Interface electronic structure at the topological insulator - ferrimagnetic insulator junction
Y. Kubota, K. Murata, J. Miyawaki, K. Ozawa, M. C. Onbasli, T. Shirasawa, B. Feng, Sh. Yamamoto, R. -Y. Liu, S. Yamamoto, S. K. Mahatha, P. Sheverdyaeva, P. Mor… 展开作者
Y. Kubota, K. Murata, J. Miyawaki, K. Ozawa, M. C. Onbasli, T. Shirasawa, B. Feng, Sh. Yamamoto, R. -Y. Liu, S. Yamamoto, S. K. Mahatha, P. Sheverdyaeva, P. Moras, C. A. Ross, S. Suga, Y. Harada, K. L. Wang, I. Matsuda
An interface electron state at the junction between a three-dimensional topological insulator (TI) film of Bi2Se3 and a ferrimagnetic insulator film of Y3Fe5O12 (YIG) was investigated by measurements of angle-resolved photoelectron spectroscopy and X-ray absorption magnetic circular dichroism (XMCD). The surface state of the Bi2Se3 film was directly observed and localized 3d spin states of the Fe3+ state in the YIG film were confirmed. The proximity effect is likely described in terms of the exchange interaction between the localized Fe 3d electrons in the YIG film and delocalized electrons of the surface and bulk states in the Bi2Se3 film. The Curie temperature (TC) may be increased by reducing the amount of the interface Fe2+ ions with opposite spin direction observable as a pre-edge in the XMCD spectra.
We propose a new drag phenomenon, an interband magnon drag, and report on interaction effects and multiband effects in magnon transport of ferrimagnetic insulators. We study a spin-Seebeck coefficient $S_{\textrm{m}}$, a magnon conductivity $σ_{\textrm{m}}$, and a magnon thermal conductivity $κ_{\textrm{m}}$ of interacting magnons for a minimal model of ferrimagnetic insulators using a $1/S$ expansion of the Holstein-Primakoff method, the linear-response theory, and a method of Green's functions. We show that the interband magnon drag enhances $σ_{\textrm{m}}$ and reduces $κ_{\textrm{m}}$, whe…
We have performed the semilocal and hybrid density-functional theory (DFT) studies of the Sn/Ge(111) surface to identify the origin of the observed insulating ${\sqrt{3}}{\times}{\sqrt{3}}$ phase below ${\sim}$30 K. Contrasting with the semilocal DFT calculation predicting a metallic 3${\times}$3 ground state, the hybrid DFT calculation including van der Waals interactions shows that the insulating ferrimagnetic structure with ${\sqrt{3}}{\times}{\sqrt{3}}$ structural symmetry is energetically favored over the metallic 3${\times}$3 structure. It is revealed that the correction of self-interact…
In the quantum Hall regime of graphene, antiferromagnetic and spin-polarized ferromagnetic states at the zeroth Landau level compete, leading to a canted antiferromagnetic state depending on the direction and magnitude of an applied magnetic field. Here, we investigate this transition at 2.7 K in graphene Hall bars that are proximity coupled to the ferrimagnetic insulator Y$_{3}$Fe$_{5}$O$_{12}$. From nonlocal transport measurements, we demonstrate an induced magnetic exchange field in graphene, which lowers the magnetic field required to modulate the magnetic state in graphene. These results …
We report on first-principles spin-polarised quantum transport calculations (from NEGF+DFT) in MgO-spaced magnetic tunnel junctions (MTJs) based on two different Mn-based Heusler ferrimagnetic metals, namely Mn$_3$Al and Mn$_3$Ga in their tetragonal DO$_{22}$ phase. The former is a fully compensated half-metallic ferrimagnet, while the latter is a low-moment high-spin-polarisation ferrimagnet, both with a small lattice mismatch from MgO. In identical symmetric and asymmetric interface reconstructions across a 3-monolayer thick MgO barrier for both ferrimagets, the linear response (low-voltage)…
FeTaX2: A ferrimagnetic quantum anomalous Hall insulator
Fudan University（复旦大学）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Institute for Nanoelectronic Devices and Quantum Computing, Fudan University（复旦大学纳米电子器件与量子计算研究所）；Hefei National Laboratory（合肥国家实验室）
We compare thermal-gradient-driven transverse voltages in ferrimagnetic-insulator/heavy-metal bilayers (Tm3Fe5O12/W and Tm3Fe5O12/Pt) to corresponding electrically-driven transverse resistances at and above room temperature. We find for Tm3Fe5O12/W that the thermal and electrical effects can be explained by a common spin-current detection mechanism, the physics underlying spin Hall magnetoresistance (SMR). However, for Tm3Fe5O12/Pt the ratio of the electrically-driven transverse voltages (planar Hall signal/anomalous Hall signal) is much larger than the ratio of corresponding thermal-gradient …
Due to its transverse nature, spin Hall effects (SHE) provide the possibility to excite and detect spin currents and magnetization dynamics even in magnetic insulators. Magnetic insulators are outstanding materials for the investigation of nonlinear phenomena and for novel low power spintronics applications because of their extremely low Gilbert damping. Here, we report on the direct imaging of electrically driven spin-torque ferromagnetic resonance (ST-FMR) in the ferrimagnetic insulator Y$_3$Fe$_5$O$_{12}$ based on the excitation and detection by SHEs. The driven spin dynamics in Y$_3$Fe$_5$…
Spin-Hall nano-oscillators (SHNOs) are promising spintronic devices to realize current controlled GHz frequency signals in nanoscale devices for neuromorphic computing and creating Ising systems. However, traditional SHNOs -- devices based on transition metals -- have high auto-oscillation threshold currents as well as low quality factors and output powers. Here we demonstrate a new type of hybrid SHNO based on a permalloy (Py) ferromagnetic-metal nanowire and low-damping ferrimagnetic insulator, in the form of epitaxial lithium aluminum ferrite (LAFO) thin films. The superior characteristics …
We theoretically study the optical generation of dc spin current (i.e., a spin-current solar cell) in ordered antiferromagnetic and ferrimagnetic insulators, motivated by a recent study on the laser-driven spinon spin current in noncentrosymmetric quantum spin chains [H. Ishizuka and M. Sato, Phys. Rev. Lett. 122, 197702 (2019)]. Using a non-linear response theory for magnons, we analyze the dc spin current generated by a linearly-polarized electromagnetic wave (typically, terahertz or gigahertz waves). Considering noncentrosymmetric two-sublattice magnets as an example, we find a finite dc sp…
Magnetic skyrmions are compact chiral spin textures that exhibit a rich variety of topological phenomena and hold potential for developing high-density memory devices and novel computing schemes driven by spin currents. Here, we demonstrate room temperature interfacial stabilization and current-driven control of skyrmion bubbles in the ferrimagnetic insulator Tm3Fe5O12 (TmIG) coupled to Pt. We track the current-induced motion of individual skyrmion bubbles. The ferrimagnetic order of the crystal together with the interplay of spin-orbit torques and pinning determine the skyrmion dynamics in Tm…
The interface between a ferro-/ferrimagnetic insulator and a normal metal can support spin currents polarized collinear with and perpendicular to the magnetization direction. The flow of angular momentum perpendicular to the magnetization direction ("transverse" spin current) takes place via spin torque and spin pumping. The flow of angular momentum collinear with the magnetization ("longitudinal" spin current) requires the excitation of magnons. In this article we extend the existing theory of longitudinal spin transport [Bender and Tserkovnyak, Phys. Rev. B 91, 140402(R) (2015)] in the zero-…
It is shown that, contrary to the naive expectation, single particle spectral gaps can be opened on the surface states of three dimensional topological insulators by using commensurate out- and in-plane antiferromagnetic or ferrimagnetic insulating thin films.
Electrically Sign-Reversible Topological Hall Effect in a Top-Gated Topological Insulator (Bi,Sb)2Te3 on a Ferrimagnetic Insulator Europium Iron Garnet
We report the observation of strong coupling between the exchange-coupled spins in gallium-doped yttrium iron garnet and a superconducting coplanar microwave resonator made from Nb. The measured coupling rate of 450 MHz is proportional to the square-root of the number of exchange-coupled spins and well exceeds the loss rate of 50 MHz of the spin system. This demonstrates that exchange coupled systems are suitable for cavity quantum electrodynamics experiments, while allowing high integration densities due to their extraordinary high spin densities. Our results furthermore show, that experiment…
Intrinsic magnetic topological insulator ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ is believed to be an axion insulator in its antiferromagnetic ground state. However, direct identification of axion insulators remains experimentally elusive because the observed vanishing Hall resistance, while indicating the onset of the axion field, is inadequate to distinguish the system from a trivial normal insulator. Using numerical Green's functions, we theoretically demonstrate the quantized magnetoelectric current in a tunnel junction of atomically thin ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ sandwiched be…
We report on first-principles calculations of spin-transfer torque (STT) in epitaxial magnetic tunnel junctions (MTJs) based on ferrimagnetic tetragonal Mn$_3$Ga electrodes, both as analyzer in an Fe/MgO stack, and also in an analogous stack with a second Mn$_3$Ga electrode (instead of Fe) as polarizer. Solving the ballistic transport problem (NEGF + DFT) for the nonequilibrium spin density in a scattering region extended to over 7.6 nm into the Mn$_3$Ga electrode, we find long-range spatial oscillations of the STT decaying on a length scale of a few tens of angstroms, both in the linear respo…
To realize the quantum anomalous Hall effect (QAHE) at elevated temperatures, the approach of magnetic proximity effect (MPE) was adopted to break the time-reversal symmetry in the topological insulator (Bi0.3Sb0.7)2Te3 (BST) based heterostructures with a ferrimagnetic insulator europium iron garnet (EuIG) of perpendicular magnetic anisotropy. Here we demonstrate phenomenally large anomalous Hall resistance (RAHE) exceeding 8 Ω (\r{ho}AHE of 3.2 μΩ*cm) at 300 K and sustaining to 400 K in 35 BST/EuIG samples, surpassing the past record of 0.28 Ω (\r{ho}AHE of 0.14 μΩ*cm) at 300 K. The remarkabl…
The abstract notion of topology has led to profound insights into real materials. Notably, the surface and edges of topological materials can host physics, such as unidirectional charge or spin transport, that is unavailable in isolated one- and two-dimensional systems. However, to fully control the mixing and interference of edge-state wave functions, one needs robust and tunable junctions. We propose to achieve this control using an antiferromagnetic topological insulator that supports two distinct types of gapless unidirectional channels on its surface, one from antiferromagnetic domain wal…
One-dimensional (1D) topologically protected states are usually formed at the interface between two-dimensional (2D) materials with different topological invariants. Therefore, 1D chiral interface channels (CICs) can be created at the boundary of two quantum anomalous Hall (QAH) insulators with different Chern numbers. Such a QAH junction can function as a chiral edge current distributer at zero magnetic field, but its realization remains challenging. Here, by employing an in-situ mechanical mask, we use molecular beam epitaxy (MBE) to synthesize QAH insulator junctions, in which two QAH insul…
Tuning Charge Density Wave in the Transition from Magnetically Frustrated Conductor to Ferrimagnetic Insulator in Carbon Nanowire within Boron Nitride Nanotube
We study spin and charge diffusion in metallic-ferromagnet/topological-insulator junctions. The coupled diffusion equations are derived perturbatively with respect to the strength of the interlayer tunneling. We calculate spin accumulation in the ferromagnet and junction magnetoresistance associated with a current bias along the interface.
We study the nonequilibrium energy transport across a topological insulator/superconductor junction, by deriving an interfacial heat current formula through scattering wave approach. Several anomalous thermal properties are uncovered, such as thermal energy's Klein tunneling, asymmetric Kapitza resistance and negative differential thermal resistance. We expect these findings could have potential applications for the energy control in various hybridized mesoscopic systems.
We have studied the tachyonic excitations in the junction of two topological insulators in the presence of an external magnetic field. The Landau levels, evaluated from an effective two-dimensional model for tachyons, and from the junction states of two topological insulators, show some unique properties not seen in conventional electrons systems or in graphene. The $ν=1/3$ fractional quantum Hall effect has also a strong presence in the tachyon system.
We have studied magnetoresistance and Hall effects for 1.8-nm-thick Pt films grown on a ferrimagnetic insulator Y3Fe5O12 in a wide temperature (0.46-300 K) and magnetic-field (-15-15 T) region. In the low-temperature regime where quantum corrections to conductivity are observed, weak antilocalization behavior observed in Pt films is critically suppressed when the film is attached to Y3Fe5O12. Hall resistance in the Pt film is also affected by Y3Fe5O12, and it exhibits logarithmic temperature dependence in a broad temperature range. The magnetotransport properties in the high-field range are si…
We investigate quantum transport via surface states in a nanostep junction on the surface of a 3D topological insulator that involves two different side surfaces. We calculate the conductance across the junction within the scattering matrix formalism and find that as the bias voltage is increased, the conductance of the nanostep junction is suppressed by a universal factor of 1/3 compared to the conductance of a similar planar junction based on a single surface of a topological insulator. We also calculate and analyze the Fano factor of the nanostep junction and predict that the Fano factor sa…
We have considered a system of two topological insulators and have determined the properties of the surface states at the junction. Here we report that these states, under certain conditions exhibit superluminous (tachyonic) dispersion of the Dirac fermions. Although superluminal excitations are known to exist in optical systems, this is the first demonstration of possible tachyonic excitations in a purely electronic system. The first ever signature of tachyons could therefore be found experimentally in a topological insulator junction.
We investigate Josephson junctions on the surface of a three-dimensional topological insulator in planar, step, and edge geometries. The elliptical nature of the Dirac cone representing the side surface states of the topological insulator results in a scaling factor in the Josephson current in a step junction as compared to the planar junction. In edge junctions, the contribution of the Andreev bound states to the Josephson current vanishes due to spin-momentum locking of the surface states. Furthermore, we consider a junction with a ferromagnetic insulator between the superconducting regions.…
We study supercurrent and proximity vortices in a Josephson junction made of disordered surface states of a three-dimensional topological insulator with a proximity induced in-plane helical magnetization. In a regime where the rotation period of helical magnetization is larger than the junction width, we find supercurrent 0-π crossovers as a function of junction thickness, magnetization strength, and parameters inherent to the helical modulation and surface states. The supercurrent reversals are associated with proximity induced vortices, nucleated along the junction width, where the number of…
We report on the fabrication of Josephson junctions using the topological crystalline insulator Pb$_{0.5}$Sn$_{0.5}$Te as the weak link. The properties of these junctions are characterized and compared to those fabricated with weak links of PbTe, a similar material yet topologically trivial. Most striking is the difference in the AC Josephson effect: junctions made with Pb$_{0.5}$Sn$_{0.5}$Te exhibit rich subharmonic structure consistent with a skewed current-phase relation. This structure is absent in junctions fabricated from PbTe. A discussion is given on the origin of this effect as an ind…
A non-band theory is developed to describe the superconductor-insulator (SI) transtition in resistively shunted, single Josephson junctions. The $I-V$ characteristic is formulated by a Landauer-like formula and evaluated by the path-integral transfer-matrix method. The result is consistent with the recent experiments at around 80 $mK$. However, the insulator phase shrinks with decreasing temperature indicating that the single Josephson junction becomes all superconducting at absolute zero temperature, as long as dissipation is present.
We present a study of the transport properties of thermally generated spin currents in an insulating ferrimagnetic-antiferromagnetic-ferrimagnetic trilayer over a wide range of temperature. Spin currents generated by the spin Seebeck effect (SSE) in a yttrium iron garnet (YIG) YIG/NiO/YIG trilayer on a gadolinium gallium garnet (GGG) substrate were detected using the inverse spin Hall effect in Pt. By studying samples with different NiO thicknesses, the NiO spin diffusion length was determined to be 4.2 nm at room temperature. Interestingly, below 30 K, the inverse spin Hall signals are associ…
We reveal the giant magnetoresistance induced by the spin-polarized current in the ferromagnet (F_1)/topological insulator (TI)/ferromagnet (F_2) junction, where two ferromagnets are deposited on the diffusive surface of the TI. We can increase and reduce the value of the giant magnetoresistance by tuning the spin-polarized current, which is controlled by the magnetization configurations. The property is intuitively understood by the non-equilibrium spin-polarized current, which plays the role of an effective electrochemical potential on the surface of the TI.
Recently, a contact-resistance-measurement method was developed to detect the minigap, hence the Andreev bound states (ABSs), in Josephson junctions constructed on the surface of three-dimensional topological insulators (3D TIs). In this work, we further generalize that method to the circumstance with radio frequency (rf) irradiation. We find that with the increase of rf power, the measured minigap becomes broadened and extends to higher energies, in a way similar to the rf power dependence of the outer border of the Shapiro step region. We show that the corresponding data of contact resistanc…
We use Superconducting QUantum Interference Device (SQUID) microscopy to characterize the current-phase relation (CPR) of Josephson Junctions from 3-dimentional topological insulator HgTe (3D-HgTe). We find clear skewness in the CPRs of HgTe junctions ranging in length from 200 nm to 600 nm. The skewness indicates that the Josephson current is predominantly carried by Andreev bound states with high transmittance, and the fact that the skewness persists in junctions that are longer than the mean free path suggests that the effect may be related to the helical nature of the Andreev bound states …
We consider a junction between two topological insulators, and calculate the properties of the interface states with an effective low energy Hamiltonian for topological insulators with a single cone on the surface. This system bears a close resemblance to bilayer graphene, as both result from the hybridization of Dirac cones. We find gapless interface states not only when the helicity direction of the topological surface states are oppositely oriented, but they can also exist if they are equally oriented. Furthermore, we find that the existence of the interface states can be understood from th…
One-dimensional Majorana modes are predicated to form in Josephson junctions based on three-dimensional topological insulators (TIs). While observations of supercurrents in Josephson junctions made on bulk-insulating TI samples are recently reported, the Fraunhofer patters observed in such TI-based Josephson junctions, which sometimes present anomalous features, are still not well understood. Here we report our study of highly gate-tunable TI-based Josephson junctions made of one of the most bulk-insulating TI materials, BiSbTeSe2, and Al. The Fermi level can be tuned by gating across the Dira…
We study the properties of a line junction which separates the surfaces of two three-dimensional topological insulators. The velocities of the Dirac electrons on the two surfaces may be unequal and may even have opposite signs. For a time reversal invariant system, we show that the line junction is characterized by an arbitrary parameter αwhich determines the scattering from the junction. If the surface velocities have the same sign, we show that there can be edge states which propagate along the line junction with a velocity and orientation of the spin which depend on αand the ratio of the ve…
We theoretically study the Josephson current in a superconductor/quantum anomalous Hall insulator/superconductor junction by using the lattice Green function technique. When an in-plane external Zeeman field is applied to the quantum anomalous Hall insulator, the Josephson current $J$ flows without a phase difference across the junction $θ$. The phase shift $φ$ appealing in the current-phase relationship $J\propto \sin(θ-φ$) is proportional to the amplitude of Zeeman fields and depends on the direction of Zeeman fields. A phenomenological analysis of the Andreev reflection processes explains t…
We experimentally investigate Andreev transport through a single junction between an s-wave indium superconductor and a thick film of a three-dimensional $Bi_2Te_3$ topological insulator. We study $Bi_2Te_3$ samples with different bulk and surface characteristics, where the presence of a topological surface state is confirmed by direct ARPES measurements. All the junctions demonstrate Andreev transport within the superconducting gap. For junctions with transparent $In-Bi_2Te_3$ interfaces we find a number of nearly periodic conductance oscillations, which are accompanied by zero-bias conductan…
We study two microscopic models of topological insulators in contact with an $s$-wave superconductor. In the first model the superconductor and the topological insulator are tunnel coupled via a layer of scalar and of randomly oriented spin impurities. Here, we require that spin-flip tunneling dominates over spin-conserving one. In the second model the tunnel coupling is realized by an array of single-level quantum dots with randomly oriented spins. It is shown that the tunnel region forms a $π$-junction where the effective order parameter changes sign. Interestingly, due to the random spin or…
We theoretically investigate tunneling magnetoresistance (TMR) devices, which are probing the spin-momentum coupled nature of surface states of the three-dimensional topological insulator Bi$_{2}$Se$_{3}$. Theoretical calculations are performed based on a realistic tight-binding model for Bi$_{2}$Se$_{3}$. We study both three dimensional devices, which exploit the surface states of Bi$_{2}$Se$_{3}$, as well as two-dimensional devices, which exploit the edge states of thin Bi$_{2}$Se$_{3}$ strips. We demonstrate that the material properties of Bi$_{2}$Se$_{3}$ allow a TMR ratio at room temperat…
We theoretically study a Josephson junction formed by two finite-size $s$-wave SCs on a topological insulator under a magnetic field. At certain conditions, the junction hosts the chiral Majorana modes enclosing the two finite-size SCs. The interplay of the extended chiral Majorana modes and the states inside the junction can results in nontrivial topological effects such as the $2n π$ fractional AC Josephson effects predicted in Ref.~\cite{ChoiSim} We show that the $2n π$ fractional AC Josephson effects can occur in a realistic situation, such as the presence of the midgap states, without req…
The ferromagnet-topological insulator-ferromagnet (FM-TI-FM) junction exhibits thermal and electrical quantum Hall effects. The generated Hall voltage and transverse temperature gradient can be controlled by the directions of magnetizations in the FM leads, which inspires the use of FM-TI-FM junctions as electrical and as heat switches in spintronic devices. Thermal and electrical Hall coefficients are calculated as functions of the magnetization directions in ferromagnets and the spin-relaxation time in TI. Both the Hall voltage and the transverse temperature gradient decrease but are not com…
The low energy physics of both graphene and surface states of three-dimensional topological insulators is described by gapless Dirac fermions with linear dispersion. In this work, we predict the emergence of a "heavy" Dirac fermion in a graphene/topological insulator hetero-junction, where the linear term almost vanishes and the corresponding energy dispersion becomes highly non-linear. By combining {\it ab initio} calculations and an effective low-energy model, we show explicitly how strong hybridization between Dirac fermions in graphene and the surface states of topological insulators can r…
We have studied thermoelectric effect of a Kane-Mele normal-insulator-superconductor (KMNIS) junction at ultra-low temperatures using a modified version of the well-known Blonder-Tinkham-Klapwijk (BTK) theory. Since both the (electronic) charge and thermal current due to the carriers are sensitive to the strengths of the spin-orbit coupling (SOC) present in the Kane-Mele model, a tunability of this junction device with regard to its thermoelectric properties can be experimentally achieved by certain techniques that are used to manipulate the values of the spin-orbit couplings. We have computed…
We study the quantum Andreev oscillation induced by interference of the edge chiral Majorana fermions in junctions made of quantum anomalous Hall (QAH) insulators and superconductors (SCs). We show two chiral Majorana fermions on a QAH edge with SC proximity generically have a momentum difference $Δk$, which depends on the chemical potentials of both the QAH insulator and the SC. Due to the spatial interference induced by $Δk$, the longitudinal conductance of QAH-SC junctions oscillates with respect to the edge lengths and the chemical potentials, which can be probed via charge transport. Furt…
The transport properties of Chern insulator junctions generated by bipolar junctions in quantum Hall graphene are theoretically studied in the coherent regime. Coherent transport across the junction exhibits two mesoscopic features: valley-isospin dependence of the quantum Hall conductance, and the Aharonov-Bohm (AB) effects with the interface channels. We demonstrate that the valley-isospin dependence can be measured in a graphene sample with perfect edge terminations, resulting in conductance oscillation for the smallest Chern number case. On the other hand, while conductance plateaus are fo…
We report on the fabrication and electrical transport properties of superconducting junctions made of β-Ag$_{2}$Se topological insulator (TI) nanowires in contact with Al superconducting electrodes. The temperature dependence of the critical current indicates that the superconducting junction belongs to a short and diffusive junction regime. As a characteristic feature of the narrow junction, the critical current decreases monotonously with increasing magnetic field. The stochastic distribution of the switching current exhibits the macroscopic quantum tunneling behavior, which is robust up to …
We theoretically investigate the transport properties of a normal-insulator-superconductor (NIS) junction of silicene in the thin barrier limit. Similar to graphene the tunneling conductance in such NIS structure exhibits an oscillatory behavior as a function of the strength of the barrier in the insulating region. However, unlike in graphene, the tunneling conductance in silicene can be controlled by an external electric field owing to its buckled structure. We also demonstrate the change in behavior of the tunneling conductance across the NIS junction as we change the chemical potential in t…
We study the Josephson transport in a high-Tc superconductor/ferromagnetic-insulator(FI)/high-Tc superconductor numerically. We found the formation of a pi-junction in such systems. More remarkably the ground state of such junction alternates between 0- and pi-states when thickness of FI is increasing by a single atomic layer. We propose an experimental setup for observing the atomic-scale 0-pi transition. Such FI-based pi-junctions can be used to implement highly-coherent quantum bits.
