Tellurene Reveals Unexpected Polar Electrical Response

Scientists are increasingly interested in unidirectional magnetoresistance, a nonlinear magnetotransport phenomenon observed in noncentrosymmetric conductors, and its potential for novel electronic devices. Claudio Iacovelli, working as an Independent Researcher, Pierpaolo Fontana from the Departament de Fısica at Universitat Aut`onoma de Barcelona, and Victor Velasco of the International School for Advanced Studies (SISSA), alongside Chang Niu from Purdue University, Peide D. Ye, Marcus V. O. Moutinho from Universidade Federal do Rio de Janeiro, Campus Duque de Caxias, Caio Lewenkopf and Marcello B. Silva Neto from Instituto de Fısica, Universidade Federal do Rio de Janeiro, have demonstrated a significant finding regarding tellurene, a two-dimensional material. Their collaborative research, spanning institutions including the Universidade Federal do Rio de Janeiro and Purdue University, reveals that tellurene exhibits a polar form of unidirectional magnetoresistance in its valence band, traditionally considered chiral. This discovery, achieved through a combination of semiclassical Boltzmann transport and detailed numerical calculations, highlights how polar effects can emerge in topologically trivial bands via multiband interactions, establishing tellurene as a promising material for geometric rectification in both electron and hole conduction regimes and broadening our understanding of magnetotransport phenomena.

Scientists have uncovered a surprising property in a two-dimensional material that could revolutionise how we manipulate electronic signals. Tellurene, a layered tellurium compound, exhibits a unique directional response to magnetic fields, offering potential for novel electronic devices. This discovery challenges conventional understanding and opens doors to more efficient and versatile circuitry.

Scientists have uncovered a surprising origin for a specific type of electrical resistance in tellurene, a two-dimensional form of tellurium. Unidirectional magnetoresistance, also known as electric magnetochiral anisotropy (eMChA), describes how a material’s electrical resistance changes when exposed to a magnetic field, and typically arises from materials lacking symmetry.

This research demonstrates that a polar component of eMChA, previously thought to be absent in the valence band of tellurene, emerges through a complex interplay of electronic bands within the material. The work challenges conventional understanding by revealing that this polar behaviour isn’t limited to materials with inherent polarity, but can arise from the intricate quantum geometry of electrons within tellurene’s structure.

This discovery builds upon previous research establishing a polar eMChA in tellurene’s conduction band, linking it to the material’s unique quantum properties and lone pair polarization. Through a detailed downfolding procedure, a method for simplifying complex electronic structures, researchers found that remote electronic bands induce gradients in the quantum metric, activating metric dipoles and generating a measurable polar coefficient.

These findings are supported by numerical calculations that quantitatively match experimental measurements of voltage changes dependent on doping levels and applied magnetic fields. The combined chiral and polar characteristics of eMChA in tellurene also explain shifts observed in the angular dependence of voltage for in-plane magnetic fields. This work establishes tellurene as a promising material for quantum-geometric rectification, converting alternating current into direct current, in both electron and hole regimes.

By demonstrating that polar eMChA can emerge in topologically trivial bands through multiband effects, this study opens new avenues for designing nanoscale devices with electrically controllable rectification capabilities. The research highlights the potential of tellurene for advanced electronic applications leveraging its unique quantum properties and intrinsic asymmetry.

Tellurene’s Magnetochiral Anisotropy Originates from Lone-Pair Polarisation and Remote Weyl Bands

Numerical calculations reveal a quantitative agreement between the doping-dependent second-harmonic measurements of the longitudinal voltage and the band structure of tellurene. Tellurene exhibits both chiral and polar contributions to the electric magnetochiral anisotropy (eMChA), with coefficients of χ = 0 and γ = 0.

These values define the material’s response to magnetic fields and current flow, establishing a unique interplay between these two anisotropy mechanisms. The study elucidates that the polar eMChA arises not only from the intrinsic lone-pair polarization but also from remote Weyl-node containing bands inducing momentum-space gradients of the quantum metric in the low-energy levels.

This downfolding procedure activates finite metric dipoles, contributing to a measurable voltage response, and the angular dependence of voltage for in-plane fields also shifts, providing further evidence for the combined chiral and polar character of the eMChA in tellurene. Calculations show that the polar eMChA can emerge even in topologically trivial bands through these multiband effects, challenging conventional understanding and broadening the scope of materials exhibiting this phenomenon. Consequently, tellurene is established as a promising platform for quantum-geometric rectification in both electron and hole regimes, offering potential for novel nanoscale devices.

Valence band parameterisation via k⋅p perturbation theory in tellurium

A k⋅p perturbation theory approach systematically describes the valence band structure of tellurium, forming the basis for understanding nonlinear transport phenomena. Beginning at the high-symmetry H point of the Brillouin zone, defined as kH = (4π/3a, 0, π/c) with a = 4.44Å and c = 5.91Å, the unperturbed Hamiltonian establishes the initial spectrum and wave functions.

To account for behaviour away from this point, the solutions to the Schrödinger equation are expanded in powers of both the k⋅p coupling and the spin-orbit interaction, introducing Bloch states and reducing the problem to an effective eigenvalue equation. The Hamiltonian is then decomposed into four terms representing the k⋅p term, the k-independent spin-orbit interaction, the k-dependent spin-orbit interaction, and the unperturbed Hamiltonian, with all matrix elements evaluated using the unperturbed states at the H point.

In the absence of spin-orbit interaction, the valence band exhibits a twofold degeneracy, which is lifted upon inclusion of the interaction, splitting the manifold into non-degenerate bands. This leads to the formulation of a 4×4 block Hamiltonian in k-space, comprising distinct blocks describing the low-energy bands, the high-energy bands, and a hybridization matrix coupling these subspaces via spin-orbit interactions. Parameters defining these Hamiltonian blocks were extracted from prior work and incorporated into the model to accurately represent the band structure and facilitate subsequent calculations of nonlinear transport properties.

Polar electronic effects substantially influence magnetochiral anisotropy in tellurene

Scientists are increasingly focused on harnessing the subtle interplay between magnetism and electron flow in materials, and recent work on tellurene reveals a nuanced picture of this relationship. For years, the phenomenon of electric magnetochiral anisotropy (eMChA) has been understood primarily through a ‘chiral’ lens, attributing its origins to the material’s inherent asymmetry.

This research, however, demonstrates that a ‘polar’ contribution to eMChA, arising from the material’s electronic band structure, is equally important and previously underestimated. Identifying this polar component isn’t merely an academic exercise; it suggests new avenues for designing materials with tailored magnetotransport properties, potentially leading to more efficient and versatile electronic devices.

The ability to control electron flow with both electric and magnetic fields is central to spintronics, and this work expands the toolkit for achieving that control. While the calculations align with experimental doping-dependent measurements, extending this understanding to other materials, and particularly to three-dimensional systems, will require further investigation.

The downfolding procedure used to simplify the calculations inherently introduces approximations. Looking ahead, the focus will likely shift towards exploring materials where these polar and chiral effects can be amplified and combined. The development of new theoretical frameworks capable of accurately predicting eMChA in complex materials is also crucial. Ultimately, this research underscores a broader trend: that seemingly well-understood phenomena often conceal hidden complexities, and that a deeper understanding of these subtleties is essential for realising the full potential of advanced materials.