Signatures of strong interlayer coupling inγ-InSe revealed by local differential conductivity

Interlayer coupling in layered semiconductors can significantly affect their optoelectronic properties.However,understanding the mechanisms behind the interlayer coupling at the atomic level is not straightforward.Here,we study modulations of the electronic structure induced by the interlayer coupling in theγ-phase of indium selenide(γ-InSe)using scanning probe techniques.We observe a strong dependence of the energy gap on the sample thickness and a small effective mass along the stacking direction,which are attributed to strong interlayer coupling.In addition,the moirépatterns observed inγ-InSe display a small band-gap variation and nearly constant local differential conductivity along the patterns.This suggests that modulation of the electronic structure induced by the moirépotential is smeared out,indicating the presence of a significant interlayer coupling.Our theoretical calculations confirm that the interlayer coupling inγ-InSe is not only of the van der Waals origin,but also exhibits some degree of hybridization between the layers.Strong interlayer coupling might play an important role in the performance ofγ-InSe-based devices.

INTERLAYER COUPLING AND FERROMAGNETIC RESONANCE IN Fe-Si/Cr MULTILAYERS

Fe-Si/Cr multilayers with amorphous Fe-Si magnetic layers and Cr nonmagnetic layers were prepared by an rf-sputtering method.When the thickness of the Cr layers varies from 0.5 to 6 nm, the interlayer coupling oscillates periodically from ferromagnetic to antiferromagnetism. For each sample only one wide uniform resonance peak is detected by the ferromagnetic resonance. The uniform resonance field Hb and the resonance line width △H_b oscillate periodically as the thickness of the Cr layers increases, which is related to the oscillation of the interlayer coupling from ferromagnetic to antiferromagnetism.The oscillation period is about 1.5nm.

Ru thickness-dependent interlayer coupling and ultrahigh FMR frequency in FeCoB/Ru/FeCoB sandwich trilayers

The antiferromagnetic(AFM) interlayer coupling effective field in a ferromagnetic/non-magnetic/ferromagnetic(FM/NM/FM) sandwich structure, as a driving force, can dramatically enhance the ferromagnetic resonance(FMR) frequency. Changing the non-magnetic spacer thickness is an effective way to control the interlayer coupling type and intensity, as well as the FMR frequency. In this study, Fe Co B/Ru/Fe Co B sandwich trilayers with Ru thickness(tRu) ranging from 1 A to 16 A are prepared by a compositional gradient sputtering(CGS) method. It is revealed that a stress-induced anisotropy is present in the Fe Co B films due to the B composition gradient in the samples. A tRu-dependent oscillation of interlayer coupling from FM to AFM with two periods is observed. An AFM coupling occurs in a range of 2 A ≤ tRu≤ 8 A and over 16 A, while an FM coupling is present in a range of tRu< 2 A and 9 A ≤ tRu≤ 14.5 A. It is interesting that an ultrahigh optical mode(OM) FMR frequency in excess of 20 GHz is obtained in the sample with tRu= 2.5 A under an AFM coupling. The dynamic coupling mechanism in trilayers is simulated, and the corresponding coupling types at different values of tRuare verified by Layadi’s rigid model. This study provides a controllable way to prepare and investigate the ultrahigh FMR films.

Evidence for interlayer coupling and moiréexcitons in twisted WS_(2)/WS_(2)homostructure superlattices

The formation of moirésuperlattices in twisted van der Waals(vdW)homostructures provides a versatile platform for designing the electronic band structure of two-dimensional(2D)materials.In graphene and transition metal dichalcogenides(TMDs)moirésystems,twist angle has been shown to be a key parameter for regulating the moirésuperlattice.However,the effect of the modulation of the twist angle on moirépotential and interlayer coupling has not been the subject of experimental investigation.Here,we report the observation of the modulation of moirépotential and intralayer excitons in the WS_(2)/WS_(2)homostructure.By accurately adjusting the torsion angle of the homobilayers,the depth of the moirépotential can be modulated.The confinement effect of the moirépotential on the intralayer excitons was further demonstrated by the changing of temperature and valley polarization.Furthermore,we show that a detection of atomic reconstructions by the low-frequency Raman mapping to map out inhomogeneities in moirélattices on a large scale,which endows the uniformity of interlayer coupling.Our results provide insights for an in-depth understanding of the behaviors of moiréexcitons in the twisted van der Waals homostructure,and promote the study of electrical engineering and topological photonics.

A scheme for realizing nonreciprocal interlayer coupling in bilayer topological systems

Nonreciprocal interlayer coupling is difcult to practically implement in bilayer non-Hermitian topological photonic systems.In this work,we identify a similarity transformation between the Hamiltonians of systems with nonreciprocal interlayer coupling and on-site gain/loss.The similarity transformation is widely applicable,and we show its application in one-and two-dimensional bilayer topological systems as examples.The bilayer non-Hermitian system with nonreciprocal interlayer coupling,whose topological number can be defned using the gauge-smoothed Wilson loop,is topologically equivalent to the bilayer system with on-site gain/loss.We also show that the topological number of bilayer non-Hermitian C6v-typed domaininduced topological interface states can be defned in the same way as in the case of the bilayer non-Hermitian Su–Schrieffer–Heeger model.Our results show the relations between two microscopic provenances of the non-Hermiticity and provide a universal and convenient scheme for constructing and studying nonreciprocal interlayer coupling in bilayer non-Hermitian topological systems.This scheme is useful for observation of non-Hermitian skin efect in three-dimensional systems.

Probing temperature-dependent interlayer coupling in a MoS2/h-BN heterostructure

Stacking of atomically thin layers of two-dimensional materials has revealed extraordinary physical phenomena owing to van der Waals(vdW)interaction at the interface.However,most of the studies focused on the transition metal dichalcogenide(TMD)/TMD heterostructure,while the interlayer coupling of the TMD/hexagonal boron nitride(h-BN)heterostructure has not been extensively explored despite its importance.In this study,the temperature-dependent interlayer coupling is demonstrated in a heterostructure of molybdenum disulfide(MoS2)and h-BN.The interface between MoS2 and the insulating substrate exerts a significant spectroscopic impact on MoS2 through substrate-induced local strain,charged impurity,and vdW interactions.Under non-resonant conditions,temperature-dependent peak shifts in Raman and photoluminescence(PL)spectra of MoS2 reveal the evolution of interlayer coupling.Phonon frequencies and PL peak energies at different temperatures demonstrate how substrate-induced strain,impurity,and vdW interactions at the interface influence phonon vibration and excitonic transition of MoS2.Under resonant conditions at low temperature,anomalous Raman modes appear in the MoS2/h-BN heterostructure because of the enhanced electron-phonon coupling and vdW interactions.The anomalous Raman modes are quantitatively investigated by the deconvolution of the resonance Raman spectra and described by interlayer coupling at low temperature,in agreement with complementary indications from the temperature-dependent evolution of non-resonant Raman and PL spectra.

Effects of interlayer coupling on the excitons and electronic structures of WS_(2)/hBN/MoS_(2) van der Waals heterostructures

Inserting hexagonal boron nitride(hBN)as barrier layers into bilayer transition metal dichalcogenides heterointerface has been proved an efficient method to improve two dimensional tunneling optoelectronic device performance.Nevertheless,the physical picture of interlayer coupling effect during incorporation of monolayer(1L-)hBN is not explicit yet.In this article,spectroscopic ellipsometry was used to experimentally obtain the broadband excitonic and critical point properties of WS_(2)/MoS_(2)and WS_(2)/hBN/MoS_(2)van der Waals heterostructures.We find that 1L-hBN can only slightly block the interlayer electron transfer from WS_(2)layer to MoS_(2)layer.Moreover,insertion of 1L-hBN weakens the interlayer coupling effect by releasing quantum confinement and reducing efficient dielectric screening.Consequently,the exciton binding energies in WS_(2)/hBN/MoS_(2)heterostructures blueshift comparing to those in WS_(2)/MoS_(2)heterostructures.In this exciton binding energies tuning process,the reducing dielectric screening effect plays a leading role.In the meantime,the quasi-particle(QP)bandgap remains unchanged before and after 1L-hBN insertion,which is attributed to released quantum confinement and decreased dielectric screening effects canceling each other.Unchanged QP bandgap as along with blueshift exciton binding energies lead to the redshift exciton transition energies in WS_(2)/hBN/MoS_(2)heterostructures.

Investigation of weak interlayer coupling in 2D layered GeS_(2) from theory to experiment

Interlayer coupling as a unique feature for two-dimensional(2D)materials may influence their thickness-dependent physical properties,especially the bandgap due to quantum confinement effect.Widely-studied 2D materials usually possess strong interlayer coupling such as most of transition metal dichalcogenides(TMDs),PtS_(2) and so on.However,2D materials with weak interlayer coupling are rarely referred that mainly focus on ReS_(2),as well as its counterpart ReSe_(2).Here we report a new member of weak interlayer coupling 2D materials,germanium disulfide(GeS_(2)).The interlayer interaction in GeS_(2) is investigated from theory to experiment.By density functional theory calculations,we find that this extraordinarily weak interlayer coupling in GeS_(2) originates from the weak hybridization of interlayer S atoms.Thickness-dependent Raman spectra of GeS_(2) flakes exhibit that the Raman peaks remain unchanged when increasing the thickness;and a small first-order temperature coefficient of-0.00857 cm^(-1)·K^(-1) is obtained from the temperature-dependent Raman spectra.These experimental results further confirm the weak interlayer coupling in GeS_(2).

Layer-number dependent high-frequency vibration modes in few-layer transition metal dichalcogenides induced by interlayer couplings

Two-dimensional transition metal dichalcogenides（TMDs） have attracted extensive attention due to their many novel properties.The atoms within each layer in two-dimensional TMDs are joined together by covalent bonds,while van der Waals interactions combine the layers together.This makes its lattice dynamics layer-number dependent.The evolutions of ultralow frequency（〈 50 cm^（-1）） modes,such as shear and layer-breathing modes have been well-established.Here,we review the layer-number dependent high-frequency（〉 50 cm^（-1）） vibration modes in few-layer TMDs and demonstrate how the interlayer coupling leads to the splitting of high-frequency vibration modes,known as Davydov splitting.Such Davydov splitting can be well described by a van der Waals model,which directly links the splitting with the interlayer coupling.Our review expands the understanding on the effect of interlayer coupling on the high-frequency vibration modes in TMDs and other two-dimensional materials.

Optical identification of interlayer coupling of graphene/MoS_(2) van der Waals heterostructures

The interlayer coupling in van der Waals(vdW)heterostructures(vdWHs)is at the frontier of the fundamental research,underlying many optical behaviors.The graphene/MoS_(2) vdWHs provide an ideal platform to reveal the good interfacial coupling between graphene and MoS_(2) constituents.Here,three groups of graphene/MoS_(2) vdWHs were prepared by transferring 1–3 layers of graphene onto monolayer MoS_(2).The interlayer coupling within graphene/MoS_(2) vdWHs were characterized and analyzed by Raman spectroscopy,photoluminescence(PL)spectroscopy and optical contrast(OC)spectroscopy.The upshift of the A_(1g) peak of MoS_(2) and the upshift of the D and 2D peaks of SLG show that the electrons move from MoS_(2) to graphene accompanied by the dielectric shielding effect on graphene.The weakened PL intensities and the slight red shift of A peak prove that the electrons move from MoS_(2) to graphene meanwhile the recombination of hole and electron pairs is blocked in vdWHs.Our results deepen the understanding of the interlayer coupling of graphene/MoS_(2) vdWHs and therefore provide guidelines for the practical design and application of optoelectronic devices based on graphene/MoS_(2) vdWHs.

Interlayer coupling effect in van der Waals heterostructures of transition metal dichalcogenides

Van der Waals(vdW)heterobilayers formed by two-dimensional(2D)transition metal dichalcogenides(TMDCs)created a promising platform for various electronic and optical properties,ab initio band results indicate that the band offset of type-Ⅱband alignment in TMDCs vdW heterobilayer could be tuned by introducing Janus WSSe monolayer,instead of an external electric field.On the basis of symmetry analysis,the allowed interlayer hopping channels of TMDCs vdW heterobilayer were determined,and a four-level k·p model was developed to obtain the interlayer hopping.Results indicate that the interlayer coupling strength could be tuned by interlayer electric polarization featured by various band offsets.Moreover,the difference in the formation mechanism of interlayer valley excitons in different TMDCs vdW heterobilayers with various interlayer hopping strength was also clarified.

Temperature-dependent interlayer exchange coupling strength in synthetic antiferromagnetic [Pt/Co]_2/Ru/[Co/Pt]_4 multilayers

In this work, we experimentally investigated the thermal stability of the interlayer exchange coupling field(Hex) and strength(-Jiec) in synthetic antiferromagnetic(SAF) structure of [Pt(0.6)/Co(0.6)]2/Ru(tRu)/[Co(0.6)/Pt(0.6)]4multilayers with perpendicular anisotropy. Depending on the thickness of the spacing ruthenium(Ru) layer, the observed interlayer exchange coupling can be either ferromagnetic or antiferromagnetic. The Hexwere studied by measuring the magnetization hysteresis loops in the temperature range from 100 K to 700 K as well as the theoretical calculation of the-Jiec. It is found that the interlayer coupling in the multilayers is very sensitive to the thickness of Ru and temperature. The Hexexhibits either a linear or a non-linear dependence on the temperature for different thickness of Ru. Furthermore, our SAF multilayers show a high thermal stability even up to 600 K(Hex= 3.19 kOe,-Jiec= 1.97 erg/cm~2 for tRu=0.6 nm, the unit 1 Oe = 79.5775 A·m-1), which was higher than the previous studies.

Colossal structural distortion and interlayer-coupling suppression in a van der Waals crystal induced by atomic vacancies

The interlayer coupling in van der Waals(vdW)crystals has substantial effects on the performance of materials.However,an indepth understanding of the microscopic mechanism on the defect-modulated interlayer coupling is often elusive,owing partly to the challenge of atomic-scale characterization.Here we report the native Se-vacancies in a charge-density-wave metal 2HNbSe2,as well as their influence on the local atomic configurations and interlayer coupling.Our low-temperature scanning tunneling microscopy(STM)measurements,complemented by density functional theory calculations,indicate that the Sevacancies in few-layer NbSe2 can generate obvious atomic distortions due to the Jahn-Teller effect,thus breaking the rotational symmetry on the nanoscale.Moreover,these vacancies can locally generate an in-gap state in single-layer NbSe2,and more importantly,lead to a colossal suppression of interlayer coupling in the bilayer system.Our results provide clear structural and electronic fingerprints around the vacancies in vdW crystals,paving the way for developing functional vdW devices.

Raman scattering investigation of twisted WS_(2)/MoS_(2) heterostructures: interlayer mechanical coupling versus charge transfer

Twisted van der Waals homo-and hetero-structures have aroused great attentions due to their unique physical properties,providing a new platform to explore the novel two-dimensional(2D)condensed matter physics.The robust dependence of phonon vibrations and electronic band structures on the twist angle has been intensively observed in transition metal dichalcogenide(TMD)homo-structures.However,the effects of twist angle on the lattice vibrational properties in the TMD heterostructures have not caused enough attention.Here,we report the distinct evolutions of Raman scattering and the underlying interlayer interactions in the twisted WS_(2)/MoS_(2) heterostructures.The shifts and linewidths of E_(2g)(Γ)and A_(1g)(Γ)phonon modes are found to be twist angle dependent.In particular,analogous to that of the twisted TMD homostructures,the frequency separations between E_(2g)(Γ)and A_(1g)(Γ)modes of MoS_(2) and WS_(2) in the twisted heterostructures varying with twist angle correlate with the interlayer mechanical coupling,essentially originating from the spacing-related repulsion between sulfur atoms.Moreover,the opposite shift behaviors and broadening of A_(1g)(Γ)modes caused by charge transfer are also observed in the twisted heterostructures.The calculated interlayer distances and band alignment of twisted WS_(2)/MoS_(2) through density functional theory further evidence our interpretations on the roles of the interlayer mechanical coupling and charge transfer in variations of Raman features.Such understanding and controlling of interlayer interaction through the stacking orientation are significant for future optoelectronic device design based on the newly emerged 2D heterostructures.

Versatile band structure and electron-phonon coupling in layered PtSe_(2) with strong interlayer interaction

The large tunability in the band structure is ubiquitous in two-dimensional(2D)materials,and PtSe_(2) is not an exception,which has attracted considerable attention in electronic and optoelectronic applications due to its high carrier mobility and long-term airstability.Such dimensional dependent properties are closely related to the evolution of electronic band structures.Critical points(CPs),the extrema or saddle points of electronic bands,are the cornerstone of condensed-matter physics and fundamentally determine the optical and transport phenomena of the layered PtSe_(2).Here,we have experimentally revealed the detailed electronic structures in layered PtSe_(2),including the CPs in the Brillouin zones(BZs),by means of reflection contrast spectroscopy and spectroscopic ellipsometry(SE).There are three critical points in the BZs attributed to the excitonic transition,quasi-particle band gap,and the band nesting effect related transition,respectively.Three CPs show red-shifting trends with increasing layer number under the mechanism of strong interlayer coupling.We have further revealed the electron–phonon(e–ph)interaction in such layered material,utilizing temperature-dependent absorbance spectroscopy.The strength of e–ph interaction and the average phonon energy also decline with the increasement of layer number.Our findings give a deep understanding to the physics of the layer-dependent evolution of the electronic structure of PtSe_(2),potentially leading to applications in optoelectronics and electronic devices.

Dependence of domain wall structures on repetition n in[Pt(0.5 nm)/Co(0.4 nm)]_n/NiO(1.1 nm)/[Co(0.4 nm)/Pt(0.5 nm)]_n multilayers

The magnetic force microscopy and a sample vibrating magnetometer have been used to investigate the domain structure in two antiferromagnetically coupled Co/Pt multilayers.In the antiferromagnetic coupled[Pt（0.5 nm）/Co（0.4 nm）]n/NiO（1.1 nm）/[Co（0.4 nm）/Pt（0.5 nm）]n multilayers with perpendicular anisotropy,the antiferromagnetic interlayer coupling strength increases linearly with the repetition number n in Co/Pt multilayers.In demagnetized states,relatively shifted domain walls in the two Co/Pt multilayers are observed,with net ferromagnetic stripes formed between them for the repetition number n less than 5,and the stripe width decreases with the increase of n.The occurrence of these features can be attributed to the competition between the interlayer coupling and magnetostatic energies.

Superconducting Transition Temperature in YBa_2Cu_4O_8/La_(2/3)Ca_(1/3)MnO_3/YBa_2Cu_4O_8 Heterostructure

YBa2Cu4O8/La2/3 Ca1/3 MnO3/YBa2Cu4O8 （ Y-124/LCMO/Y- 124） heterostructure was prepared by facing-target sputtering technique. The oscillatory superconducting transition temperature was observed when the thickness of LCMO d L is larger than critical thickness d L^CR. The metal-insulator transition temperature can only be detected at d L 〉 d L^CR. The dependence on the spacer layer in LCMO/Y-124 systems suggests strongly the interplay of ferromagnetic and superconducting couplings.

Sulfur-vacancy-tunable interlayer magnetic coupling in centimeter-scale M0S2 bilayer

Endowing bilayer transition-metal dichalcogenides(TMDs)with tunable magnetism is significant to investigate the coupling of multiple electron degrees of freedom(DOFs).However,effectively inducing and tuning the magnetic interaction of bilayer TMDs are still challenges.Herein,we report a strategy to tune the interlayer exchange interaction of centimeter-scale MoS2 bilayer with substitutional doping of Co ion,by introducing sulfur vacancy(V_(s))to modulate the interlayer electronic coupling.This strategy could transform the interlayer exchange interaction from antiferromagnetism(AFM)to ferromagnetism(FM),as revealed by the magnetic measurements.Experimental characterizations and theoretical calculations indicate that the enhanced magnetization is mainly because the hybridization of Co 3d band and Vs-induced impurity band alters the forms of interlayer orbital hybridizations between the partial Co atoms in upper and lower layers,and also enhances the intralayer FM.Our work paves the way for tuning the interlayer exchange interaction with defects and could be extended to other two-dimensional(2D)magnetic materials.

MAGNETORESISTANCE EFFECT OBSERVED IN Fe/Mo MULTILAYERS PREPARED BY ELECTRON BEAM EVAPORATION

The Fe/Mo multilayers were prepared by electron beam evaporation, the micro structure and magnetic properties of the multilayers were studied by X-ray diffraction, vibrating-sample magnetometer (VSM) et al. The experimental results revealed that the Fe/Mo multilayers in our experimental conditions behaved magnetoresistance effect with a sharp peak on magnetoresistance (MR) ratio curve, and magnetoresistance is easily saturated at low applied magnetic fields. For [Fe(1.5nm)/Mo(1.0nm)]4,2 multilayers, MR ratio could arrive to 0.1%. The antiferromagnetic interlayer coupling could be observed in some films at room temperature. The strength of the antiferromagnetic interlayer coupling J in the films is low because of the low saturation field Hs. The relationship between magnetic properties and micro structure was also discussed in this paper.

Interlayer interaction mechanism and its regulation on optical properties of bilayer SiCNSs

Silicon carbide nanosheets(SiCNSs)have a very broad application prospect in the field of new two-dimensional(2D)materials.In this paper,the interlayer interaction mechanism of bilayer SiCNSs(BL-SiCNSs)and its effect on optical properties are studied by first principles.Taking the charge and dipole moment of the layers as parameters,an interlayer coupling model is constructed which is more convenient to control the photoelectric properties.The results show that the stronger the interlayer coupling,the smaller the band gap of BL-SiCNSs.The interlayer coupling also changes the number of absorption peaks and causes the red or blue shift of absorption peaks.The strong interlayer coupling can produce obvious dispersion and regulate the optical transmission properties.The larger the interlayer distance,the smaller the permittivity in the vertical direction.However,the permittivity of the parallel direction is negative in the range of 150-300 nm,showing obvious metallicity.It is expected that the results will provide a meaningful theoretical basis for further study of SiCNSs optoelectronic devices.