Ferroicity-driven nonlinear photocurrent switching in time-reversal invariant ferroic materials

Enhancing shift current response via virtual multiband transitions

Materials exhibiting a significant shift current response could potentially outperform conventional solar cell materials. The myriad of factors governing shift-current response, however, poses significant challenges in finding such strong shift-current materials. Here we propose a general design principle that exploits inter-orbital mixing to excite virtual multiband transitions in materials with multiple flat bands to achieve an enhanced shift current response. We further relate this design principle to maximizing Wannier function spread as expressed through the formalism of quantum geometry. We demonstrate the viability of our design using a 1D stacked Rice-Mele model. Furthermore, we consider a concrete material realization - alternating angle twisted multilayer graphene (TMG) - a natural platform to experimentally realize such an effect. We identify a set of twist angles at which the shift current response is maximized via virtual transitions for each multilayer graphene and highlight the importance of TMG as a promising material to achieve an enhanced shift current response at terahertz frequencies. Our proposed mechanism also applies to other 2D systems and can serve as a guiding principle for designing multiband systems that exhibit an enhanced shift current response.

Enormous and Tunable Bulk Charge/Spin Photovoltaic Effect in Piezoelectric Binary Materials T-IV-VI and T-V-V

Understanding the nonlinear response of light and materials is crucial for fundamental physics and next-generation electronic devices. In this work, we have investigated the second-order nonlinear bulk photovoltaic (BPV) and bulk spin photovoltaic (BSPV) effects in the piezoelectric binary materials T-IV-VI and T-V-V (IV = Ge, Sn; VI = S, Se; and V = P, As, Sb, Bi). The independent nonzero conductivity tensors of charge current are derived for these binaries through the symmetry analysis, along with the mechanism for generating pure spin current. These binaries, with their unique folded structure, exhibit significant charge and spin currents under illumination. Furthermore, we find that strain engineering can effectively modulate charge/spin currents by influencing charge density distribution and built-in electric field due to the piezoelectric effect. Our research suggests that the piezoelectric binary materials possess enormous and tunable charge/spin currents, underscoring their potential for applications in nonlinear flexible optoelectronics and spintronics.

Spin-orbit-splitting-driven nonlinear Hall effect in NbIrTe4

The Berry curvature dipole (BCD) serves as a one of the fundamental contributors to emergence of the nonlinear Hall effect (NLHE). Despite intense interest due to its potential for new technologies reaching beyond the quantum efficiency limit, the interplay between BCD and NLHE has been barely understood yet in the absence of a systematic study on the electronic band structure. Here, we report NLHE realized in NbIrTe4 that persists above room temperature coupled with a sign change in the Hall conductivity at 150 K. First-principles calculations combined with angle-resolved photoemission spectroscopy (ARPES) measurements show that BCD tuned by the partial occupancy of spin-orbit split bands via temperature is responsible for the temperature-dependent NLHE. Our findings highlight the correlation between BCD and the electronic band structure, providing a viable route to create and engineer the non-trivial Hall effect by tuning the geometric properties of quasiparticles in transition-metal chalcogen compounds.

Ferroelastic Twin-Wall-Mediated Ferroelectriclike Behavior and Bulk Photovoltaic Effect in SrTiO_{3}

Ferroelastic twin walls in nonpolar materials can give rise to a spontaneous polarization due to symmetry breaking. Nevertheless, the bistable polarity of twin walls and its reversal have not yet been demonstrated. Here, we report that the polarity of SrTiO_{3} twin walls can be switched by an ultralow strain gradient. Using first-principles-based machine-learning potential, we demonstrate that the twin walls can be deterministically rotated and realigned in specific directions under the strain gradient, which breaks the inversion symmetry of a sequence of walls and leads to a macroscopic polarization. The system can maintain polarity even after the constraint is removed. As a result, the polarization of twin walls can exhibit a ferroelectriclike hysteresis loop upon cyclic bending, namely flexoferroelectricity. Finally, we propose a scheme to experimentally detect the polarity of the twin wall by measuring the bulk photovoltaic responses. Our findings suggest a twin-wall-mediated flexoferroelectricity in SrTiO_{3}, which could be potentially exploited as functional elements in nanoelectronic devices design.

Quantifying the photocurrent fluctuation in quantum materials by shot noise

The DC photocurrent can detect the topology and geometry of quantum materials without inversion symmetry. Herein, we propose that the DC shot noise (DSN), as the fluctuation of photocurrent operator, can also be a diagnostic of quantum materials. Particularly, we develop the quantum theory for DSNs in gapped systems and identify the shift and injection DSNs by dividing the second-order photocurrent operator into off-diagonal and diagonal contributions, respectively. Remarkably, we find that the DSNs can not be forbidden by inversion symmetry, while the constraint from time-reversal symmetry depends on the polarization of light. Furthermore, we show that the DSNs also encode the geometrical information of Bloch electrons, such as the Berry curvature and the quantum metric. Finally, guided by symmetry, we apply our theory to evaluate the DSNs in monolayer GeS and bilayer MoS2 with and without inversion symmetry and find that the DSNs can be larger in centrosymmetric phase.

Domain-dependent strain and stacking in two-dimensional van der Waals ferroelectrics

Van der Waals (vdW) ferroelectrics have attracted significant attention for their potential in next-generation nano-electronics. Two-dimensional (2D) group-IV monochalcogenides have emerged as a promising candidate due to their strong room temperature in-plane polarization down to a monolayer limit. However, their polarization is strongly coupled with the lattice strain and stacking orders, which impact their electronic properties. Here, we utilize four-dimensional scanning transmission electron microscopy (4D-STEM) to simultaneously probe the in-plane strain and out-of-plane stacking in vdW SnSe. Specifically, we observe large lattice strain up to 4% with a gradient across ~50 nm to compensate lattice mismatch at domain walls, mitigating defects initiation. Additionally, we discover the unusual ferroelectric-to-antiferroelectric domain walls stabilized by vdW force and may lead to anisotropic nonlinear optical responses. Our findings provide a comprehensive understanding of in-plane and out-of-plane structures affecting domain properties in vdW SnSe, laying the foundation for domain wall engineering in vdW ferroelectrics.

Manipulation of nonlinear optical responses in layered ferroelectric niobium oxide dihalides

Realization of highly tunable second-order nonlinear optical responses, e.g., second-harmonic generation and bulk photovoltaic effect, is critical for developing modern optical and optoelectronic devices. Recently, the van der Waals niobium oxide dihalides are discovered to exhibit unusually large second-harmonic generation. However, the physical origin and possible tunability of nonlinear optical responses in these materials remain to be unclear. In this article, we reveal that the large second-harmonic generation in NbOX2 (X = Cl, Br, and I) may be partially contributed by the large band nesting effect in different Brillouin zone. Interestingly, the NbOCl2 can exhibit dramatically different strain-dependent bulk photovoltaic effect under different polarized light, originating from the light-polarization-dependent orbital transitions. Importantly, we achieve a reversible ferroelectric-to-antiferroelectric phase transition in NbOCl2 and a reversible ferroelectric-to-paraelectric phase transition in NbOI2 under a certain region of external pressure, accompanied by the greatly tunable nonlinear optical responses but with different microscopic mechanisms. Our study establishes the interesting external-field tunability of NbOX2 for nonlinear optical device applications.

Giant room-temperature nonlinearities in a monolayer Janus topological semiconductor

Nonlinear optical materials possess wide applications, ranging from terahertz and mid-infrared detection to energy harvesting. Recently, the correlations between nonlinear optical responses and certain topological properties, such as the Berry curvature and the quantum metric tensor, have attracted considerable interest. Here, we report giant room-temperature nonlinearities in non-centrosymmetric two-dimensional topological materials-the Janus transition metal dichalcogenides in the 1 T' phase, synthesized by an advanced atomic-layer substitution method. High harmonic generation, terahertz emission spectroscopy, and second harmonic generation measurements consistently show orders-of-the-magnitude enhancement in terahertz-frequency nonlinearities in 1 T' MoSSe (e.g., > 50 times higher than 2H MoS2 for 18th order harmonic generation; > 20 times higher than 2H MoS2 for terahertz emission). We link this giant nonlinear optical response to topological band mixing and strong inversion symmetry breaking due to the Janus structure. Our work defines general protocols for designing materials with large nonlinearities and heralds the applications of topological materials in optoelectronics down to the monolayer limit.

Giant Bulk Electrophotovoltaic Effect in Heteronodal-Line Systems

The realization of a giant and continuously tunable second-order photocurrent is desired for many nonlinear optical (NLO) and optoelectronic applications, which remains a great challenge. Here, based on a two-band model, we propose a concept of the bulk electrophotovoltaic effect, that is, an out-of-plane external electric field (E_{ext}) that can continuously tune in-plane shift current along with its sign flip in a heteronodal-line (HNL) system. While strong linear optical transition around the nodal loop may potentially generate giant shift current, an E_{ext} can effectively control the radius of the nodal loop, which can continuously modulate the shift-vector components inside and outside the nodal loop holding opposite signs. This concept has been demonstrated in the HNL HSnN/MoS_{2} system using first-principles calculations. The HSnN/MoS_{2} heterobilayer can not only produce a shift-current conductivity with magnitude that is one to two orders larger than other reported systems, but it can also realize a giant bulk electrophotovoltaic effect. Our finding opens new routes to create and manipulate NLO responses in 2D materials.

Ferroelectricity-Driven Phonon Berry Curvature and Nonlinear Phonon Hall Transports

Berry curvature (BC) governs topological phases of matter and generates anomalous transport. When a magnetic field is applied, phonons can acquire BC indirectly through spin-lattice coupling, leading to a linear phonon Hall effect. Here, we show that polar lattice distortion directly couples to a phonon BC dipole, which causes a switchable nonlinear phonon Hall effect. In a SnS monolayer, the in-plane ferroelectricity induces a phonon BC and leads to the phononic version of the nonvolatile BC memory effect. As a new type of ferroelectricity-phonon coupling, the phonon Rashba effect emerges and opens a mass gap in tilted Weyl phonon modes, resulting in a large phonon BC dipole. Furthermore, our ab initio non-equilibrium molecular dynamics simulations reveal that nonlinear phonon Hall transport occurs in a controllable manner via ferroelectric switching. The ferroelectricity-driven phonon BC and corresponding nonlinear phonon transports provide a novel scheme for constructing topological phononic transport/memory devices.

Nonlinear Optical and Photocurrent Responses in Janus MoSSe Monolayer and MoS2-MoSSe van der Waals Heterostructure

Two-dimensional (2D) transition metal dichalcogenides are promising materials platforms for a variety of optoelectronic device applications. Janus 2D materials are a rising class of 2D materials with low symmetry, which leads to the emergence of out-of-plane electric polarization and piezoelectricity. Using first-principles density functional theory, we show that monolayer and bilayer heterostructure Janus MoSSe moieties exhibit strong nonlinear optical responses that are vanishing in the non-Janus form. The absence of horizontal mirror plane symmetry enables a circular photocurrent as well as a large out-of-plane second harmonic generation (SHG) and shift photocurrent. Through a comparative study of the Janus heterostructure MoS₂-MoSSe on five distinct stacking configurations, we find that the magnitude of the out-of-plane SHG in the Janus heterostructure is enhanced due to the interlayer coupling and interference effect compared to that of monolayer MoSSe. Thus, Janus 2D materials offer a unique opportunity for exploring nonlinear optical phenomena and designing configurable layered nonlinear optical materials.

Ferroelastic-Ferroelectric Multiferroicity in van der Waals Rhenium Dichalcogenides

2D multiferroics with combined ferroic orders have gained attention owing to their novel functionality and underlying science. Intrinsic ferroelastic-ferroelectric multiferroicity in single-crystalline van der Waals rhenium dichalcogenides, whose symmetries are broken by the Peierls distortion and layer-stacking order, is demonstrated. Ferroelastic switching of the domain orientation and accompanying anisotropic properties is achieved with 1% uniaxial strain using the polymer encapsulation method. Based on the electron localization function and bond dissociation energy of the Re-Re bonds, the change in bond configuration during the evolution of the domain wall and the preferred switching between the two specific orientation states are explained. Furthermore, the ferroelastic switching of ferroelectric polarization is confirmed using the photovoltaic effect. The study provides insights into the reversible bond-switching process and potential applications based on 2D multiferroicity.

Rippling Ferroic Phase Transition and Domain Switching In 2D Materials

Ripples are a class of native structural defects widely existing in 2D materials. They originate from the out-of-plane flexibility of 2D materials introducing spatially evolving electronic structure and friction behavior. However, the effect of ripples on 2D ferroics has not been reported. Here a molecular dynamics study of the effect of ripples on the temperature-induced ferroic phase transition and stress-induced ferroic domain switching in ferroelastic-ferroelectric monolayer GeSe is presented. Ripples stabilize the short-range ferroic orders in the high-temperature phase with stronger ferroicity and longer lifetime, thereby increasing the transition temperature upon cooling. In addition, ripples significantly affect the domain switching upon loading, changing it from a highly correlated process into a ripple-driven localized one where ripples act as source of dynamical random stress. These results reveal the fundamental role of ripples on 2D ferroicity and provide theoretical guidance for ripple engineering of controlled phase transition and domain switching with potential applications in flexible 2D electronics.

In-plane ferroelectricity in few-layered GeS and its van der Waals ferroelectric diodes

Two-dimensional ferroelectric semiconductors (2DFeSs) have been attracting extensive research attention on account of their unique properties and versatile applications in random-access memory, digital signal processors, and neuromorphic computing. Germanium sulfide (GeS) is predicted as a typical 2DFeS with a large spontaneous polarization of 484 pC m^-1. Furthermore, the moderate band gap equivalent to 1.63 eV of GeS provides it with significant potential to create a strong bulk photovoltage in the visible light range. However, the fabrication of chemically stable few-to-monolayer GeS has not been reported so far, owing to the strong interlayer force and high chemical reactivity of the surface. Herein we demonstrate a new method for fabricating high quality, air-stable, ultrathin GeS nanoflakes. The electrical characterization confirms the formation of few-layered GeS with a remarkable in-plane ferroelectric hysteresis, which is forbidden by the inversion symmetry in bulk GeS crystals. After applying a coercive field of about 18.1 kV cm^-1, a switchable shift current can also be observed in the polarized GeS nanoflakes under light irradiation. To further enhance the photoresponsivity, few-layered InSe was transferred onto the GeS nanoflakes to form van der Waals ferroelectric diodes. The interfacial perturbation breaking the inversion symmetry results in the enhancement of robust dipoles in the GeS side along the interface, which can be tuned by the in-plane electric field. Overall, this work opens the door for exploring the low-dimensional ferroelectric memory and energy conversion applications based on 2D GeS nanoflakes and provides a deeper understanding of the photovoltaic mechanism with in-plane 2D ferroelectric diodes.

Geometric Photon-Drag Effect and Nonlinear Shift Current in Centrosymmetric Crystals

The nonlinear shift current, also known as the bulk photovoltaic current generated by linearly polarized light, has long been known to be absent in crystals with inversion symmetry. Here we argue that a nonzero shift current in centrosymmetric crystals can be activated by a photon-drag effect. Photon-drag shift current proceeds from a "shift current dipole" (a geometric quantity characterizing interband transitions) and manifests a purely transverse response in centrosymmetric crystals. This transverse nature proceeds directly from the shift-vector's pseudovector nature under mirror operation and underscores its intrinsic geometric origin. Photon-drag shift current can be greatly enhanced by coupling to polaritons and provides a new and sensitive tool to interrogate the subtle interband coherences of materials with inversion symmetry previously thought to be inaccessible via photocurrent probes.

Two-Dimensional Materials with Giant Optical Nonlinearities near the Theoretical Upper Limit

Nonlinear optical (NLO) phenomena such as harmonic generation and Kerr and Pockels effects are of great technological importance for lasers, frequency converters, modulators, switches, etc. Recently, two-dimensional (2D) materials have drawn significant attention due to their strong and peculiar NLO properties. Here, we describe an efficient first-principles workflow for calculating the quadratic optical response and apply it to 375 non-centrosymmetric semiconductor monolayers from the Computational 2D Materials Database (C2DB). Sorting the nonresonant nonlinearities with respect to bandgap E_g reveals an upper limit proportional to E_g^-4, which is neatly explained by two distinct generic models. We identify multiple promising candidates with giant nonlinearities and bandgaps ranging from 0.4 to 5 eV, some of which approach the theoretical upper limit and greatly outperform known materials. Our comprehensive library of ab initio NLO spectra for all 375 monolayers is freely available via the C2DB Web site.

Large family of two-dimensional ferroelectric metals discovered via machine learning

Ferroelectricity and metallicity are usually believed not to coexist because conducting electrons would screen out static internal electric fields. In 1965, Anderson and Blount proposed the concept of "ferroelectric metal", however, it is only until recently that very rare ferroelectric metals were reported. Here, by combining high-throughput ab initio calculations and data-driven machine learning method with new electronic orbital based descriptors, we systematically investigated a large family (2964) of two-dimensional (2D) bimetal phosphates, and discovered 60 stable ferroelectrics with out-of-plane polarization, including 16 ferroelectric metals and 44 ferroelectric semiconductors that contain seven multiferroics. The ferroelectricity origins from spontaneous symmetry breaking induced by the opposite displacements of bimetal atoms, and the full-d-orbital coinage metal elements cause larger displacements and polarization than other elements. For 2D ferroelectric metals, the odd electrons per unit cell without spin polarization may lead to a half-filled energy band around Fermi level and is responsible for the metallicity. It is revealed that the conducting electrons mainly move on a single-side surface of the 2D layer, while both the ionic and electric contributions to polarization come from the other side and are vertical to the above layer, thereby causing the coexistence of metallicity and ferroelectricity. Van der Waals heterostructures based on ferroelectric metals may enable the change of Schottky barrier height or the Schottky-Ohmic contact type and induce a dramatic change of their vertical transport properties. Our work greatly expands the family of 2D ferroelectric metals and will spur further exploration of 2D ferroelectric metals.

Microscopic Manipulation of Ferroelectric Domains in SnSe Monolayers at Room Temperature

Two-dimensional (2D) van der Waals ferroelectrics provide an unprecedented architectural freedom for the creation of artificial multiferroics and nonvolatile electronic devices based on vertical and coplanar heterojunctions of 2D ferroic materials. Nevertheless, controlled microscopic manipulation of ferroelectric domains is still rare in monolayer-thick 2D ferroelectrics with in-plane polarization. Here we report the discovery of robust ferroelectricity with a critical temperature close to 400 K in SnSe monolayer plates grown on graphene and the demonstration of controlled room-temperature ferroelectric domain manipulation by applying appropriate bias voltage pulses to the tip of a scanning tunneling microscope (STM). This study shows that STM is a powerful tool for detecting and manipulating the microscopic domain structures in 2D ferroelectric monolayers, which are difficult for conventional approaches such as piezoresponse force microscopy, thus facilitating the hunt for other 2D ferroelectric monolayers with in-plane polarization with important technological applications.

Enhanced Shift Currents in Monolayer 2D GeS and SnS by Strain-Induced Band Gap Engineering

Group IV monochalcogenides exhibit spontaneous polarization and ferroelectricity, which are important in photovoltaic materials. Since strain engineering plays an important role in ferroelectricity, in the present work, the effect of equibiaxial strain on the band structure and shift currents in monolayer two-dimensional (2D) GeS and SnS has systematically been investigated using the first-principles calculations. The conduction bands of those materials are more responsive to strain than the valence bands. Increased equibiaxial compressive strain leads to a drastic reduction in the band gap and finally the occurrence of phase transition from semiconductor to metal at strains of -15 and -14% for GeS and SnS, respectively. On the other hand, tensile equibiaxial strain increases the band gap slightly. Similarly, increased equibiaxial compressive strain leads to a steady almost four times increase in the shift currents at a strain of -12% with direction change occurring at -8% strain. However, at phase transition from semiconductor to metal, the shift currents of the two materials completely vanish. Equibiaxial tensile strain also leads to increased shift currents. For SnS, shift currents do not change direction, just as the case of GeS at low strain; however, at a strain of +8% and beyond, direction reversal of shift currents beyond the band gap in GeS occur.

Sub-Angstrom Characterization of the Structural Origin for High In-Plane Anisotropy in 2D GeS2

Materials with layered crystal structures and high in-plane anisotropy, such as black phosphorus, present unique properties and thus promise for applications in electronic and photonic devices. Recently, the layered structures of GeS₂ and GeSe₂ were utilized for high-performance polarization-sensitive photodetection in the short wavelength region due to their high in-plane optical anisotropy and wide band gap. The highly complex, low-symmetric (monoclinic) crystal structures are at the origin of the high in-plane optical anisotropy, but the structural nature of the corresponding nanostructures remains to be fully understood. Here, we present an atomic-scale characterization of monoclinic GeS₂ nanostructures and quantify the in-plane structural anisotropy at the sub-angstrom level in real space by Cs-corrected scanning transmission electron microscopy. We elucidate the origin of this high in-plane anisotropy in terms of ordered and disordered arrangement of [GeS₄] tetrahedra in GeS₂ monolayers, through density functional theory (DFT) calculations and orbital-based bonding analyses. We also demonstrate high in-plane mechanical, electronic, and optical anisotropies in monolayer GeS₂ and envision phase transitions under uniaxial strain that could potentially be exploited for nonvolatile memory applications.