Studies of angle-dependent magnetoresistance oscillations (AMRO) in the interlayer conductivity of layered metals have generally considered semi-classical electron transport. We consider a quantum correction to the semi-classical conductivity that arises from what can be described as an interlayer Cooperon. This depends on both the disorder potential within a layer and the correlations of the disorder potential between layers. We compare our results with existing experimental data on organic charge transfer salts that are not explained within the standard semi-classical transport picture. In particular, our results may be applicable to effects that have been seen when the applied magnetic field is almost parallel to the conducting layers. We predict the presence of a peak in the resistivity as the field direction approaches the plane of the layers. The peak can occur even when there is weakly incoherent transport between layers.
We investigate the effect of the interlayer spin-flip tunneling for the interlayer magnetoresistance under magnetic fields in alpha-(BEDT-TTF)2I3, which is a multilayer massless Dirac fermion system under pressure. The mean field of the spin-flip correlation associated with the interlayer Coulomb interaction enables the interlayer spin-flip tunneling. Assuming the non-vertical interlayer spin-flip tunneling, we calculate the interlayer magnetoresistance using the Kubo formula. The crossover magnetic field, at which the interlayer magnetoresistance changes from positive to negative is shifted b…
We investigate the monotonic growth of longitudinal interlayer magnetoresistance $\bar{R}_{zz}(B_z) $, analytically and numerically in the self-consistent Born approximation. We show that in a weak magnetic field the monotonic part of $\bar{R}_{zz}(B_z)$ is almost constant and starts to grow only above the crossover field $B_{c}$, when the Landau levels (LL) become isolated, i.e. when the LL separation becomes greater than the LL broadening. In higher field $B_{z}>>B_{c}$, $\bar{R}_{zz}(B_{z}) \propto B_{z}^{1/2}$ in agreement with previous works.
The longitudinal interlayer magnetoresistance $R_{zz}(B_{z})$ is calculated in strongly anisotropic layered metals, when the interlayer band width $4t_{z}$ is less than the Landau level separation $\hbar ω_{c}$. The impurity scattering has much stronger effect in this regime than in 3D metals and leads to a linear longitudinal interlayer magnetoresistance $R_{zz}\propto B_{z}$ in the interval $\hbar ω_{c}>4t_{z}>>\sqrt{Γ_{0}\hbar ω_{c}}$ changing to a square-root dependence $R_{zz}\propto B_{z}^{1/2}$ at higher field or smaller $t_{z}$. The crossover field allows to estimate the interlayer tra…
Due to the chiral nature of electrons in a monolayer of graphite (graphene) one can expect weak antilocalisation and a positive weak-field magnetoresistance in it. However, trigonal warping (which breaks p/-p symmetry of the Fermi line in each valley) suppresses antilocalisation, while inter-valley scattering due to atomically sharp scatterers in a realistic graphene sheet or by edges in a narrow wire tends to restore conventional negative magnetoresistance. We show this by evaluating the dependence of the magnetoresistance of graphene on relaxation rates associated with various possible ways …
We present a theoretical description of the interlayer magnetoresistance in the layered Dirac fermion system with the application to the organic conductor α-(BEDT-TTF)_2I_3 under pressure. Assuming a non-vertical interlayer tunneling and including higher Landau level effects we calculate the interlayer conductivity using the Kubo formula.We propose a physical picture of the experimentally observed crossover from the negative interlayer magnetoresistance, where the Dirac fermion zero-energy Landau level plays a central role, to the positive interlayer magnetoresistance that is the consequence o…
It is shown, that the monotonic part of interlayer electronic conductivity strongly decreases in high magnetic field perpendicular to the conducting layers. We consider only the coherent interlayer tunnelling, and the obtained result strongly contradicts the standard theory. This effect appears in very anisotropic layered quasi-two-dimensional metals, when the interlayer transfer integral is less than the Landau level separation.
It is shown that in rather strong magnetic field the interlayer electron conductivity is exponentially damped by the Coulomb barrier arising from the formation of polaron around each localized electron state. The theoretical model is developed to describe this effect, and the calculation of the temperature and field dependence of interlayer magnetoresistance is performed. The results obtained agree well with the experimental data in GaAs/AlGaAs heterostructures and in strongly anisotropic organic metals. The proposed theory allows to use the experiments on interlayer magnetoresistance to inves…
Interlayer magnetoresistance (ILMR) effect is explored in a vertical stack of weakly coupled multilayer graphene as grown by chemical vapor deposition (CVD). This effect has been characterized as a function of temperature and tilt angle of the magnetic field with respect to the interlayer current. To our knowledge, this is the first experimental report on angle dependent ILMR effect in graphitic systems. Our data agrees qualitatively with the existing theories of ILMR in multilayer massless Dirac Fermion systems. However, a sharper change in ILMR has been observed as the tilt angle of the magn…
We theoretically study the effect of the motion and the merging of Dirac cone on the interlayer magnetoresistance in multilayer graphene like systems. This merging, which could be induced by a uniaxial strain, gives rise in monolayer Dirac electron system to a topological transition from a semi-metallic phase to an insulating phase where Dirac points disappear. Based on a universal Hamiltonian proposed to describe the motion and the merging of Dirac points in two dimensional Dirac electron crystals, we calculate the interlayer conductivity of a stack of deformed graphene like layers using Kubo…
We show that in a layered metal, the angle dependent, finite frequency, interlayer magnetoresistance is altered due to the presence of a non-zero Berry curvature at the Fermi surface. At zero frequency, we find a conservation law which demands that the `magic angle' condition for interlayer magnetoresistance extrema as a function of magnetic field tilt angle is essentially both field and Berry curvature independent. In the finite frequency case, however, we find that surprisingly large signatures of a finite Berry curvature occur in the periodic orbit resonances. We outline a method whereby th…
We analyze the beating behavior of the magnetic quantum oscillations in a layered metal under the conditions when the cyclotron energy $\hbar ω_c $ is comparable to the interlayer transfer energy $t$. We find that the positions of the beats in the interlayer resistance are considerably shifted from those in the magnetization oscillations, and predict that the shift is determined by the ratio $\hbar ω_c/t$. A comparative study of the Shubnikov-de Haas and de Haas-van Alphen effects in the quasi-two-dimensional organic metal $β$-(BEDT-TTF)$_2$IBr$_2$ appears to be consistent with the theoretical…
Magnetoresistance and Hall coefficient of a graphene layer are investigated in the presence of a tilted magnetic field. We consider the graphene layer is assembled by either another graphene layer or a two-dimensional electron gas (2DEG) and an interlayer electron-electron interaction is modeled within Random Phase Approximation. Our calculated magnetoresistances show different interlayer screening effects between decoupled graphene-graphene and graphene-2DEG systems. We also analyze the dependence of dielectric materials as well as the distance between layers on magnetoresistances. The angle …
Different types of angular magnetoresistance oscillations in quasi-one-dimensional layered materials, such as organic conductors (TMTSF)2X, are explained in terms of Aharonov-Bohm interference in interlayer electron tunneling. A two-parameter pattern of oscillations for generic orientations of a magnetic field is visualized and compared with the experimental data. Connections with angular magnetoresistance oscillations in other layered materials are discussed.
We have performed the first experimental investigation of quantum interference corrections to the conductivity of a bilayer graphene structure. A negative magnetoresistance - a signature of weak localisation - is observed at different carrier densities, including the electro-neutrality region. It is very different, however, from the weak localisation in conventional two-dimensional systems. We show that it is controlled not only by the dephasing time, but also by different elastic processes that break the effective time-reversal symmetry and provide invervalley scattering.
We have for the first time experimentally investigated the weak localisation magnetoresistance in a AlGaAs/GaAs p-type quantum well. The peculiarity of such systems is that spin-orbit interaction is strong. On the theoretical side it is not possible to treat the spin-orbit interaction as a perturbation. This is in contrast to all prior investigations of weak localisation. In this letter we compare the experimental results with a newly developed diffusion theory, which explicitly describes the weak localisation regime when the spin-orbit coupling is strong. The spin relaxation rates calculated …
A detailed investigation of the metallic behaviour in high quality GaAs-AlGaAs two dimensional hole systems reveals the presence of quantum corrections to the resistivity at low temperatures. Despite the low density ($r_{s}>10$) and high quality of these systems, both weak localisation (observed via negative magnetoresistance) and weak hole-hole interactions (giving a correction to the Hall constant) are present in the so-called metallic phase where the resistivity decreases with decreasing temperature. The results suggest that even at high $r_{s}$ there is no metallic phase at T=0 in two dime…
We report interlayer electronic transport in CaMnBi$_{2}$ single crystals. Quantum oscillations and angular magnetoresistance suggest coherent electronic conduction and valley polarized conduction of Dirac states. Small cyclotron mass, large mobility of carriers and nontrivial Berry's phase are consistent with the presence of Dirac fermions on the side wall of the warped cylindrical Fermi surface. Similar to SrMnBi$_{2}$ that features an anisotropic Dirac cone, our results suggest that magnetic field-induced changes in the interlayer conduction are also present in layered bismuth-based materia…
We investigate the conductivity in layered metals in magnetic field in the weakly incoherent limit, when the interlayer transfer integral is smaller than the Landau level broadening due to the impurity potential, but the interlayer electron tunnelling conserves the intralayer momentum. It is shown that the impurity potential has much stronger effect in this regime, than in the quasi-2D metals in the coherent limit. The weakly incoherent regime has several new qualitative features, not found in the previous theoretical approaches. The background interlayer magnetoresistance in this regime monot…
Magnetoresistance results are presented for p-SiGe samples on the metallic side of the B=0 metal-insulator transition. The results cannot be understood within the framework of standard theories for quantum corrections of a weakly interacting 2- dimensional system. In particular no logarithmic dependence on temperature is observed, at low fields, in either the longitudinal or Hall resistivities despite evidence in the magnetoresistance of weak localisation effects. Further, the Hall coefficient shows a strong logarithmic dependence on field. The results are better explain by renormalisation gro…
Strong magnetoresistance effects are often observed in ferromagnet-nonmagnet multilayers, which are exploited in state-of-the-art magnetic field sensing and data storage technologies. In this work we report a novel current-perpendicular-to-plane magnetoresistance effect in multilayer graphene as grown on a catalytic nickel surface by chemical vapor deposition. A negative magnetoresistance effect of 10^4% has been observed, which persists even at room temperature. This effect is correlated with the shape of the 2D peak as well as with the occurrence of D peak in the Raman spectrum of the as-gro…
Recent demonstrations of magnetic ordering and spin transport in two-dimensional heterostructures have opened research venues in these material systems. In order to control and enhance the related physical phenomena, quantitative descriptions linking experimental observations to atomic details must be produced. Here we combine first principles and quantum ballistic transport calculations to shed important insights from an atomistic viewpoint on the underlying mechanisms governing spin transport in graphene/CrI$_3$ junctions. Descriptions of the electronic structure reveal that tunneling is the…
The angle-dependent interlayer magnetoresistance of the layered organic metal $α$-(BEDT-TTF)$_2$KHg(SCN)$_4$ is found to undergo a dramatic change from the classical conventional behavior at low magnetic fields to an anomalous one at high fields. This field-induced crossover and its dependence on the sample purity and temperature imply the existence of two parallel channels in the interlayer transport: a classical Boltzmann conductivity $σ_{c}$ and an incoherent channel $σ_{i}$. We propose a simple model for $σ_{i}$ explaining its metallic temperature dependence and low sensitivity to the inpl…
Spin currents can modify the magnetic state of ferromagnetic ultrathin films through spin-orbit torque. They may be generated by means of spin-orbit interaction by either bulk or interfacial phenomena. Electrical transport measurements reveal a six-fold increase of the spin-orbit torque accompanied by a drastic reduction of the spin Hall magnetoresistance upon the introduction of a Cu interlayer in a Pt/Cu/Co/Pt structure with perpendicular magnetic anisotropy. We analyze the dependence of the spin Hall magnetoresistance with the thickness of the interlayer in the frame of a drift diffusion mo…
Relativistic fermions in topological quantum materials are characterized by linear energy-momentum dispersion near band crossing points. Under magnetic field, relativistic fermions acquire Berry phase of π in cyclotron motion, leading to a zeroth Landau level (LL) at the crossing point. Such field-independent zeroth LL, which distinguishes relativistic fermions from conventional electron systems, is hardly probed in transport measurements since the Fermi energy (EF) is usually not right at the band crossing points in most topological materials. Here we report the observation of exotic quantum …
The field dependence of interlayer magnetoresistance of the pressurized (to the normal state) layered organic metal $α$-(BEDT-TTF)$_{2}$KHg(SCN)$_{4}$ is investigated. The high quasi-two-dimensional anisotropy, when the interlayer hopping time is longer than the electron mean-free time and than the cyclotron period, leads to a dimensional crossover and to strong violations of the conventional three-dimensional theory of magnetoresistance. The monotonic field dependence is found to change from the conventional behavior at low magnetic fields to an anomalous one at high fields. The shape of Land…
Quantum limit is quite easy to achieve once the band crossing exists exactly at the Fermi level ($E_F$) in topological semimetals. In multilayered Dirac fermion system, the density of Dirac fermions on the zeroth Landau levels (LLs) increases in proportion to the magnetic field, resulting in intriguing angle- and field-dependent interlayer tunneling conductivity near the quantum limit. BaGa$_2$ is an example of multilayered Dirac semimetal with anisotropic Dirac cone close to $E_F$, providing a good platform to study its interlayer transport properties. In this paper, we report the negative in…
Dirac semimetals (DSMs), which host Dirac fermions and represent new state of quantum matter, have been studied intensively in condensed matter physics. The exploration of new materials with topological states is im- portant in both physics and materials science. In this article, we report the synthesis and the transport properties of high quality single crystals of YbMnSb$_2$. YbMnSb$_2$ is a new compound with metallic behavior. Quantum oscillations, including Shubnikov-de Haas (SdH) oscillation and de Haas-van Alphen (dHvA) type oscillation, have been observed at low temperature and high mag…
We study the flow of a pure spin current through zinc oxide by measuring the spin Hall magnetoresistance (SMR) in thin film trilayer samples consisting of bismuth-substituted yttrium iron garnet (Bi:YIG), gallium-doped zinc oxide (Ga:ZnO), and platinum. We investigate the dependence of the SMR magnitude on the thickness of the Ga:ZnO interlayer and compare to a Bi:YIG/Pt bilayer. We find that the SMR magnitude is reduced by almost one order of magnitude upon inserting a Ga:ZnO interlayer, and continuously decreases with increasing interlayer thickness. Nevertheless, the SMR stays finite even f…
We report on the occurrence of strong interlayer Dzyaloshinskii-Moriya interaction (DMI) between an in-plane magnetized Co layer and a perpendicularly magnetized TbFe layer through a Pt spacer. The DMI causes a chiral coupling that favors one-handed orthogonal magnetic configurations of Co and TbFe, which we reveal through Hall effect and magnetoresistance measurements. The DMI coupling mediated by Pt causes effective magnetic fields on either layer of up to 10-15 mT, which decrease monotonously with increasing Pt thickness. Ru, Ta, and Ti spacers mediate a significantly smaller coupling compa…
By exploiting proximity coupling, we probe the spin state of the surface layers of CrI3, a van der Waals magnetic semiconductor, by measuring the induced magnetoresistance (MR) of Pt in Pt/CrI3 nano-devices. We fabricate the devices with clean and stable interfaces by placing freshly exfoliated CrI3 flake atop pre-patterned thin Pt strip and encapsulating the Pt/CrI3 heterostructure with hexagonal boron nitride (hBN) in a protected environment. In devices consisting of a wide range of CrI3 thicknesses (30 to 150 nm), we observe that an abrupt upward jump in Pt MR emerge at a 2 T magnetic field…
Transport of electrons in a bulk metal is usually well captured by their particle-like aspects, while their wave-like nature is commonly harder to observe. Microstructures can be are fully designed to reveal the quantum phase, for example mesoscopic metal rings resembling interferometers. Here we report a new type of phase coherent oscillation of the out-of-plane magnetoresistance in the layered delafossites PdCoO$_2$ and PtCoO$_2$. The oscillation period is equivalent to that determined by the magnetic flux quantum, $h/e$, threading an area defined by the atomic interlayer separation and the …
The spin-orbit torque, a torque induced by a charge current flowing through the heavy-metal conducting layer with strong spin-orbit interactions, provides an efficient way to control the magnetization direction in heavy-metal/ferromagnet nanostructures, required for applications in the emergent magnetic technologies like random access memories, high-frequency nano oscillators, or bio-inspired neuromorphic computations. We study the interface properties, magnetization dynamics, magnetostatic features and spin-orbit interactions within the multilayer system Ti(2)/Co(1)/Pt(0-4)/Co(1)/MgO(2)/Ti(2)…
We calculate the energy spectrum of a Dirac double layer, where each layer has the Dirac electronic dispersion, in the presence of a tilted magnetic field and small interlayer tunneling. We show that the energy splitting between the Landau levels has an oscillatory dependence on the in-plane magnetic field and vanishes at a series of special tilt angles of the magnetic field. Using a semiclassical analysis, we show that these special tilt angles are determined by the Berry phase of the Dirac Hamiltonian. The interlayer tunneling conductance also exhibits an oscillatory dependence on the magnet…
Bilayer graphene (two coupled graphitic monolayers arranged according to Bernal stacking) is a two-dimensional gapless semiconductor with a peculiar electronic spectrum different from the Dirac spectrum in the monolayer material. In particular, the electronic Fermi line in each of its valleys has a strong p -> -p asymmetry due to a trigonal warping, which suppresses the weak localization effect. We show that weak localisation in bilayer graphene may be present only in devices with pronounced intervalley scattering, and we evaluate the corresponding magnetoresistance.
We discuss the surface magnetotransport in the quantum Hall (QH) ferromagnetic state expected in the organic Dirac fermion system α-(BEDT-TTF)_2I_3. The QH ferromagnetic state is one of the possible ν=0 QH states in the two-dimensional Dirac fermion system resulting from the degeneracy breaking of the n=0 Landau level. It is characterized by the helical edge state. We have studied the interlayer surface transport via helical edge state in the multilayer QH ferromagnet, in which the bulk region is insulating. We have clarified that the surface conductivity is much less than e^2/h and decreases …
Helical Edge Transport in the ν= 0 Quantum Hall Ferromagnetic State of an Organic Dirac Fermion System
University of Tokyo（东京大学）；Institute for Solid State Physics, University of Tokyo（东京大学固体物理研究所）；National Institute for Materials Science（国立材料科学研究所）；Ewha Womans University（梨花女子大学）
We report single layer resistivities of 2-dimensional electron and hole gases in an electron-hole bilayer with a 10nm barrier. In a regime where the interlayer interaction is stronger than the intralayer interaction, we find that an insulating state ($dρ/dT < 0$) emerges at $T\sim1.5{\rm K}$ or lower, when both the layers are simultaneously present. This happens deep in the $"$metallic" regime, even in layers with $k_{F}l>500$, thus making conventional mechanisms of localisation due to disorder improbable. We suggest that this insulating state may be due to a charge density wave phase, as has …
The recent discovery of magnetism in atomically thin layers of van der Waals (vdW) crystals has created new opportunities for exploring magnetic phenomena in the two-dimensional (2D) limit. In most 2D magnets studied to date the c-axis is an easy axis, so that at zero applied field the polarization of each layer is perpendicular to the plane. Here, we demonstrate that atomically thin CrCl3 is a layered antiferromagnetic insulator with an easy-plane normal to the c-axis, that is the polarization is in the plane of each layer and has no preferred direction within it. Ligand field photoluminescen…
Layered systems shows anisotropic transport properties. The interlayer conductivity show a general temperature dependence for a wide class of materials. This can be understood if conduction occurs in two different channels activated at different temperatures. We show that the characteristic temperature dependence can be explained using a polaron model for the transport. The results show an intuitive interpretation in terms of coherent and incoherent quasi-particles within the layers. Further, we extract results for the magnetoresistance, thermopower, spectral function and optical conductivity …
Effect of pressure on the magnetic properties of (Co$_{0.5}$Fe$_{0.5}$)$_5$GeTe$_2$
Budapest University of Technology and Economics（布达佩斯技术与经济大学）；MTA-BME Correlated van der Waals Structures Momentum Research Group（匈牙利科学院-布达佩斯技术与经济大学关联范德华结构动量研究组）；Zernike Institute for Advanced Materials, University of Groningen（格罗宁根大学泽尼克先进材料研究所）；University of Manchester（曼彻斯特大学）；Chalmers University of Technology（查尔姆斯理工大学）
