Nonlinear Transport Phenomena Research Articles

Nonlinear edge transport in a quantum Hall system.

Nonlinear transport phenomena in condensed matter reflect the geometric nature, quantum coherence, and many-body correlation of electronic states. Electric currents in solids are classified into (i) ohmic current, (ii) supercurrent, and (iii) geometric or topological current. While the nonlinear current-voltage (I-V) characteristics of the former two categories have been extensive research topics recently, those of the last category remains unexplored. Among them, the quantum Hall current is a representative example. Realized in two-dimensional electronic systems under a strong magnetic field, the topological protection quantizes the Hall conductance in the unit of e2/h (e, elementary charge; and h, Planck constant), of which the edge transport picture gives a good account. Here, we theoretically study the nonlinear I-VH characteristic of the edge transport up to third order in VH. We find that nonlinearity arises in the Hall response from electron-electron interaction between the counterpropagating edge channels with the nonlinear energy dispersions. We also discuss possible experimental observations.

Graph neural network-based multiscale thermal modeling for heterogeneous materials with complex structures

This study presents a novel GNN-based model for multiscale thermal characterization of heterogeneous materials with complex microstructures. It incorporates relationships between composition, structure, and thermal transport across multiple scales, leveraging the structure of GNNs. Results demonstrate enhanced performance of the GNN-based model compared with existing methods. Specifically, the GNN model improved thermal conductivity prediction with a mean absolute error of 0.18 W/mK (15 % improvement over the Bayesian neural network-based model) and provided a 30x speedup in computation time. The model successfully connected atomic-scale interactions to macroscale properties, achieving less than 5 % error in predicting effective thermal conductivity from one scale to another. Furthermore, it demonstrated the ability to capture nonlinear thermal transport phenomena with 92 % accuracy. The model also improved the prediction of the transient thermal responses by 20 %, accurately capturing the time-varying behaviour of materials. This work also proved the model’s ability to handle new material systems with transfer learning, achieving 88 % accuracy. Finally, Bayesian neural networks integrated into the model provided uncertainty quantification, with 95 % of experimental measurements falling within the predicted bounds. This work demonstrated the ability of the framework to handle complex microstructures, nonlinear phenomena, and transient responses while maintaining a computationally efficient model that can enable real-time applications in design and optimization needed in modern materials innovation. It represents a powerful tool for data-driven multiscale mechanics that could accelerate materials research and development for the aerospace, electronics cooling, and additive manufacturing industries.

Exciton-Exciton Interactions in Van der Waals Heterobilayers

Exciton-exciton interactions are key to understanding nonlinear optical and transport phenomena in van der Waals heterobilayers, which emerged as versatile platforms to study correlated electronic states. We present a combined theory-experiment study of excitonic many-body effects based on first-principle band structures and Coulomb interaction matrix elements. Key to our approach is the explicit treatment of the fermionic substructure of excitons and dynamical screening effects for density-induced energy renormalization and dissipation. We demonstrate that dipolar blueshifts are almost perfectly compensated by many-body effects, mainly by screening-induced self-energy corrections. Moreover, we identify a crossover between attractive and repulsive behavior at elevated exciton densities. Theoretical findings are supported by experimental studies of spectrally narrow, mobile interlayer excitons in atomically reconstructed, h-BN-encapsulated MoSe2/WSe2 heterobilayers. Both theory and experiment show energy renormalization on a scale of a few meV even for high injection densities in the vicinity of the Mott transition. Our results revise the established picture of dipolar repulsion dominating exciton-exciton interactions in van der Waals heterostructures and open up opportunities for their external design. Published by the American Physical Society 2024

Nonlinear electrical transport phenomena as fingerprints of a topological phase transition in ZrTe5

Topological phase transitions, influenced by magnetic fields, dopants, pressure, and temperature, create Berry curvature in band structures, challenging to detect due to resolution and scattering issues in spectroscopy and transport. Here, we propose nonlinear electrical transport phenomena as fingerprints of a topological phase transition in ZrTe5 under magnetic fields. Both a nonlinear longitudinal conductivity ΔσL in a magnetic-field-aligned electric field and a third-order nonlinear Hall (transverse) conductivity Δσxy in a magnetic-field-perpendicular electric field arise below a characteristic temperature T*. The sensitivity of nonlinear transport to the band topology allows the detection of a subtle change in the band topology hidden in linear transport coefficients. Extending the previous scaling theory between linear transport coefficients (σxx and σxy), we also propose scaling relations for both linear (σxx and σxy) and nonlinear (ΔσL and Δσxy) transport coefficients. These scaling relations will help understand the interplay between the mechanisms of nonlinear transport coefficients and the influence of Berry curvature.

Ultrafast nonequilibrium dynamics and high-harmonic generation in two-dimensional quantum spin Hall materials

We develop the theoretical framework of nonequilibrium ultrafast photonics in monolayer quantum spin Hall insulators supporting a multitude of topological states. In these materials, ubiquitous strong light-matter interactions in the femtosecond scale lead to nonadiabatic quantum dynamics, resulting in topology-dependent nonlinear optoelectronic transport phenomena. We investigate the mechanism driving topological Dirac fermions interacting with strong ultrashort light pulses and uncover various experimentally accessible physical quantities that encode fingerprints of the quantum material's topological electronic state from the high-harmonic generated spectrum. Our work sets the theoretical cornerstones to realize the full potential of time-resolved harmonic spectroscopy for understanding nonequilibrium processes in quantum topological systems and identifying topological invariants in two-dimensional quantum spin Hall solid state systems.

Nonlinear transport phenomena and current-induced hydrodynamics in ultrahigh mobility two-dimensional electron gas

We report on nonlinear transport phenomena at high filling factor and DC current-induced electronic hydrodynamics in an ultrahigh mobility $\text{(}\ensuremath{\mu}=20\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}/\mathrm{Vs}\text{)}$ two-dimensional electron gas in a narrow ($15\ensuremath{-}\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}$ wide) GaAs/AlGaAs Hall bar for DC current densities reaching 0.67 A/m. The various phenomena and the boundaries between the phenomena are captured together in a two-dimensional differential resistivity map as a function of magnetic field (up to 250 mT) and DC current. This map, which resembles a phase diagram, demarcate distinct regions dominated by Shubnikov-de Haas (SdH) oscillations (and phase inversion of these oscillations) around zero DC current; negative magnetoresistance and a double-peak feature (both ballistic in origin) around zero field; and Hall field-induced resistance oscillations (HIROs) radiating out from the origin. From a detailed analysis of the data near zero field, we show that increasing the DC current suppresses the electron-electron scattering length that drives a growing hydrodynamic contribution to both the differential longitudinal and transverse (Hall) resistivities. Our approach to induce hydrodynamics with DC current differs from the more usual approach of changing the temperature. We also find a significant (factor of two to four) difference between the quantum lifetime extracted from SdH oscillations, and the quantum lifetime extracted from HIROs. In addition to observing HIRO peaks up to the seventh order, we observe an unexpected HIRO-like feature close to midway between the first-order and the second-order HIRO maxima at high DC current.

Collective Transport for Nonlinear Current-Voltage Characteristics of Doped Conducting Polymers.

Origin of nonlinear transport phenomena in conducting polymers has long been a topic of intense controversies. Most previous knowledge has attributed the macroscopic nonlinear I-V characteristics to individual behaviors of elementary resistors in the network. In this Letter, we show via a systematic dimensionality-dependent transport investigation, that understanding the nonlinear transport in conducting polymers must include the collective transport effect in a percolation network. The possible mediation of percolation threshold p_{c} by controlling the samples' dimensionality unveiled the collective effect in growth of percolation paths driven by electric field, enabling us to draw a smooth connection between two typically observed nonlinear phenomena, dissipative tunnelinglike and threshold-limited transport, which have been controversial for years. The possible microscopic origins of the collective transport are discussed within the Coulomb blockade theory.

Edge Currents Induced by AC Electric Field in Two-Dimensional Dirac Structures

Edges in two-dimensional structures are the source of nonlinear transport and optical phenomena which are particularly important in small-size flakes. We present a microscopic theory of the edge photogalvanic effect, i.e., the formation of DC electric current flowing along the sample edges in response to AC electric field of the incident terahertz radiation, for two-dimensional Dirac materials including the systems with massive and massless charge carriers. The edge current direction is controlled by the AC field polarization. The spectral dependence of the current is determined by the carrier dispersion and the mechanism of carrier scattering, as shown for single-layer and bilayer graphene as examples.

Nonlinear Landauer formula: Nonlinear response theory of disordered and topological materials

The Landauer formula provides a general scattering formulation of electrical conduction. Despite its utility, it has been mainly applied to the linear-response regime, and a scattering theory of nonlinear response has yet to be fully developed. Here, we extend the Landauer formula to the nonlinear-response regime. We show that while the linear conductance is directly related to the transmission probability, the nonlinear conductance is given by its derivatives with respect to energy. This sensitivity to the energy derivatives is shown to produce unique nonlinear transport phenomena of mesoscopic systems including disordered and topological materials. By way of illustration, we investigate nonlinear conductance of disordered chains and identify their universal behavior according to symmetry. In particular, we find large singular nonlinear conductance for zero modes, including Majorana zero modes in topological superconductors. We also show the critical behavior of nonlinear response around the mobility edges due to the Anderson transitions. Moreover, we study nonlinear response of graphene as a prime example of topological materials featuring quantum anomaly. Furthermore, considering the geometry of electronic wave functions, we develop a scattering theory of the nonlinear Hall effect. We establish a new connection between the nonlinear Hall response and the nonequilibrium quantum fluctuations. We also discuss the influence of disorder and Anderson localization on the nonlinear Hall effect. Our work opens a new avenue in quantum physics beyond the linear-response regime.

Terahertz-induced high-order harmonic generation and nonlinear charge transport in graphene

We theoretically study the terahertz-induced high-order harmonic generation (HHG) and nonlinear electric transport in graphene based on the quantum master equation with the relaxation time approximation. To obtain microscopic insight into the phenomena, we compare the results of the fully dynamical calculations with those under a quasistatic approximation, where the electronic system is approximated as a nonequilibrium steady state. As a result, we find that the THz-induced electron dynamics in graphene can be accurately modeled with the nonequilibrium steady state at each instance. The population distribution analysis further clarifies that the THz-induced HHG in graphene originates from the reduction of effective conductivity due to a large displacement of electrons in the Brillouin zone. By comparing the present nonequilibrium picture with a thermodynamic picture, we explore the role of the nonequilibrium nature of electron dynamics on the extremely nonlinear optical and transport phenomena in graphene.

Real-time, dynamic monitoring of selectively driven ion-concentration polarization

Selective ion extraction is a vital element of many resource recovery systems. Carrier-based membranes offer the ability to remove specific, targeted ions from brine and waste streams, but these materials have delivered inconsistent outcomes in their active transport applications. To study non-ideal behaviors of target-ion selective membranes, we introduce a direct, real-time system for selectively measuring concentrations within electro-membrane boundary layers. In a carrier-based membrane system, we applied our method to monitor adverse, current-limiting behaviors. During its operation, we detected loss of transport selectivity and counter-ion discharge. It provided sufficient evidence to identify the mechanism underlying these adverse, over-limiting effects—the internal concentration polarization of free-carrier. Our method may raise new prospects for direct experimental characterization of nonlinear transport phenomena in electro-membrane systems.

Ultrafast and Low-Threshold THz Mode Switching of Two-Dimensional Nonlinear Metamaterials.

Judiciously designed two-dimensional THz metamaterials consisting of resonant metallic structures embedded in a dielectric environment locally enhance the electromagnetic field of an incident THz pulse to values sufficiently high to cause nonlinear responses of the environment. In semiconductors, the response is attributed to nonlinear transport phenomena via intervalley scattering, impact ionization, or interband tunneling and can affect the resonant behavior of the metallic structure, which results, for instance, in mode switching. However, details of mode switching, especially time scales, are still debated. By using metallic split-ring resonators with nm-size gaps on intrinsic semiconductors with different bandgaps, we identify the most relevant carrier generation processes. In addition, by combining nonlinear THz time-domain spectroscopy with simulations, we establish the fastest time constant for mode switching to around hundred femtoseconds. Our results not only elucidate dominant carrier generation mechanisms and dynamics but also pave the route toward optically driven modulators with THz bandwidth.

Transport phenomena in complex systems (part 2).

This theme issue, in two parts, continues research studies of transport phenomena in complex media published in the first part (Alexandrov & Zubarev 2021 Phil. Trans. R. Soc. A 379, 20200301. (doi:10.1098/rsta.2020.0301)). The issue is concerned with theoretical, numerical and experimental investigations of nonlinear transport phenomena in heterogeneous and metastable materials of different nature, including biological systems. The papers are devoted to the new effects arising in such systems (e.g. pattern and microstructure formation in materials, impacts of external processes on their properties and evolution and so on). State-of-the-art methods of numerical simulations, stochastic analysis, nonlinear physics and experimental studies are presented in the collection of issue papers.This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

Study of Activation Energy on the Movement of Gyrotactic Microorganism in a Magnetized Nanofluids Past a Porous Plate

The present study deals with the swimming of gyrotactic microorganisms in a nanofluid past a stretched surface. The combined effects of magnetohydrodynamics and porosity are taken into account. The mathematical modeling is based on momentum, energy, nanoparticle concentration, and microorganisms’ equation. A new computational technique, namely successive local linearization method (SLLM), is used to solve nonlinear coupled differential equations. The SLLM algorithm is smooth to establish and employ because this method is based on a simple univariate linearization of nonlinear functions. The numerical efficiency of SLLM is much powerful as it develops a series of equations which can be subsequently solved by reutilizing the data from the solution of one equation in the next one. The convergence was improved through relaxation parameters in the study. The accuracy of SLLM was assured through known methods and convergence analysis. A comparison of the proposed method with the existing literature has also been made and found an excellent agreement. It is worth mentioning that the successive local linearization method was found to be very stable and flexible for resolving the issues of nonlinear magnetic materials processing transport phenomena.

Unsteady nonlinear magnetohydrodynamic micropolar transport phenomena with Hall and Ion-slip current effects: Numerical study

Unsteady viscous two-dimensional magnetohydrodynamic micropolar flow, heat and mass transfer from an infinite vertical surface with Hall and Ion-slip currents is investigated theoretically and numerically. The simulation presented is motivated by electro-conductive polymer (ECP) materials processing in which multiple electromagnetic effects arise. The primitive boundary layer conservation equations are transformed into a non-similar system of coupled non-dimensional momentum, angular momentum, energy and concentration equations, with appropriate boundary conditions. The resulting two-point boundary value problem is solved numerically by an exceptionally stable and well-tested implicit finite difference technique. A stability analysis is included for restrictions of the implicit finite difference method (FDM) employed. Validation with a Galerkin finite element method (FEM) technique is included. The influence of various parameters is presented graphically on primary and secondary shear stress, Nusselt number, Sherwood number and wall couple stress. Secondary (cross flow) shear stress is strongly enhanced with greater magnetic parameter (Hartmann number) and micropolar wall couple stress is also weakly enhanced for small time values with Hartmann number. Increasing thermo-diffusive Soret number suppresses both Nusselt and Sherwood numbers whereas it elevates both primary and secondary shear stress and at larger time values also increases the couple stress. Secondary shear stress is strongly boosted with Hall parameter. Ion slip effect induces a weak modification in primary and secondary shear stress distributions. The present study is relevant to electroconductive non-Newtonian (magnetic polymer) materials processing systems.

Nonlinear quantum transport of light in a cold atomic cloud

We outline the non-perturbative theory of multiple scattering of resonant, intense laser light off a dilute cloud of cold atoms. A combination of master equation and diagrammatic techniques allows, for the first time, a quantitative description of nonlinear diffusive transport as well as of coherent backscattering of the injected electromagnetic field, notwithstanding the exponential growth of Hilbert space with the number of atomic scatterers. As an exemplary application, we monitor the laser light's intensity profile within the medium, the spectrum of the backscattered light and the coherent backscattering peak's height with increasing pump intensity. Our theory establishes a general, microscopic, scalable approach to nonlinear transport phenomena in complex quantum materials.

Modeling Faradaic Reactions and Electrokinetic Phenomena at a Nanochannel-Confined Bipolar Electrode

We present the most comprehensive two-dimensional numerical model to date for a nanoconfined bipolar electrochemical system. By accounting for the compact Stern layer and resolving the diffuse part of the electrical double layer at the bipolar electrode (BPE) surface and channel walls, our model captures the impact of surface polarization and ionic charge-screening effects on the heterogeneous charge-transfer kinetics, as well as nonlinear electrokinetic transport phenomena such as induced-charge electroosmosis and concentration polarization. We employ the Poisson-Nernst-Planck and Stokes flow system of equations, unified with generalized Frumkin-Butler-Volmer reaction kinetics, to describe water electrolysis reactions and the resulting transport of ions and dissolved gases in the confined BPE system. Our results demonstrate that under a sufficiently large applied electric field, the rapid reaction kinetics on our Pt BPE dynamically transition from charge-transfer-limited to mass-transfer-limited temporal regimes as regions depleted of redox species form and propagate outward from the respective BPE poles. This phenomenon was visualized experimentally with a pH-sensitive fluorescein dye and showed excellent phenomenological agreement with our numerical calculations, providing a foundation for further understanding and developing bipolar electrochemical processes in confined geometries. We introduce two prospective applications arising from our work: (1) a hybrid hydrodynamic/electrochemical peristaltic pump and (2) deducing information about chemical kinetics through simulation.

Nonlinear chiral transport from holography

Nonlinear transport phenomena induced by the chiral anomaly are explored within a 4D field theory defined holographically as U(1)V × U(1)A Maxwell-Chern-Simons theory in Schwarzschild-AdS5. First, in presence of external electromagnetic fields, a general form of vector and axial currents is derived. Then, within the gradient expansion up to third order, we analytically compute all (over 50) transport coefficients. A wealth of higher order (nonlinear) transport phenomena induced by chiral anomaly are found beyond the Chiral Magnetic and Chiral Separation Effects. Some of the higher order terms are relaxation time corrections to the lowest order nonlinear effects. The charge diffusion constant and dispersion relation of the Chiral Magnetic Wave are found to receive anomaly-induced non-linear corrections due to e/m background fields. Furthermore, there emerges a new gapless mode, which we refer to as Chiral Hall Density Wave, propagating along the background Poynting vector.

Gradient resummation for nonlinear chiral transport: an insight from holography

Nonlinear transport phenomena induced by chiral anomaly are explored within a 4D field theory defined holographically as U(1)_Vtimes U(1)_A Maxwell–Chern–Simons theory in Schwarzschild-AdS_5. In presence of weak constant background electromagnetic fields, the constitutive relations for vector and axial currents, resummed to all orders in the gradients of charge densities, are encoded in nine momenta-dependent transport coefficient functions (TCFs). These TCFs are first calculated analytically up to third order in gradient expansion, and then evaluated numerically beyond the hydrodynamic limit. Fourier transformed, the TCFs become memory functions. The memory function of the chiral magnetic effect (CME) is found to differ dramatically from the instantaneous response form of the original CME. Beyond hydrodynamic limit and when external magnetic field is larger than some critical value, the chiral magnetic wave (CMW) is discovered to possess a discrete spectrum of non-dissipative modes.

Energy and concentration nonequilibrium and nonlinear charge transport phenomena in semiconductors in a magnetic field in hot electrons approximation

When external electric (Ex) and magnetic (Hy) fields are applied to a semiconductor nonequilibrium charge carriers appear that are redistributed perpendicularly to the fields. We show that under weak recombination the nonequilibrium electron together with the hole concentration and nonequilibrium electron temperature are related by a linear function of the coordinate z. The nonequilibrium electron temperature and electron and the hole concentration have a term proportional to HyEx and another term proportional to Ex2. The nonequilibrium temperature shows a dependence of the z-coordinate and includes the effects of the electron-phonon interaction as well as the absorption of heat over the surfaces of the sample. Additionally, the nonequilibrium temperature and charge carriers modified the density of current from the Ohm law. The redistribution of charge carriers originate two new contributions to the magnetoresistance, one of the contributions is linked to the diffusion of charge carriers along the z-axis, the other one is related to the thickness 2b of the sample and the heat absorption over the surfaces. Another effect that modified the density of current is associated with the absorption of heat over the surfaces of the sample, this contribution is proportional to HyEx and can change sign if the electric or magnetic field is inverted. In the case of a null magnetic field, the nonlinear temperature and electron (and hole) concentration are originated by the external electric field and the relaxation mechanism over the surfaces of the sample. The current-voltage characteristic deviates from the linear response due to the nonequilibrium charge carriers.