Scattering-induced and highly tunable by gate damping-like spin-orbit torque in graphene doubly proximitized by two-dimensional magnet Cr$_2$Ge$_2$Te$_6$ and WS$_2$
Klaus Zollner, Marko D. Petrovic, Kapildeb Dolui, Petr Plechac, Branislav K. Nikolic, Jaroslav Fabian
Graphene sandwiched between semiconducting monolayers of ferromagnet Cr$_2$Ge$_2$Te$_6$ and transition-metal dichalcogenide WS$_2$ acquires both spin-orbit (SO), of valley-Zeeman and Rashba types, and exchange couplings. Using first-principles combined with quantum transport calculations, we predict that such doubly proximitized graphene within van der Waals heterostructure will exhibit SO torque driven by unpolarized charge current. This system lacking spin Hall current, putatively considered to be necessary for efficient damping-like (DL) SO torque that plays a key role in magnetization switching, demonstrates how DL torque component can be generated solely by skew-scattering off spin-independent potential barrier or impurities in purely two-dimensional electronic transport due to the presence of proximity SO coupling and its spin texture tilted out-of-plane. This leads to current-driven nonequilibrium spin density emerging in all spatial directions, whose cross product with proximity magnetization yields DL SO torque, unlike the ballistic regime with no scatterers in which only field-like (FL) SO torque appears. In contrast to SO torque on conventional metallic ferromagnets in contact with three dimensional SO-coupled materials, the ratio of FL and DL torque can be tuned by more than an order of magnitude via combined top and back gates.
Transport in magnetic-topological-insulator nanoribbons containing multiple superconductor-proximitized sectors
Institute for Cross-Disciplinary Physics and Complex Systems IFISC (CSIC-UIB)（交叉物理与复杂系统研究所）；Department of Physics, University of the Balearic Islands（巴利阿里大学物理系）
Magnetic molecules deposited on surfaces are a promising platform to individually address and manipulate spins. Long spin excitation lifetimes are necessary to utilize them in quantum information processing and data storage. Normally, coupling of the molecular spin with the conduction electrons of metallic surfaces causes fast relaxation of spin excitations into the ground state. However, the presence of superconducting paring effects in the substrate can protect the excited spin from decaying. In this work, we show that a proximity-induced superconducting gold film can sustain spin excitation…
Multiple chiral Majorana states in proximitized magnetic topological insulator heterostructures
Universidad Autónoma de Madrid（马德里自治大学）；Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid（马德里自治大学凝聚态物理中心（IFIMAC））；Instituto de Estructura de la Materia IEM-CSIC（CSIC物质结构研究所）；Instituto Nicolás Cabrera, Universidad Autónoma de Madrid（马德里自治大学尼古拉斯·卡布雷拉研究所）
We measure the charge periodicity of Coulomb blockade conductance oscillations of a hybrid InSb-Al island as a function of gate voltage and parallel magnetic field. The periodicity changes from $2e$ to $1e$ at a gate-dependent value of the magnetic field, $B^*$, decreasing from a high to a low limit upon increasing the gate voltage. In the gate voltage region between the two limits, which our numerical simulations indicate to be the most promising for locating Majorana zero modes, we observe correlated oscillations of peak spacings and heights. For positive gate voltages, the $2e$-$1e$ transit…
We identify the leading processes of electron transport across finite-length segments of proximitized nanowires and build a quantitative theory of their two-terminal conductance. In the presence of spin-orbit interaction, a nanowire can be tuned across the topological transition point by an applied magnetic field. Due to a finite segment length, electron transport is controlled by the Coulomb blockade. Upon increasing of the field, the shape and magnitude of the Coulomb blockade peaks in the linear conductance is defined, respectively, by Andreev reflection, single-electron tunneling, and reso…
We study the magnetic-field dependence of Landau levels in graphene proximitized by large spin-orbit coupling materials, such as transition-metal dichalcogenides or topological insulators. In addition to the Rashba coupling, two types of intrinsic spin-orbit interactions, uniform (Kane-Mele type) and staggered (valley Zeeman type), are included, to resolve their interplay with magnetic orbital effects. Employing a continuum model approach, we derive analytic expressions for low-energy Landau levels, which can be used to extract local orbital and spin-orbit coupling parameters from scanning pro…
We study the magnetic and superconducting proximity effects in a semiconducting nanowire (NW) attached to superconducting leads and a ferromagnetic insulator (FI). We show that a sizable equilibrium spin polarization arises in the NW due to the interplay between the superconducting correlations and the exchange field in the FI. The resulting magnetization has a nonlocal contribution that spreads in the NW over the superconducting coherence length and is opposite in sign to the local spin polarization induced by the magnetic proximity effect in the normal state. For a Josephson-junction setup, …
We investigate the formation of edge states in graphene ribbons and flakes with proximity induced valley-Zeeman and Rashba spin-orbit couplings in the presence of a perpendicular magnetic field $B$. Two types of edges states appear in the spin-orbit gap at the Fermi level at zero field: strongly localized pseudohelical (intervalley) states and weakly localized intravalley states. We show that if the magnetic field is stronger than a crossover field $B_c$, which is a few mT for realistic systems such as graphene/WSe$_2$, only the pseudohelical edge states remain in zigzag graphene ribbons; the …
In condensed matter systems, zero-dimensional or one-dimensional Majorana modes can be realized respectively as the end and edge states of one-dimensional and two-dimensional topological superconductors. In this $\textit{top-down}$ approach, $(d-1)$-dimensional Majorana modes are obtained as the boundary states of a topologically nontrivial $d$-dimensional bulk. In a $\textit{bottom-up}$ approach instead, $d$-dimensional Majorana modes in a $d$-dimensional system can be realized as the continuous limit of a periodic lattice of coupled $(d-1)$-dimensional Majorana modes. We illustrate this idea…
We demonstrate an Al superconducting quantum interference device in which the Josephson junctions are implemented through gate-controlled proximitized Cu mesoscopic weak-links. The latter behave analogously to genuine superconducting metals in terms of the response to electrostatic gating, and provide a good performance in terms of current-modulation visibility. We show that, through the application of a static gate voltage, we are able to modify the interferometer current-flux relation in a fashion which seems compatible with the introduction of $π$-channels within the gated weak-link. Our re…
Conventional $s$-wave superconductivity is understood to arise from singlet pairing of electrons with opposite Fermi momenta, forming Cooper pairs whose net momentum is zero [1]. Several recent studies have focused on structures where such conventional $s$-wave superconductors are coupled to systems with an unusual configuration of electronic spin and momentum at the Fermi surface. Under these conditions, the nature of the paired state can be modified and the system may even undergo a topological phase transition [2, 3]. Here we present measurements and theoretical calculations of several HgTe…
Using a van der Waals vertical heterostructure consisting of monolayer graphene, monolayer hBN and NbSe$_2$, we have performed local characterization of induced correlated states in different configurations. At a temperature of 4.6 K, we have shown that both superconductivity and charge density waves can be induced in graphene from NbSe2 by proximity effects. By applying a vertical magnetic field, we imaged the Abrikosov vortex lattice and extracted the coherence length for the proximitized superconducting graphene. We further show that the induced correlated states can be completely blocked b…
Motivated by recent experiments demonstrating intricate quantum Hall physics on the surface of elemental bismuth, we consider proximity coupling an $s$-wave superconductor to a two-dimensional electron gas with strong Rashba spin-orbit interactions in the presence of a strong perpendicular magnetic field. We focus on the high-field limit so that the superconductivity can be treated as a perturbation to the low-lying Landau levels. In the clean case, wherein the superconducting order parameter takes the form of an Abrikosov vortex lattice, we show that a lattice of hybridized Majorana modes eme…
Superconducting diodes are a recently-discovered quantum analogueue of classical diodes. The superconducting diode effect relies on the breaking of both time-reversal and inversion symmetry. As a result, the critical current of a superconductor can become dependent on the direction of the applied current. The combination of these ingredients naturally occurs in proximitized semiconductors under a magnetic field, which is also predicted to give rise to exotic physics such as topological superconductivity. In this work, we use InSb nanowires proximitized by Al to investigate the superconducting …
Two-dimensional electron gasses (2DEG) in InAs quantum wells proximitized by aluminum are promising platforms for topological qubits based on Majorana zero modes. However, there are still substantial uncertainties associated with the nature of the electronic states at the interfaces of these systems. It is challenging to probe the properties of these hybridized states as they are buried under a relatively thick aluminum layer. In this work, we have investigated a range of InAs/In$ _{1-\text{x}} $Ga$ _\text{x} $As heterostructures with Al overlayers using high precision time-domain THz spectros…
The coherent tunnelling of Cooper pairs across Josephson junctions (JJs) generates a nonlinear inductance that is used extensively in quantum information processors based on superconducting circuits, from setting qubit transition frequencies and interqubit coupling strengths, to the gain of parametric amplifiers for quantum-limited readout. The inductance is either set by tailoring the metal-oxide dimensions of single JJs, or magnetically tuned by parallelizing multiple JJs in superconducting quantum interference devices (SQUIDs) with local current-biased flux lines. JJs based on superconducto…
The bilayer heterostructures composed of an ultrathin ferromagnetic metal (FM) and a material hosting strong spin-orbit (SO) coupling are principal resource for SO torque and spin-to-charge conversion nonequilibrium effects in spintronics. We demonstrate how hybridization of wavefunctions of Co layer and a monolayer of transition metal dichalcogenides (TMDs)---such as semiconducting MoSe$_2$ and WSe$_2$ or metallic TaSe$_2$---can lead to dramatic transmutation of electronic and spin structure of Co within some distance away from its interface with TMD, when compared to the bulk of Co or its su…
Emergent spin quantum Hall edge states at the boundary of two-dimensional electron gas proximitized by an $s$-wave superconductor
L. D. Landau Institute for Theoretical Physics（列夫·朗道理论物理研究所）；Laboratory for Condensed Matter Physics, HSE University（高等经济大学凝聚态物理实验室）；P. N. Lebedev Physical Institute, Russian Academy of Sciences（俄罗斯科学院列别捷夫物理研究所）；Osipyan Institute of Solid State Physics, Russian Academy of Sciences（俄罗斯科学院奥西普扬固体物理研究所）；HSE University（高等经济大学）
We reveal that the interplay between Rashba spin-orbit coupling and proximity-induced magnetization in a two-dimensional electron gas leads to peculiar transport properties and large anisotropy of magnetoresistance. While the related tunneling anisotropic magnetoresistance (TAMR) has been extensively studied before, we predict an effect with a different origin arising from the evolution of a resonant condition with the in-plane rotation of magnetization and having a much larger magnitude. The resonances in the tunneling emerge from a spin-parity-time symmetry of the scattering states. However,…
We investigate the electronic band structure of graphene on a series of two-dimensional magnetic transition-metal phosphorus trichalcogenide monolayers, MPX$_3$ with M={Mn,Fe,Ni,Co} and X={S,Se}, with first-principles calculations. A symmetry-based model Hamiltonian is employed to extract orbital parameters and sublattice resolved proximity-induced exchange couplings ($λ_{\textrm{ex}}^\textrm{A}$ and $λ_{\textrm{ex}}^\textrm{B}$) from the low-energy Dirac bands of the proximitized graphene. Depending on the magnetic phase of the MPX$_3$ layer (ferromagnetic and three antiferromagnetic ones), c…
We analyze theoretically two different setups for s-wave superconductivity (SC) proximitized $j=3/2$ particles in Luttinger materials that are able to host Majorana bound states (MBSs). First, we consider a one-dimensional SC wire with intrinsic bulk inversion asymmetry (BIA). In contrast to wires, modeled by a quadratic dispersion with Rashba spin-orbit coupling, there are two topological phase transitions in our systems at finite magnetic fields. Second, we analyze a two-dimensional Josephson junction on the Luttinger model finding a topological region even in the absence of BIA and Rashba s…
Topological Superconductors in Doubly-Coupled Nanowires with Altermagnetism
International Centre for Quantum Design of Functional Materials and Department of Physics, University of Science and Technology of China（中国科学技术大学量子功能材料设计与物理系）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）；Wilczek Quantum Center, Shanghai Institute for Advanced Studies, University of Science and Technology of China（中国科学技术大学上海高等研究院斐兹克量子中心）
The density of states of proximitized normal nanowires interrupting superconducting rings can be tuned by the magnetic flux piercing the loop. Using these as the contacts of a single-electron transistor allows to control the energetic mirror asymmetry of the conductor, this way introducing rectification properties. In particular, we show that the system works as a diode that rectifies both charge and heat currents and whose polarity can be reversed by the magnetic field and a gate voltage. We emphasize the role of dissipation at the island. The coupling to substrate phonons enhances the effect…
We present results from a study of the nonlinear intermodal coupling between different flexural vibrational modes of a single high-stress, doubly-clamped silicon nitride nanomechanical beam. The measurements were carried out at 100 mK and the beam was actuated using the magnetomotive technique. We observed the nonlinear behavior of the modes individually and also measured the coupling between them by driving the beam at multiple frequencies. We demonstrate that the different modes of the resonator are coupled to each other by the displacement induced tension in the beam, which also leads to th…
We theoretically investigate the supercurrent-induced magnetization dynamics of a two-dimensional lattice of ferromagnetically ordered spins placed on a conventional superconductor with broken spatial inversion symmetry and strong spin-orbit coupling. We develop a phenomenological description of the coupled dynamics of the superconducting condensate and the spin system, and demonstrate that supercurrents produce a reactive spin-orbit torque on the magnetization. By performing a microscopic self-consistent calculation, we show that the spin-orbit torque originates from a spin-polarization of th…
Employing analytical methods and quantum transport simulations we investigate the relaxation of quasiparticle spins in graphene proximitized by an $s$-wave superconductor in the presence of resonant magnetic and spin-orbit active impurities. Off resonance, the relaxation increases with decreasing temperature when electrons scatter off magnetic impurities---the Hebel-Slichter effect---and decreases when impurities have spin-orbit coupling. This distinct temperature~dependence (not present in the normal state) uniquely discriminates between the two scattering mechanisms. However, we show that th…
An in-plane magnetic field applied to an Ising superconductor converts spin-singlet Cooper pairs to spin-triplet ones. In this work, we study a Josephson junction formed by two Ising superconductors that are proximitized by ferromagnetic layers. This leads to highly tunable spin-triplet pairing correlations which allow to modulate the charge and spin supercurrents through the in-plane magnetic exchange fields. For a junction with a nonmagnetic barrier, the charge current is switchable by changing the relative alignment of the in-plane exchange fields, and a $π$-state can be realized. Furthermo…
We explore proximity-induced magnetocaloric effect (MCE) on transition metal dichalcogenides, focusing on a two-dimensional (2D) MoTe$_2$ monolayer deposited on a ferromagnetic semiconductor EuO substrate connected to a heat source. We model this heterostructure using a tight-binding model, incorporating exchange and Rashba fields induced by proximity to EuO, and including temperature through Fermi statistics. The MCE is induced on the 2D MoTe$_2$ layer due to the EuO substrate, revealing large spin-polarized entropy changes for energies out of the band gap of the MoTe$_2$-EuO system. By gatin…
We study the energy spectrum and the electromagnetic response of Andreev bound states in short Josephson junctions made of semiconducting nanowires. We focus on the joint effect of Zeeman and spin-orbit coupling on the Andreev level spectra. Our model incorporates the penetration of the magnetic field in the proximitized wires, which substantially modifies the spectra. We pay special attention to the occurrence of fermion parity switches at increasing values of the field and to the magnetic field dependence of the absorption strength of microwave-induced transitions. Our calculations can be us…
We have developed and tested a doubly tunable resonator, with the intention to simulate fast motion of the resonator boundaries in real space. Our device is a superconducting coplanar-waveguide half-wavelength microwave resonator, with fundamental resonant frequency ~5 GHz. Both of its ends are terminated by dc-SQUIDs, which serve as magnetic-flux-controlled inductances. Applying a flux to either SQUID allows tuning of the resonant frequency by approximately 700 MHz. By using two separate on-chip magnetic-flux lines, we modulate the SQUIDs with two tones of equal frequency, close to twice that…
The effect of multiple topological transitions for electron-hole excitations is discovered in full shell proximitized semiconducting nanowires with trapped superconducting vortices, recently shown to be a promising platform for the realization of Majorana states at moderate longitudinal magnetic fields. The mechanism of such multiple transitions is uncovered and explained to be governed by the interplay of normal and Andreev reflections from the shell and by the textured spin-orbit coupling inside the semiconductor. The extensive analysis of emerging propagating and Majorana-type evanescent qu…
By tilting the samples in the magnetic field, we measured and compared the Skyrmion excitations in the bilayer quantum Hall (QH) state at the Landau-level filling factor $ν=2$ and in the monolayer QH state at $ν=1$. The observed number of flipped spins is $N_s=14$ in the bilayer system with a large tunneling gap, and $N_s=7$ in the bilayer system with a small tunneling gap, while it is $N_s=7$ in the monolayer system. The difference is interpreted due to the interlayer exchange interaction. Moreover, we have observed seemingly preferred numbers $N_s=14,7,1$ for the flipped spins by tilting bil…
