacing Rh with Ir enhances the $d_{z^2}$ orbital contribution near the Fermi level at the expense of $d_{xz}$ states. This transforms the type-I WPs into type-II resulting in a conversion of hybrid WSM TaRhTe$_4$ to type-II WSM TaIrTe$_4$. This systematic study opens new routes for engineering topological materials relying beyond strong SOC and sheds light on the effect of orbital degree of freedom on the electronic properties of tellurides. We further report an enhancement of planar Hall effects due to orbital-driven topological phase transition in TaXTe$_4$ and we make resort to a tight-binding model to correlate the above findings with the velocity modulated off-diagonal effective mass anisotropy in different types of WSMs.

cond-mat.mtrl-sci↗

arXiv2025

Skyrmion manipulation and logic gate functionality in transition metal multilayers

Magnetic skyrmions, due to their topological stability and high mobility, are strong candidates for information carriers in spintronic devices. To advance their practical applications, a detailed understanding of their nucleation and current-driven dynamics is essential. We investigate the formation and manipulation of skyrmions in a square nano structure (200 $\times$ 200 nm$^{2}$, 1 nm thick) of PdFe/Ir(111) multilayers subjected to nano second current pulses with magnitude ranging from (1-5)$\times$10$^{11}$ A/m$^2$. Using micromagnetic simulations, we demonstrate controlled motion of skyrmion under different types of spin-transfer torque (STT). The calculated skyrmion Hall angle (SkH) for Slonczewski type STT is ${θ_{SkH}^{SL}} = 89.53^{\circ}$ for PdFe/Ir(111) multilayers which ensures the edge accululation of skyrmion like a track within the nano structure and we extend this idea further for different shape engineering of skyrmion in 4d tranisition metal multilayers by manipulating the magnitude and direction of current pulses. Next, we investigate the influence of voltage-controlled magnetic anisotropy ranging from (1.4 - 4.2) $\times$ 10$^6$ J/m$^3$ with external magnetic field B$_{ext}$ = 2 T, and (0 - 2.8) $\times$ 10$^6$ J/m$^3$ with B$_{ext}$ = 3 T respectively, on skyrmion dynamics for designing anisotropy-engineered barriers to guide their trajectories in PdFe/Ir(111) multilayers. We use further these barriers to implement basic logic operations, including OR and AND gates, with skyrmions representing binary states. The calculatd skyrmion Hall angle for Zhang-Li type STT in PdFe/Ir(111) multilayers is ${θ_{SkH}^{ZL}} = 3.26^{\circ}$. Consequently, the skyrmions propagate predominantly along the direction of the applied current with minimal deflection, a feature that renders them highly suitable for logic operations.

cond-mat.mtrl-sci↗

arXiv2024

Interplay between interfacial Dzyaloshinskii Moriya interaction and magnetic anisotropy in 4d transition metal multilayers for skyrmion nucleation

Skyrmions refer to small swirling spin structures that emerge in ferromagnetic materials and show promising features to be used as a `bit' of information in future spintronic devices. Our research explores the possibility of nucleating skyrmions in X-Fe/Ir(111) multilayer nano-structure where, X is one of the 4d transition metals, such as, Pd, Rh, Ru, Mo and Nb. The resulting final state is determined by the competition between the frustrated exchange interaction, primarily contributed by the top 4d transition metal layer, and the Dzyaloshinskii-Moriya interactions induced significantly by the 5d heavy metal Ir(111) layer. We apply a perpendicular dc magnetic field to the nano-structure and observe gradual phase transformation from the spin spiral ground state to a stable relaxed state of nano-scale skyrmions . A proper choice of magnetic anisotropy and interfacial Dzyaloshinskii-Moriya interaction leads to a range of external magnetic fields essential for the existence and stability of skyrmions. By raising the temperature, we assess the thermal stability of the nucleated skyrmions to evaluate their potential as information carriers in future spintronic devices.

cond-mat.mtrl-sci↗

arXiv2024

Engineering skyrmion from spin spiral in transition metal multilayers

Skyrmions having topologically protected field configurations with particle-like properties play an important role in {\bl{various fields of science}}. Our present study focus on the generation of skyrmion from spin spiral in the magnetic multilayers of 4d/Fe/Ir(111) with 4d = Y, Zr, Nb, Mo, Ru, Rh. Here we investigate the impact of 4d transition metals on the isotropic Heisenberg exchanges and anti-symmetric Dzyaloshinskii-Moriya interactions originating from the broken inversion symmetry at the interface of 4d/Fe/Ir(111) multilayers. We find a strong exchange frustration due to the hybridization of the Fe-3d layer with both 4d and Ir-5d layers which modifies due to band filling effects of the 4d transition metals. We strengthen the analysis of exchange frustration by shedding light on the orbital decomposition of isotropic exchange interactions of Fe-3d orbitals. Our spin dynamics and Monte Carlo simulations indicate that the magnetic ground state of 4d/Fe/Ir(111) transition multilayers is a spin spiral in the $ab$-plane with a period of 1 to 2.5 nm generated by magnetic moments of Fe atoms and propagating along the $a$-direction. The spiral wavelengths in Y/Fe/Ir(111) are much larger compared to Rh/Fe/Ir(111). In order to manipulate the skyrmion phase in 4d/Fe/Ir(111), we investigate the magnetic ground state of 4d/Fe/Ir(111) transition multilayers with different external magnetic field. An increasing external magnetic field of $\sim$ 12 T is responsible for deforming the spin spiral into a isolated skyrmion which flips into skyrmion lattice phase around $\sim$ 18 T in Rh/Fe/Ir(111). Our study predict that the stability of magnetic skyrmion phase in Rh/Fe/Ir(111) against thermal fluctuations is upto temperature T $\leq 90$ K.

cond-mat.mtrl-sci↗

arXiv2024

Large bulk photovoltaic effect and Fermi surface mediated its enhancement with chemical potential in ZnGeP$_2$

Bulk photovoltaic effect is a non-linear response in noncentrosymmetric materials that converts light into DC current. In this work, we investigate the optical linear and non-linear responses in a chalcopyrite semiconductor ZnGeP$_2$. We report large bulk photovoltaics namely shift and circular photogalvanic current conductivities which are 4.46 $μ$A/V$^2$ and -5.49 $μ$A/V$^2$ respectively with the incident photo energy around $\sim$ 5 eV at the chemical potential of E$_f$ = 0 eV which increase about 38\% and 81\% respectively at a chemical potential of E$_f$ = 1.52 eV. The systematic evolution of the bulk Fermi surface along with the high symmetry points in three dimensional Brillouin zone reveals the enhancement of bulk photovoltaics with the chemical potential in ZnGeP$_2$. To verify our findings, we further explore the distribution of bulk projected bands and surface Fermi surface distribution in the energy landscape using tight binding Hamiltonian within semi infinite slab geometry. This shows that the augmentation of bulk photovoltaics with the chemical potential is due to the surface Fermi surface states along the high symmetry $Γ-Z$ direction in Brillouin zone. Our thorough and detailed study not only provides a deeper understanding about the role of Fermi surface contribution to the bulk photovoltaic responses with chemical potential, but also suggests ZnGeP$_2$ as an ideal candidate for optoelectronics and bulk photovoltaics.

cond-mat.mtrl-sci↗

arXiv2024

Sb2Se3 and SbBiSe3 Surface Capping and Biaxial Strain Co-Engineering for Tuning the Surface Electronic Properties of Bi2Se3 Nanosheet- A Density Functional Theory based Investigation

In this work, for the first time, a density functional theory (DFT) based comprehensive theoretical study is performed on the surface electronic properties of Bi2Se3 nanosheet in the presence of a surface capping layer as well as mechanical strain. The study systematically introduces a biaxial compressive and tensile strain up to 5% in natural, Sb2Se3 surface capped, and SbBiSe3 surface capped Bi2Se3, and the subsequent effects on the electronic properties are assessed from the surface energy band (E-k) structure, the density of states (DOS), band edge energy and bandgap variations, surface conducting state localization, and Fermi surface spin-textures. The key findings of this work are systematically analyzed from conducting surface state hybridization through bulk in the presence of surface capping layers and applied biaxial strain. The result demonstrates that the interplay of surface capping and strain can simultaneously tune the surface electronic structure, spin-momentum locking results from change in electronic localization and interactions. In essence, this work presents an extensive theoretical and design-level insight into the surface capping and biaxial strain co-engineering in Bi2Se3, which can potentially facilitate different topological transport for modern optoelectronics, spintronics, valleytronics, bulk photovoltaics applications of engineered nanostructured topological materials in the future.

cond-mat.mtrl-sci↗

arXiv2024

Microscopic effect of spin-lattice couplings on dynamical magnetic interactions of a skyrmion system PdFe/Ir(111)

PdFe/Ir(111) has attracted tremendous attention for next-generation spintronics devices due to existence of magnetic skyrmions with the external magnetic field. Our density functional theoretical calculations in combination with spin dynamics simulation suggest that the spin spiral phase in fcc stacked PdFe/Ir(111) flips into the skyrmion lattice phase around B$_{ext} \sim$ 6 T. This leads to the microscopic understanding of the thermodynamic and kinetic behaviours affected by the intrinsic spin-lattice couplings (SLCs) in this skyrmion material for magneto-mechanical properties. Here we calculate fully relativistic SLC parameters from first principle computations and investigate the effect of SLC on dynamical magnetic interactions in skyrmion multilayers PdFe/Ir(111). The exchange interactions arising from next nearest-neighbors (NN) in this material are highly frustrated and responsible for enhancing skyrmion stability. We report the larger spin-lattice effect on both dynamical Heisenberg exchanges and Dzyaloshinskii-Moriya interactions for next NN compared to NN which is in contrast with recently observed spin-lattice effect in bulk bcc Fe and CrI$_3$ monolayer. Based on our analysis, we find that the effective measures of SLCs in fcc (hcp) stacking of PdFe/Ir(111) are $\sim 2.71 ( \sim 2.36)$ and $\sim 14.71 ( \sim21.89)$ times stronger for NN and next NN respectively, compared to bcc Fe. The linear regime of displacement for SLC parameters is $\leq$ 0.02 Å which is 0.72\% of the lattice constant for PdFe/Ir(111). The microscopic understanding of SLCs provided by our current study could help in designing spintronic devices based on thermodynamic properties of skyrmion multilayers.

cond-mat.mtrl-sci↗

arXiv2024

Topological magnon in exchange frustration driven incommensurate spin spiral of a kagome lattice YMn$_6$Sn$_6$

YMn$_6$Sn$_6$ consists of two types of Mn-based kagome planes stacked along $c$-axis having a complex magnetic interactions. We report a spin reconstruction in YMn$_6$Sn$_6$ from ferromagnet (FM) into a combination of two incommensurate spin spirals (SSs) originating from two different type of Mn kagome planes driven by frustrated magnetic exchanges along the $c$-axis with inclusion of Hubbard U. The pitch angle and wave vector of the incommensurate SSs are $\sim$89.3$^{\circ}$ and $\sim$ (0 0 0.248) respectively which are in excellent agreement with experiment. We employed an effective model Hamiltonian constructed out of exchange interactions to capture experimentally observed non-equivalent nature of the two incommensurate SSs which also explain FM-SS crossover due to antiferromagntic spin exchange with correlation. We further report the existence of topological magnon with spin-orbit coupling in incommensurate SS phase of YMn$_6$Sn$_6$ by calculating the topological invariants and Berry curvature profile. The location of Dirac magnon in energy landscape at 73 meV matches with another experimental report. We demonstrate the accuracy of our results by highlighting experimental features in YMn$_6$Sn$_6$.

cond-mat.mtrl-sci↗

arXiv2023

Spin transport properties in a topological insulator sandwiched between two-dimensional magnetic layers

Nontrivial band topology along with magnetism leads to different novel quantum phases. When time-reversal-symmetry is broken in three-dimensional topological insulators (TIs) by applying high enough magnetic field or proximity effect, different phases such as quantum Hall or quantum anomalous Hall(QAH) emerge and display interesting transport properties for spintronic applications. The QAH phase displays sidewall chiral edge states which leads to the QAH effect. In a finite slab, contribution of the surface states depends on both the cross-section and thickness of the system. Having a small cross-section and a thin thickness leads to direct coupling of the surfaces, on the other hand, a thicker slab results in a higher contribution of the non-trivial sidewall states which connect top and bottom surfaces. In this regard, we have considered a heterostructure consisting of a TI, namely Bi2Se3, which is sandwiched between two-dimensional magnetic monolayers of CrI3 to study its topological and transport properties. Combining DFT and tight-binding calculations along with non-equilibrium Green's function formalism, we show that a well-defined exchange gap appears in the band structure in which spin polarised edge states flow. We also study the width and finite-size effect on the transmission and topological properties of this magnetised TI nanoribbon.

cond-mat.mes-hall↗

arXiv2023

Effect of chirality imbalance on Hall transport of PrRhC$_2$

Much has been learned about the topological transport in real materials. We investigate the interplay between magnetism and topology in the magneto-transport of PrRhC$_2$. The four-fold degeneracy reduces to two-fold followed by non-degenerate Weyl nodes when the orientation of the magnetic quantization axis is changed from easy axis to body-diagonal through face-diagonal. This engenders chirality imbalance between positive and negative chirality Weyl nodes around the Fermi energy. We observe a significant enhancement in the chiral anomaly mediated response such as planar Hall conductivity and longitudinal magneto-conductivity, due to the emergence of chirality imbalance upon orienting the magnetic quantization axis to body-diagonal. The angular variations of the above quantities for different magnetic quantization axis clearly refer to the typical signature of planar Hall effect in Weyl semimetals. We further investigate the profiles of anomalous Hall conductivities as a function of Fermi energy to explore the effects of symmetries as well as chirality imbalance on Berry curvature.

cond-mat.mes-hall↗

arXiv2022

Magnetization dynamics in Fe$_x$Co$_{1-x}$ in presence of chemical disorder

In this paper, we present a theoretical formulation of magnetization dynamics in disordered binary alloys based on Kubo linear response theory interfaced with the combination of seamlessly three approaches; density functional based tight-binding linear muffin-tin orbitals, generalized recursion and Augmented space formalism. We apply this method to study the magnetization dynamics in chemically disordered Fe$_x$Co$_{1-x}$ ($x$ = 0.2, 0.5, 0.8) alloys. We reported that the magnon energies decrease with an increase in Co concentration. Significant magnon softening has been observed in Fe$_{20}$Co$_{80}$ at the Brillouin zone boundary. The magnon-electron scattering increases with increasing Co content which in turn modifies the hybridization between the Fe and Co atoms. This reduces the exchange energy between the atoms and soften down the magnon energy. The lowest magnon lifetime in found in Fe$_{50}$Co$_{50}$, where disorder is maximum. This clearly indicates that the damping of magnon energies in Fe$_x$Co$_{1-x}$ is governed by the hybridization between Fe and Co whereas the magnon lifetime is controlled by disorder configuration. Our atomistic spin dynamics simulations show a reasonable agreement with our theoretical approach in magnon dispersion for different alloy compositions.

cond-mat.mtrl-sci↗

arXiv2022

Pressure driven topological phase transition in chalcopyrite ZnGeSb$_2$

Recently topologically non-trivial phases have been identified in few time-reversal invariant systems that lack of inversion symmetry. Using density functional theory based first-principles calculations, we report a strong topologically non-trivial phase in chalchopyrite ZnGeSb$_2$, which can act as a model system of strained HgTe. The calculations reveal the non-zero topological invariant ($Z_2$), the presence of Dirac cone crossing in the surface spectral functions with spin-momentum locking. We also show that the application of moderate hydrostatic pressure ($\sim$7 GPa) induces topological phase transition from topological non-trivial phase to a topologically trivial phase. A discontinuity in the tetragonal distortion of non-centrosymmetric ZnGeSb$_2$ plays a crucial role in driving this topological phase transition.

cond-mat.mtrl-sci↗

arXiv2021

Electronic structure and unconventional non-linear response in double Weyl semimetal SrSi$_2$

Considering a non-centrosymmetric, non-magnetic double Weyl semimetal (WSM) SrSi$_2$, we investigate the electron and hole pockets in bulk Fermi surface behavior that enables us to characterize the material as a type-I WSM. We study the structural handedness of the material and correlate it with the distinct surface Fermi surface at two opposite surfaces following an energy evolution. The Fermi arc singlet becomes doublet with the onset of spin orbit coupling that is in accordance with the topological charge of the Weyl Nodes (WNs). A finite energy separation between WNs of opposite chirality in SrSi$_2$ allows us to compute circular photogalvanic effect (CPGE). Followed by the three band formula, we show that CPGE is only quantized for Fermi level chosen in the vicinity of WN residing at higher value of energy. Surprisingly, for the other WN of opposite chirality in the lower value of energy, CPGE is not found to be quantized. Such a behavior of CPGE is in complete contrast to the time reversal breaking WSM where CPGE is quantized to two opposite plateau depending on the topological charge of the activated WN. We further analyze our finding by examining the momentum resolved CPGE. Finally we show that two band formula for CPGE is not able to capture the quantization that is apprehended by the three band formula.

cond-mat.mes-hall↗

arXiv2021

Spin-lattice couplings in two-dimensional CrI$_3$ from first-principles study

Since thermal fluctuations become more important as dimensions shrink, it is expected that low-dimensional magnets are more sensitive to lattice distortions and phonons than bulk systems are. Here we present a fully relativistic first-principles study on the spin-lattice coupling, i.e. how the magnetic interactions depend on local lattice distortions, of the prototypical two-dimensional ferromagnet CrI$_3$. We extract an effective measure of the spin-lattice coupling in CrI$_3$ which is up to ten times larger than what is found for bcc Fe. The magnetic exchange interactions, including Heisenberg and relativistic Dzyaloshinskii-Moriya interactions, are sensitive both to the in-plane motion of Cr atoms and out-of-plane motion of ligand atoms. We find that significant magnetic pair interactions change sign from ferromagnetic (FM) to anti-ferromagnetic (AFM) for atomic displacements larger than 0.16 Å. We explain the observed strong spin-lattice coupling by analyzing the orbital decomposition of isotropic exchange interactions, involving different crystal-field-split Cr$-3d$ orbitals. The competition between the AFM t$_{2g}$ - t$_{2g}$ and FM t$_{2g}$ - e$_{g}$ contributions depends on the bond angle formed by Cr and I atoms as well as Cr-Cr distance. In particular, if a Cr atom is displaced, the FM-AFM sign change when the I-Cr-I bond angle approaches 90$^\circ$. The obtained spin-lattice coupling constants, along with the microscopic orbital analysis can act as a guiding principle for further studies of the thermodynamic properties and combined magnon-phonon excitations in two-dimensional magnets.

cond-mat.mtrl-sci↗

arXiv2021

Role of time reversal symmetry and tilting in circular photogalvanic responses

We study the role of time reversal symmetry (TRS) in the circular photogalvanic (CPG) responses considering chiral Weyl semimetal (WSM) while a quantized CPG response is guaranteed by broken of both inversion symmetry (IS) and mirror symmetries. The TRS broken WSM yields one left and one right chiral Weyl nodes (WNs) while there are two left and right chiral WNs for TRS invariant WSM. We show that these features can potentially cause the quantization of CPG response at higher values compared to the topological charge of the underlying WSM. This is further supported by the fact that Berry curvature and velocity behave differently whether the system preserves or breaks the TRS. We find the CPG responses for TRS invariant type-II WSM to be quantized at two and four times the topological charge of the activated WNs while the chemical potential are respectively chosen in the vicinity of energies associated with left and right chiral WNs. By contrast, irrespective of the above choice of the chemical potential, the quantization in CPG response is directly given by the topological charge of the activated WNs for TRS broken case. Interestingly, we notice non-quantized peak in CPG response when energies of WNs associated with opposite chiralities are close to each other as it is the case for TRS invariant type-I WSM considered here. Moreover, we show that the tilt can significantly modify the CPG response as velocity in the tilt direction changes which enters into the CPG tensor through the Fermi distribution function. Given these exciting outcomes, the second order CPG response emerges as a useful indicator to characterize the system under consideration. Furthermore, we investigate the momentum resolved structure of CPG response to relate with the final results and strengthen our analysis from the perspective of the lattice models.

cond-mat.mes-hall↗