Rashba-type Spin-orbit Coupling Research Articles

Phase diagram of interacting Fermi gas in spin–orbit coupled square lattices

The spin–orbit (SO) coupled optical lattices have attracted considerable interest. In this paper, we investigate the phase diagram of the interacting Fermi gas with Rashba-type spin–orbit coupling (SOC) on a square optical lattice. The phase diagram is investigated in a wide range of atomic interactions and SOC strength within the framework of the cluster dynamical mean-field theory (CDMFT). We show that the interplay between the atomic interactions and SOC results in a rich phase diagram. In the deep Mott insulator regime, the SOC can induce diverse spin ordered phases. Whereas near the metal–insulator transition (MIT), the SOC tends to destroy the conventional antiferromagnetic fluctuations, giving rise to distinctive features of the MIT. Furthermore, the strong fluctuations arising from SOC may destroy the magnetic orders and trigger an order to disorder transition in close proximity of the MIT.

Tunneling-assisted spin-orbit coupling in bilayer Bose-Einstein condensates

Motivated by a goal of realizing spin-orbit coupling (SOC) beyond one-dimension (1D), we propose and analyze a method to generate an effective 2D SOC in bilayer BECs with laser-assisted inter-layer tunneling. We show that an interplay between the inter-layer tunneling, SOC and intra-layer atomic interaction can give rise to diverse ground state configurations. In particular, the system undergoes a transition to a new type of stripe phase which spontaneously breaks the time-reversal symmetry. Different from the ordinary Rashba-type SOC, a fractionalized skyrmion lattice emerges spontaneously in the bilayer system without external traps. Furthermore, we predict the occurrence of a tetracritical point in the phase diagram of the bilayer BECs, where four different phases merge together. The origin of the emerging different phases is elucidated.

Odd-frequency pairing in topological superconductivity in a one-dimensional magnetic chain

A chain of magnetic atoms with non-collinear spin configuration on a superconductor is a promising new system that can host Majorana Fermions (MFs). In this study, we clarify that in the presence of MFs, an odd-frequency Cooper pair is generated at the edge of the chain. Furthermore, it is revealed that this feature is robust against the distance between magnetic atoms. We also elucidate the close relationship between the pair amplitude of the odd-frequency pair, the parity of the wave function, and the direction of the MF spin. If Rashba-type spin-orbit coupling is included, MFs can be realized even in a collinear alignment of magnetic atoms, $i.e.$, in a ferromagnetic or anti-ferromagnetic chain on a superconductor. Then, the odd-frequency pairing is generated at the edge, similar to the non-collinear case. Based on our results, it can be concluded that the detection of the zero energy peak of the local density of states by scanning tunneling microscopy at the edge of the magnetic chain is strong evidence for the generation of odd-frequency pairing.

One-dimensional edge states with giant spin splitting in a bismuth thin film.

To realize a one-dimensional (1D) system with strong spin-orbit coupling is a big challenge in modern physics, since the electrons in such a system are predicted to exhibit exotic properties unexpected from the 2D or 3D counterparts, while it was difficult to realize genuine physical properties inherent to the 1D system. We demonstrate the first experimental result that directly determines the purely 1D band structure by performing spin-resolved angle-resolved photoemission spectroscopy of Bi islands on a silicon surface that contains a metallic 1D edge structure with unexpectedly large Rashba-type spin-orbit coupling suggestive of the nontopological nature. We have also found a sizable out-of-plane spin polarization of the 1D edge state, consistent with our first-principles band calculations. Our result provides a new platform to realize exotic quantum phenomena at the 1D edge of the strong spin-orbit-coupling systems.

Collective modes in two- and three-dimensional electron systems with Rashba spin-orbit coupling

In addition to charge plasmons, a 2D electron system with Rashba-type spin-orbit coupling (SOC) also supports three collective modes in the spin sector: the chiral-spin modes. We study the dispersions of the charge and spin modes and their coupling to each other within a generalized Random Phase Approximation for arbitrarily strong SOC, and both in 2D and 3D systems. In both 2D and 3D, we find that the charge plasmons are coupled to only one of the three chiral-spin modes. This coupling is shown to affect the dispersions of the modes at finite but not at zero wavenumbers. In 3D, the chiral-spin modes are strongly damped by particle-hole excitations and disappear for weak electron-electron interaction. Landau damping of the chiral-spin modes in 3D is directly related to the fact that, in contrast to 2D, there is no gap for particle-hole excitations between spin-split subbands. The gapless continuum is also responsible for Landau damping of the charge plasmon in 3D - a qualitatively new feature of the SOC system. We also discuss the optical conductivity of clean 2D and 3D systems and show that SOC introduces spectral weight at finite frequency in a such way that the sum rule is satisfied. The in-plane tranverse chiral-spin mode shows up as dispersing peak in the optical conductivity at finite number which can can be measured in the presence of diffraction grating. We also discuss possible experimental manifestations of chiral-spin modes in semiconductor quantum wells such InGaAs/AlGaAs and 3D giant Rashba materials of the BiTeI family.

Equivalence of Rashba-Hubbard and Hubbard chains

We review the fact that U(1) gauge symmetry enables the mapping of one-dimensional Hubbard chains with Rashba-type spin orbit coupling to renormalized Hubbard Hamiltonians. The existence of the mapping has important consequences for the interpretation of ARPES experiments on one-dimensional chains subject to Rashba spin orbit coupling and can be exploited to check for the applicability of the mapping. We show numerical applications of the mapping and consider the implications for bosonization as well as for the Heisenberg-limit of the Hubbard model. In addition we point out the consequences for various generalized Hubbard models.

Possible polaron formation of zigzag graphene nano-ribbon in the presence of Rashba spin–orbit coupling

In this article we study the role of Rashba spin–orbit coupling and electron–phonon interaction on the electronic structure of zigzag graphene nanoribbon with different width. The total Hamiltonian of nanoribbon is written in the tight binding form and the electron–electron interaction is modeled in the Hubbard term. We used a unitary transformation to reach an effective Hamiltonian for nano ribbon in the presence of electron–phonon interaction. Our results show that small Rashba spin orbit coupling annihilates the anti-ferromagnetic phase in the zigzag edges of ribbon and the electron–phonon interaction yields small polaron formation in graphene nano ribbon. Furthermore, Rashba type spin–orbit coupling increases (decreases) the polaron formation energy for up (down) spin state.

Gapless topological Fulde-Ferrell superfluidity induced by an in-plane Zeeman field

Topological superfluids are recently discovered quantum matters that host topologically protected gapless edge states known as Majorana fermions - exotic quantum particles that act as their own anti-particles and obey non-Abelian statistics. Their realizations are believed to lie at the heart of future technologies such as fault-tolerant quantum computation. To date, the most efficient scheme to create topological superfluids and Majorana fermions is based on the Sau-Lutchyn-Tewari-Das Sarma model with a Rashba-type spin-orbit coupling on the }\textbf{\textit{x-y}}\textbf{ plane and a large out-of-plane (perpendicular) Zeeman field along the }\textbf{\textit{z}}\textbf{-direction. Here we propose an alternative setup, where the topological superfluid phase is driven by applying an in-plane Zeeman field. This scheme offers a number of new features, notably Cooper pairings at finite centre-of-mass momentum (i.e., Fulde-Ferrell pairing) and gapless excitations in the bulk. As a result, a novel gapless topological quantum matter with inhomogeneous pairing order parameter appears. It features unidirected Majorana surface states at boundaries, which propagate in the same direction and connect two Weyl nodes in the bulk. We demonstrate the emergence of such an exotic topological matter and the associated Majorana fermions in spin-orbit coupled atomic Fermi gases and determine its parameter space. The implementation of our scheme in semiconductor/superconductor heterostructures is briefly discussed.

Spin dependent transport through triangular graphene quantum dot in the presence of Rashba type spin–orbit coupling

Electronic, magnetic and transport properties of a triangle graphene quantum dot have been studied in the presence of Rashba type spin–orbit coupling. The non-interacting part is written in the tight-binding model, and we use the Kene–Mele–Hubbard (KMH) Hamiltonian to describe the electron–electron and the Rashba spin–orbit interaction. While the Hubbard term split the spin up and down states, the Rashba term mixed these states. The competition between these two effects produces an interesting situation in a nano-device. Our results indicate that the magnetization of zigzag edge and spin coherence are decreased due to the Rashba spin–orbit interaction in the triangle graphene quantum dot. It is shown that the reduction of spin coherence is non-negligible even in the case of weak Rashba spin–orbit interaction.

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Electronic, magnetic and transport properties of a triangle graphene quantum dot have been studied in the presence of Rashba type spin–orbit coupling. The non-interacting part is written in the tight-binding model, and we use the Kene–Mele–Hubbard (KMH) Hamiltonian to describe the electron–electron and the Rashba spin–orbit interaction. While the Hubbard term split the spin up and down states, the Rashba term mixed these states. The competition between these two effects produces an interesting situation in a nano-device. Our results indicate that the magnetization of zigzag edge and spin coherence are decreased due to the Rashba spin–orbit interaction in the triangle graphene quantum dot. It is shown that the reduction of spin coherence is non-negligible even in the case of weak Rashba spin–orbit interaction.

Current-induced magnetization dynamics at the edge of a two-dimensional electron system with strong spin-orbit coupling

We experimentally investigate electron transport through the interface between a permalloy ferromagnet and the edge of a two-dimensional electron system with strong Rashba-type spin-orbit coupling. We observe strongly non-linear transport around zero bias at millikelvin temperatures. The observed nonlinearity is fully suppressed above some critical values of temperature, magnetic field, and current through the interface. We interpret this behavior as the result of spin accumulation at the interface and its current-induced absorption as a magnetization torque.

Spin-orbit-coupled transport and spin torque in a ferromagnetic heterostructure

Ferromagnetic heterostructures provide an ideal platform to explore the nature of spin-orbit torques arising from the interplay mediated by itinerant electrons between a Rashba-type spin-orbit coupling and a ferromagnetic exchange interaction. For such a prototypic system, we develop a set of coupled diffusion equations to describe the diffusive spin dynamics and spin-orbit torques. We characterize the spin torque and its two prominent---out-of-plane and in-plane---components for a wide range of relative strength between the Rashba coupling and ferromagnetic exchange. The symmetry and angular dependence of the spin torque emerging from our simple Rashba model is in an agreement with experiments. The spin diffusion equation can be generalized to incorporate dynamic effects such as spin pumping and magnetic damping.

Topological uniform superfluid and Fulde-Ferrell-Larkin-Ovchinnikov phases in three-dimensional to one-dimensional crossover of spin-orbit-coupled Fermi gases

We consider the quasi-one-dimensional (quasi-1D) system realized by an array of weakly coupled parallel one-dimensional ``tubes'' in a two-dimensional lattice which permits free motion of atoms in an axial direction in the presence of a Zeeman field, Rashba type spin-orbit coupling (SOC), and an $s$-wave attractive interaction, while the radial motion is tightly confined. We solve the zero-temperature ($T=0$) Bogoliubov--de Gennes (BdG) equations for the quasi-1D Fermi gas with the dispersion modified by tunneling between the tubes and show that the $T=0$ phase diagram hosts the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase with nonzero center-of-mass momentum Cooper pairs for small values of the SOC while for larger values of the SOC and high Zeeman fields the uniform superfluid phase with zero center-of-mass momentum Cooper pairs has an instability towards the topological uniform superfluid phase with Majorana fermions at the tube ends. Also, we show that tuning the two-dimensional optical lattice strength in this model allows one to explore the crossover behaviors of the phases during the transition between the three-dimensional and 1D systems and in general the FFLO (for small SOC) and the topological uniform superfluid phase (for large SOC) are favored as the system becomes more one dimensional. We also find evidence of the existence of a Zeeman-tuned topological quantum phase transition (TQPT) within the FFLO phase itself and, for large values of the Zeeman field and small SOC, the TQPT gives rise to a topologically distinct FFLO phase.

Andreev reflection at the edge of a two-dimensional electron system with strong spin-orbit coupling

We experimentally investigate transport properties of a single planar junction between the niobium superconductor and the edge of a two-dimensional electron system in a narrow $In_{0.75}Ga_{0.25}As$ quantum well with strong Rashba-type spin-orbit coupling. We experimentally demonstrate suppression of Andreev reflection at low biases at ultra low temperatures. From the analysis of temperature and magnetic field behavior, we interpret the observed suppression as a result of a spin-orbit coupling. There is also an experimental sign of the topological superconductivity realization in the present structure.

Effect of gate-driven spin resonance on the conductance through a one-dimensional quantum wire

We consider quasiballistic electron transmission in a one-dimensional quantum wire subject to both time-independent and periodic potentials of a finger gate that results in a coordinate- and time-dependent Rashba-type spin-orbit coupling. A spin-dependent conductance is calculated as a function of external constant magnetic field, the electric field frequency, and the potential strength. The results demonstrate the effect of the gate-driven electric dipole spin resonance in a transport phenomenon such as spin-flip electron transmission.

Superconductivity with Rashba spin–orbit coupling and magnetic field

Two-dimensional electron systems at oxide interfaces are often influenced by a Rashba type spin–orbit coupling, which is tunable by a transverse electric field. Ferromagnetism near the interface can simultaneously induce strong local magnetic fields. This combination of spin–orbit coupling and magnetism leads to asymmetric two-sheeted Fermi surfaces, on which either intra- or inter-band pairing is favored. The superconducting order parameters are derived within a microscopic pairing model realizing both the Bardeen–Cooper–Schrieffer superconductor with inter-band pairing and a mixed parity state with finite-momentum intra-band pairing. We present a phase diagram for the superconducting groundstates and analyze the density of states, the spectra, and the momentum distribution functions of the different phases. The results are discussed in the context of superconductivity and ferromagnetism at LaAlO3–SrTiO3 interfaces and superconductors with broken inversion symmetry.

Correlated topological phases and exotic magnetism with ultracold fermions

Motivated by the recent progress in engineering artificial non-Abelian gauge fields for ultracold fermions in optical lattices, we investigate the time-reversal-invariant Hofstadter–Hubbard model. We include an additional staggered lattice potential and an artificial Rashba-type spin–orbit coupling term available in experiment. Without interactions, the system can be either a (semi)-metal, a normal or a topological insulator, and we present the non-Abelian generalization of the Hofstadter butterfly. Using a combination of real-space dynamical mean-field theory (RDMFT), analytical arguments, and Monte-Carlo simulations we study the effect of strong on-site interactions. We determine the interacting phase diagram, and discuss a scenario of an interaction-induced transition from a normal to a topological insulator. At half-filling and large interactions, the system is described by a quantum spin Hamiltonian, which exhibits exotic magnetic order due to the interplay of Rashba-type spin–orbit coupling and the artificial time-reversal-invariant magnetic field term. We determine the magnetic phase diagram: both for the itinerant model using RDMFT and for the corresponding spin model in the classical limit using Monte-Carlo simulations.

Engineering three-dimensional topological insulators in Rashba-type spin-orbit coupled heterostructures

Topological insulators represent a new class of quantum phase defined by invariant symmetries and spin-orbit coupling that guarantees metallic Dirac excitations at its surface. The discoveries of these states have sparked the hope of realizing non-trivial excitations and novel effects such as a magnetoelectric effect and topological Majorana excitations. Here we develop a theoretical formalism to show that a three-dimensional topological insulator can be designed artificially via stacking bilayers of two-dimensional Fermi gases with opposite Rashba-type spin-orbit coupling on adjacent layers, and with interlayer quantum tunneling. We demonstrate that in the stack of bilayers grown along a (001)-direction, a non-trivial topological phase transition occurs above a critical number of Rashba bilayers. In the topological phase, we find the formation of a single spin-polarized Dirac cone at the -point. This approach offers an accessible way to design artificial topological insulators in a set up that takes full advantage of the atomic layer deposition approach. This design principle is tunable and also allows us to bypass limitations imposed by bulk crystal geometry.

Superconducting Pairing Symmetry on the Extended Hubbard Model in the Presence of the Rashba-Type Spin–Orbit Coupling

In order to study the pairing symmetry in non-centrosymmetric superconductors, we solve the linearized Eliashberg's equation on the two-dimensional extended Hubbard model in the presence of the Rashba-type spin-orbit coupling (RSOC) within the random phase approximation. In the presence of the RSOC, three types of pairing symmetries appear in the phase diagram with respect to the on-site Coulomb repulsion U and off-site one V. Each of pairing symmetries is admixture of spin-singlet and -triplet ones. On the basis of analytical study, it is found that the admixture of spin-singlet and -triplet components depends on not only the predominant pairing symmetry but also dispersion relation and pairing interaction.

Interaction Induced Staggered Spin-Orbit Order in Two-Dimensional Electron Gas

We propose and formulate an interaction induced staggered spin-orbit order as a new emergent phase of two-dimensional Fermi gases. We show that when some form of inherent spin splitting via Rashba-type spin-orbit coupling renders two helical Fermi surfaces to become significantly "nested," a Fermi surface instability arises. To lift this degeneracy, a spontaneous symmetry-breaking spin-orbit density wave develops, causing a surprisingly large quasiparticle gapping with chiral electronic states. Since the staggered spin-orbit order is associated with a condensation energy, quantified by the gap value, destroying such spin-orbit interaction costs sufficiently large perturbation field or temperature or dephasing time. The BiAg(2) surface state is shown to be a representative system for realizing such novel spin-orbit interaction with tunable and large strength, and the spin splitting is decoupled from charge excitations. These functional properties are relevant for spin electronics, spin caloritronics, and spin-Hall effect applications.