Session D14: Dirac and Weyl Semimetals: Theory II

Tunable Giant Berry Curvature Dipole in Two-Dimensional Xenes

The anomalous Hall effect in time-reversal symmetry broken systems is underpinned by the concept of Berry curvature in band theory. However, recent experiments [1] reveal that the nonlinear Hall effect can be observed in non-magnetic systems without an external magnetic field [2]. The emergence of the nonlinear Hall effect under time-reversal symmetric conditions can be well-explained in terms of Berry curvature dipole arising from inversion symmetry breaking [3]. Using realistic tight-binding models and symmetry analyses, we have discovered that the combined effect of transverse electric field and strain leads to a giant Berry curvature dipole in the elemental buckled honeycomb lattices, i.e., Xenes [4]. The topology of the electronic wavefunction switches from the band-inverted quantum spin Hall state to an electric field-driven normal insulating one about the gapless point, which is further accompanied by an enhanced and switchable Berry curvature dipole near the Fermi level. Furthermore, strain engineering on puckered phosphorene layers grown on a suitable substrate exhibits a large Berry curvature dipole [5]. Our results predict an externally controllable nonlinear Hall effect in a new class of elemental systems that can be experimentally verified.

[1] Ma et al., Nature 565, 337 (2019).

[2] Du et al., Nature Reviews Physics, 1 (2021).

[3] Sodemann et al. Physical review letters 115, 216806 (2015).

[4] Bandyopadhyay et al. 2D Materials 9, 035013 (2022).

[5] Bandyopadhyay et al. (under review, 2023)   

Berry-induced nonlinear Hall effect in a graphene - bilayer WSe2 system

Charge transport in two-dimensional nanodevices has become increasingly important due to its technological applications. Very significant in this field was the discovery of the integer quantum Hall effect (IQHE), which revealed the quantization of the resistance transversal to an applied bias current. Remarkably, this relies on the breaking of time reversal (TR) symmetry owed to the presence of a strong external magnetic field or, as in the anomalous Hall effect, magnetic order. The search for a Hall-like effect that shows up even in TR symmetric systems has led to the discovery of the nonlinear Hall effect (NLHE), that occurs in systems with TR but lacking an inversion center. Notably, this effect can only be observed at second order in the applied bias. In this work, we investigate this phenomenon in a superstructure made up of graphene and 60^o twisted bilayer tungsten diselenide. Of all the mechanisms leading to NLHE, we focus on the Berry dipole contribution, which depends solely on the geometry of the Bloch wavefunction. Although there exist effective, symmetry-based two-band models giving the NLHE, here we use first principle (DFT) and tight binding calculations to find a Hamiltonian for graphene alone and calculate the nonlinear current in a semiclassical formalism, with a focus on energies around the charge neutrality point. With this, we get a sense of the order of magnitude of the nonlinear current and compare it with the current literature.   

Investigation of Berry curvature dipole in transition metal dichalcogenides

Conventional Hall effect requires a broken time-reversal (TR) symmetry for the generation of a transverse voltage in response to an applied electric field. Recently, Sodeman and Fu (2015) proposed another addition to the Hall effect family, a non-linear Hall (NLH) response, present in systems that preserve TR symmetry. This NLH current results from Berry curvature dipole (BCD) generated in non-centrosymmetric materials due to the asymmetric distribution of Berry curvature in the momentum space. From the initial prediction by Sodemann and Fu, breaking inversion is the key requirement to finite BCD, along with the constraint that the material has low crystal symmetries. In 2D materials, the maximum allowed symmetry for non-zero BCD is a single mirror plane. The distorted octahedral phase of transition metal dichalcogenides (TMDCs) is non-centrosymmetric with reduced symmetries, making them an excellent platform to observe and engineer NLH effect. Using first-principles DFT calculations and tight binding models, we have successfully identified monolayer and bilayer TMDCs that display finite BCD and hence, NLH currents^1,2. The identification and study of materials that display BCD can lead to a better understanding of its underlying quantum nature, all the while being promising platforms to observe and engineer non-linear Hall effects and their expected applications. 

 

¹ Joseph et.al., Materials Research Express 8:124001 (2021). 

² Joseph et.al., Journal of Physics: Condensed Matter 33:465001 (2021).    

Non-Linear Thermoelectric Response Induced by Berry Curvature Quadrupole in Systems With Broken Time-Reversal Symmetry

Recent theoretical work has shown that higher-order moments of the Berry curvature, e.g., Berry curvature quadrupole or hexapole moments can produce the leading order non-linear anomalous Hall response (NLAH) in systems with special magnetic point group symmetry. Recent experimental work has reported the observation of the Berry curvature quadrupole-induced third-order NLAH (i.e., Hall voltage proportional to the third power of the external electric field) from cryogenic conditions to room temperature in an epitaxially grown material platform with broken time-reversal symmetry. In this paper, using semiclassical Boltzmann formalism in the relaxation time approximation, we compute the Berry curvature quadrupole-induced non-linear anomalous thermal Hall and Nernst coefficients in time reversal broken systems. In systems where Berry curvature monopole and dipole moments vanish by symmetry, our results predict the behavior of the leading order transverse anomalous thermoelectric coefficients proportional to the third power of the applied longitudinal temperature gradient, and are guaranteed to exist in systems that have already exhibited the third order non-linear anomalous Hall effect in recent experiments.   

Localized interfacial phonon modes at the electronic axion domain wall

One of the most salient features of the topological state is the existence of exotic electronic modes localized at the surface or interface of a sample. In this work, we show that along with the electronic state, the phonon mode can also be localized at the domain wall between topologically trivial and non-trivial regions. We consider the electron-phonon interaction in a gapped Dirac semimetal and by treating the phonon degrees of freedom as a pseudo-gauge field, we find that the valley axion term in a gapped Dirac semimetal can influence the phonon dynamics which leads to localized interfacial phonon modes at the domain wall between trivial and non-trivial regimes (determined by the valley axion parameter). We also discuss the physical properties of this interfacial phonon mode and a possible experimental probe.   

Edge theory of the non-Hermitian skin modes in higher dimensions

In this work, we propose a universal edge theory for the higher-dimensional non-Hermitian edge-skin modes. In contrast to the well-understood corner-skin effect, we demonstrate that the edge-skin effect requires the protection of reciprocity or inversion. Through an exact mapping, we show that these skin modes share the same bulk-edge correspondence as the Fermi-arc states in a Hermitian Dirac semimetal. Based on this mapping, we introduce a bulk projection criterion to identify the skin edge, and utilize the non-Bloch Hamiltonian under specific cylinder geometry to characterize the localization features of edge-skin modes. We find that the edge-skin modes are made of components with real-valued momenta along the edge, and interestingly the decay direction typically deviates from the normal direction of the edge, a phenomenon we term skewness. Furthermore, we reveal the remarkable sensitivity of the cylinder-geometry spectrum to disturbances that violate fragile reciprocity. When this symmetry is disrupted, the cylinder-geometry spectrum undergoes an abrupt transition towards the near open-boundary spectrum, underscoring a key difference between corner-skin and edge-skin effects.   

Origin of flat bands in three-dimensional coupled kagome lattices

Two-dimensional kagome lattices are known to host a flat band and Dirac point due to the destructive quantum interference of electronic wavefunctions [1-3]. In this work, we have introduced an exact analytical decimation transformation scheme to explore the coexistence of flat band and Dirac point in three-dimensional coupled kagome systems. Our proposed technique allows coarse-graining of the parameter space, which maps the original system to an analogous low-level lattice [4]. The decimated system facilitates defining a descriptor that controls the appearance of a flat band and provides a definite criterion for absolute flatness. We confirm our predictions on the emergence of the flat band and Dirac points for a class of materials employing material databases in conjunction with density functional theory calculations. The present work explores the intricate electronic properties of coupled kagome lattices and provides an analytical formalism that can efficiently investigate the rich physics of such lattice models.

References:

Magic momenta and three dimensional Landau levels from a three dimensional graphite moir'e superlattice

Twisted bilayer graphene (TBG) and other quasi-two-dimensional moir'e superlattices have attracted significant attention due to the emergence of various correlated and topological states associated with the flat bands in these systems. In this work, we theoretically explore the physical properties of a new type of three dimensional graphite moir'e superlattice, the bulk alternating twisted graphite (ATG) system with homogeneous twist angle, which is grown by in situ chemical vapor decomposition method. Compared to TBG, the bulk ATG system is bestowed with an additional wavevector degrees of freedom due to the extra dimensionality. As a result, we find that when the twist angle of bulk ATG is smaller than twice of the magic angle of TBG, there always exist “magic momenta” at which the in-plane Fermi velocities of the moir'e bands vanish. Moreover, topologically distinct flat bands of TBG at different magic angles can even co-exist at different out-of-plane wavevectors in a single bulk ATG system. Most saliently, when the twist angle is relatively large, exactly dispersionless three dimensional zeroth Landau level would emerge in the bulk ATG, which may give rise to robust three dimensional quantum Hall effects over a large range of twist angles.   

Geometry-Enforced Topological Chiral Fermions in Amorphous Chiral Metals

The recent recognition of a link between topological and structural chirality precipitated the experimental discovery of large families of ideal topological chiral (e.g. Weyl) semimetals, such as B-20 RhSi, with dramatic long topological surface Fermi arcs and tunable chirality-dependent spin, orbital, and response properties.  

However outside of the limit of perfect translation symmetry, especially among the numerous experimentally accessible amorphous materials in nature, it remains an open question whether there similarly exist mechanisms for generating and identifying topologically chiral nodal degeneracies. 

We present extensive analytic and numerical calculations demonstrating the existence of multitudinous chiral fermions in amorphous metals, whose degeneracy and chiral charges are tunable via the interplay of average symmetry and geometry.

We introduce an amorphous Wilson-loop numerical method to, for the first time, characterize chiral fermions with quantized Berry curvature fluxes in fully disordered 3D metals.

We further analyze the role of disorder on the bulk-boundary correspondence and response.

Our findings indicate a clear route towards engineering geometry-enforced topology in non-crystalline materials and metamaterials.   

Scattering Dynamics of a Non-Hermitian Dirac Equation

Non-Hermitian systems can exhibit many interesting properties that differ qualitatively from their Hermitian counterparts. Here, we explore the properties of a non-Hermitian variant of the (2+1)-dimensional Dirac wave equation. This non-Hermitian Dirac equation (NHDE) can arise in the long-wavelength limit of a non-Hermitian lattice obeying a set of symmetries we call "semi-Hermiticity". Going beyond the more well-known parity/time-reversal (PT) symmetry, semi-Hermiticity allows a non-Hermitian system to exhibit not only a real energy spectrum but also pairwise-orthogonal eigenstates, which are required for the emergence of a Dirac cone. We derive the phase diagram of the NHDE, showing that it is governed by two Hermitian Dirac sub-systems with independently-variable Dirac masses. The NHDE exhibits an anomalous form of Klein tunneling, whereby flux conservation can be violated at the interface between two domains with real bulk spectra. Such an interface can even function as a simultaneous laser and coherent perfect absorber of infinitesimal thinness. We show that the key properties of the NHDE can be probed with experimentally-realizable non-Hermitian metamaterials based on acoustics or photonics.   

Interaction renormalization of generalized semi-Dirac fermions

We present a generalization of semi-Dirac fermions, and study the effects of long range Coulomb electron-electron interactions on the low energy excitations of such systems. We consider a class of two-dimensional Hamiltonians with a dispersion that is linear in one momentum direction, and an even monomial (of degree 2n) in the other.  This allows us to illustrate how the degree of flatness in the non-relativistic direction affects the underlying physics. Such flat anisotropic fermionic spectra may be realized at a Lifshitz transition characterized by the merger of two lower degree generalized semi-Dirac points.

 

A first-order perturbative treatment of interactions produces infrared divergences in the self-energy corrections to the coupling parameters (velocity and generalized mass). We discuss the exact solutions of the perturbative renormalization group equations, within the RPA framework, which yield an extraordinarily strong spectrum renormalization at low energies whereby the flatness in the non-relativistic direction is dramatically reduced, resulting in quasi-linear behavior. Thus Coulomb interactions have a profound effect on the fermionic spectrum, and subsequently on all physical observables at low temperature.   

Magnetoresistance due to classical memory effects in a three-dimensional electron gas

Magnetoresistance (MR) provides a powerful tool for probing the non-Markovian nature of transport in a magnetic field. Long-range disorder gives rise to a nontrivial MR due to classical memory effects, arising from multiple returns to the same position. While the presence of such disorder has been indicated in various materials, there have been few rigorous studies on these effects in 3D systems. In this talk, I will discuss the results of our analysis of the transverse (TMR), as well as longitudinal MR (LMR) of a 3D electron gas, due to a long-range a) random magnetic field and b) random potential, within a semiclassical Boltzmann approach, with and without short-range disorder. To account for non-Markovian processes, the disorder is incorporated as a random force on the LHS of the Boltzmann equation, analogous to previous studies in 2D. We perform a perturbative expansion for the Green's function of the Boltzmann equation, and thus for the conductivity, in the correlation function of the long-range disorder. In the absence of short-range disorder, the unperturbed Green's function is singular due to a zero mode, and the field-dependence of the conductivity is estimated by resumming the perturbation series to all orders. From our analysis, we obtain a prominent TMR as well as LMR, which generally peak or saturate at a characteristic field scale where the correlation length becomes comparable to the cyclotron radius.   

Large anomalous Nernst effect in polycrystalline thin films of the Weyl ferromagnet Co2MnGa

Recent discoveries of topological magnets have opened up diverse spintronic applications of their large responses beyond magnetization scaling observed in conventional ferromagnets. A prominent example is the anomalous Nernst effect (ANE), a transverse magneto-thermoelectric phenomenon that produces an electromotive force orthogonal to the heat flux and magnetization. Unlike the Seebeck effect (SE) generating an electromotive force parallel to the heat flux, transverse thermoelectric properties of ANE well fit in the lateral configurations of devices fabricated through conventional thin-film fabrication processes. This feature enables distinct device applications through a simplified fabrication process, reduced production cost, extensive area coverage, and enhanced flexibility. In this study, we report the highest ANE ever recorded among all reported polycrystalline films to date by using a topological ferromagnet. In particular, we have successfully fabricated high-quality polycrystalline thin films of the Weyl ferromagnet Co₂MnGa that exhibit a large ANE of more than 5 μV/K. By retaining a high film density, we demonstrate the sizable ANE in the films obtained using a simple fabrication process well-suited for device developments. Establishing a thin-film fabrication technique capable of producing a giant ANE facilitates spintronic applications of the Weyl ferromagnet, including diverse ANE-based device applications.   

Spin-orbit enabled unconventional Stoner magnetism

The Stoner instability remains a cornerstone for understanding metallic ferromagnets. This instability captures the interplay of Coulomb repulsion, Pauli exclusion, and two-fold fermionic spin degeneracy. In materials with spin-orbit coupling, fermionic spin is generalized to a two-fold degenerate pseudospin. Here we identify a new fermionic pseudospin with a symmetry that forbids it to couple to a Zeeman field. This spinless pseudospin exists in five non-symmorphic space groups and appears at the Brillouin zone (BZ) boundary. With Coulomb repulsion, this spinless pseudospin gives rise to Stoner instabilities into magnetic states that are not usual ferromagnets. These spinless-pseudospin ferromagnets break time-reversal symmetry, have a vanishing magnetization, and are generally non-collinear. The non-collinear magnetization enables a scalar spin chirality-driven Berry curvature. In addition, much like altermagnets, these pseudospin ferromagnets exhibit energy band spin-splittings that vanish by symmetry along lines in the BZ, allowing for drumhead surface states. We discuss candidate materials.