Zeeman Coupling Research Articles

Spin susceptibility of superconductors with strong spin-orbit coupling

We show that in some trigonal and hexagonal crystals the Zeeman coupling of band electrons with an external magnetic field is strongly anisotropic and necessarily vanishes along the main symmetry axis. This leads to qualitative changes in the temperature dependence of the electron spin susceptibility in the superconducting state. In particular, the power-law exponents at low temperatures due to the contribution of the nodal quasiparticles are considerably modified compared to their textbook values.

Critical Temperature in the BCS-BEC Crossover with Spin-Orbit Coupling

We review the study of the superfluid phase transition in a system of fermions whose interaction can be tuned continuously along the crossover from Bardeen–Cooper–Schrieffer (BCS) superconducting phase to a Bose–Einstein condensate (BEC), also in the presence of a spin–orbit coupling. Below a critical temperature the system is characterized by an order parameter. Generally a mean field approximation cannot reproduce the correct behavior of the critical temperature Tc over the whole crossover. We analyze the crucial role of quantum fluctuations beyond the mean-field approach useful to find Tc along the crossover in the presence of a spin–orbit coupling, within a path integral approach. A formal and detailed derivation for the set of equations useful to derive Tc is performed in the presence of Rashba, Dresselhaus and Zeeman couplings. In particular in the case of only Rashba coupling, for which the spin–orbit effects are more relevant, the two-body bound state exists for any value of the interaction, namely in the full crossover. As a result the effective masses of the emerging bosonic excitations are finite also in the BCS regime.

Role of Berry curvature in the generation of spin currents in Rashba systems

We study the background (equilibrium), linear and nonlinear spin currents in 2D Rashba spin-orbit coupled systems with Zeeman splitting and in 3D noncentrosymmetric metals using modified spin current operator by inclusion of the anomalous velocity. The linear spin Hall current arises due to the anomalous velocity of charge carriers induced by the Berry curvature. The nonlinear spin current occurs due to the band velocity and/or the anomalous velocity. For 2D Rashba systems, the background spin current saturates at high Fermi energy (independent of the Zeeman coupling), linear spin current exhibits a plateau at the Zeeman gap and nonlinear spin currents are peaked at the gap edges. The magnitude of the nonlinear spin current peaks enhances with the strength of Zeeman interaction. The linear spin current is polarized out of plane, while the nonlinear ones are polarized in-plane. We witness pure anomalous nonlinear spin current with spin polarization along the direction of propagation. In 3D noncentrosymmetric metals, background and linear spin currents are monotonically increasing functions of Fermi energy, while nonlinear spin currents vary non-monotonically as a function of Fermi energy and are independent of the Berry curvature. These findings may provide useful information to manipulate spin currents in Rashba spin-orbit coupled systems.

Formation and detection of Majorana modes in quantum spin Hall trenches

We propose a novel realization for a topologically superconducting phase hosting Majorana zero modes on the basis of quantum spin Hall systems. Remarkably, our proposal is completely free of ferromagnets. Instead, we confine helical edge states around a narrow defect line of finite length in a two-dimensional topological insulator. We demonstrate the formation of a new topological regime, hosting protected Majorana modes in the presence of $s$-wave superconductivity and Zeeman coupling. Interestingly, when the system is weakly tunnel coupled to helical edge state reservoirs, a particular transport signature is associated with the presence of a non-Abelian Majorana zero mode.

Atomic Line Defects and Topological Superconductivity in Unconventional Superconductors

Topological superconductors (TSCs) are correlated quantum states with simultaneous off-diagonal long-range order and nontrivial topological invariants. They produce gapless or zero energy boundary excitations, including Majorana zero modes and chiral Majorana edge states with topologically protected phase coherence essential for fault-tolerant quantum computing. Candidate TSCs are very rare in nature. Here, we propose a novel route toward emergent quasi-one-dimensional (1D) TSCs in naturally embedded quantum structures such as atomic line defects in unconventional spin-singlet $s$-wave and $d$-wave superconductors. We show that inversion symmetry breaking and charge transfer due to the missing atoms lead to the occupation of incipient impurity bands and mixed parity spin singlet and triplet Cooper pairing of neighboring electrons traversing the line defect. Nontrivial topological invariants arise and occupy a large part of the parameter space, including the time reversal symmetry breaking Zeeman coupling due to applied magnetic field or defect-induced magnetism, creating TSCs in different topological classes with robust Majorana zero modes at both ends of the line defect. Beyond providing a novel mechanism for the recent discovery of zero-energy bound states at both ends of an atomic line defect in monolayer Fe(Te,Se) superconductors, the findings pave the way for new material realizations of the simplest and most robust 1D TSCs using embedded quantum structures in unconventional superconductors with large pairing energy gaps and high transition temperatures.

Spin-polarized dwell time for electrons in a δ-doped magnetic nanostructure

We theoretically investigate dwell time for electrons in a magnetic nanostructure with a [Formula: see text]-doping, which is formed on [Formula: see text] heterostructure by depositing a ferromagnetic (FM) stripe. We find that dwell time depends strongly on electron-spins owing to Zeeman coupling and broken symmetry. We also demonstrate that spin-polarized dwell time can be manipulated by [Formula: see text]-doping. Thus, electron spins can be separated in time dimension and such a magnetic nanostructure can be employed as a structurally-controllable temporal spin splitter for spintronics device applications.

Finite-momentum condensate brought on by a Zeeman field

We study superfluid states in a two-dimensional fermionic attractive Hubbard model with Zeeman coupling to an external field. Focusing our attention on singlet pairing in both weak and strong coupling regimes, we reveal a rich phase diagram of finite momentum condensates which exhibits both Fulde-Ferrell and Larkin-Ovchinnikov orders at zero temperature. The latter are commensurate stripe states that spontaneously break a lattice symmetry; many stable ordering wavevectors are found as a function of particle density and Zeeman field. Stronger coupling significantly enhances the stability of the finite momentum condensates, but our numerical mean-field calculations underestimate the effect of fluctuations and indicate a possible localization near half-filling.

Spiral magnetic field and bound states of vortices in noncentrosymmetric superconductors

We discuss the unconventional magnetic response and vortex states arising in noncentrosymmetric superconductors with chiral octahedral and tetrahedral ($O$ or $T$) symmetry. We microscopically derive Ginzburg-Landau free energy. It is shown that due to spin-orbit and Zeeman coupling magnetic response of the system can change very significantly with temperature. For sufficiently strong coupling this leads to a crossover from type-1 superconductivity at elevated temperature to vortex states at lower temperature. The external magnetic field decay in such superconductors does not have the simple exponential law. We show that in the London limit, magnetic field can be solved in terms of complex force-free fields $\vec{W}$, which are defined by $\nabla \times \vec{W} = \text{const} \vec{W}$. Using that we demonstrate that the magnetic field of a vortex decays in spirals. Because of such behavior of the magnetic field, the intervortex and vortex-boundary interaction becomes non-monotonic with multiple minima. This implies that vortices form bound states with other vortices, antivortices, and boundaries.

Channel-selective non-Fermi liquid behavior in the two-channel Kondo lattice model under a magnetic field

Stimulated by anomalous behaviors found in non-Kramers $f$-electron systems in an applied magnetic field, we study a two-channel Kondo lattice model by using a cluster extension of the dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method. We include the effect of the external magnetic field in two ways: the Zeeman coupling to conduction electron spins and an effective coupling to the quadrupole degree of freedom through the crystalline electric field splitting. We show that the magnetic field suppresses the antiferroic-spin order (physically, corresponding to the antiferroic-quadrupole order), and yields a channel-selective non-Fermi liquid state where one of the two channels (physically, spin-up or -down) exhibits non-Fermi liquid behavior while the other shows Fermi liquid behavior, before entering the Fermi liquid regime in higher fields. This anomalous state appears in a dome-shaped region which extends from inside the antiferroic-spin ordered phase to the paramagnetic phase. We find that the composite correlation, which is a measure of differentiation in the Kondo coupling between the two channels, is enhanced in this dome-shaped region. We also find that the specific heat coefficient is enhanced in this region in the paramagnetic side, indicating heavy fermion behavior not only in the vicinity of the critical field where the antiferroic-spin order vanishes but also in a certain region of the field and temperature. We discuss the results in comparison with the ordinary Kondo lattice model. We also discuss the implication of our findings to the peculiar behavior observed in the 1-2-20 compounds such as $\rm{PrIr_2Zn_{20}}$, $\rm{PrRh_2Zn_{20}}$, and $\rm{PrV_2Al_{20}}$ under a magnetic field.

Topological phase transition and nontrivial thermal Hall signatures in honeycomb lattice magnets

We investigate spinon band topology and engineering from the interplay between long-ranged magnetic order and fractionalized spinons, as well as Zeeman coupling under external magnetic fields, in honeycomb lattice magnets. The synergism of N\'eel order and magnetic fields could reconstruct the spinon bands and drive a topological phase transition from the coexisting phase of long-ranged order and chiral spin liquid with semion topological order to the conventional magnetic order. Our prediction can be immediately tested through thermal Hall transport measurements among the honeycomb lattice magnets that are tuned to be proximate to the quantum critical point. Our theory should also shed light on the critical behavior of honeycomb Kitaev materials with emergent Majorana fermion bands. We suggest a possible relevance to the spin-1/2 honeycomb spin liquid candidate material In$_3$Cu$_2$VO$_9$.

Optomagnonic Barnett effect

Combining the technologies of quantum optics and magnonics, we find that the circularly polarized laser can dynamically realize the quasiequilibrium magnon Bose-Einstein condensates (BEC). The Zeeman coupling between the laser and spins generates the optical Barnett field, and its direction is controllable by switching the laser chirality. We show that the optical Barnett field develops the total magnetization in insulating ferrimagnets with reversing the local magnetization, which leads to the quasiequilibrium magnon BEC. This laser-induced magnon BEC transition through optical Barnett effect, dubbed the optomagnonic Barnett effect, provides an access to coherent magnons in the high frequency regime of the order of terahertz. We also propose a realistic experimental setup to observe the optomagnonic Barnett effect using current device and measurement technologies as well as the laser chirping. The optomagnonic Barnett effect is a key ingredient for the application to ultrafast spin transport.

Engineering quantum Hall phases in a synthetic bilayer graphene system

Synthetic quantum Hall bilayer (SQHB), realized by optically driven monolayer graphene in the quantum Hall regime, provides a flexible platform for engineering quantum Hall phases as discussed in [Phys. Rev. Lett. 119, 247403]. The coherent driving which couples two Landau levels mimicks an effective tunneling between synthetic layers. The tunneling strength, the effective Zeeman coupling, and two-body interaction matrix elements are tunable by varying the driving frequency and the driving strength. Using infinite density matrix renormalization group (iDMRG) techniques combined with exact diagonalization (ED), we show that the system exhibits a non-abelian bilayer Fibonacci phase at filling fraction $\nu = 2/3$. Moreover, at integer filling $\nu = 1$, the SQHB exhibits quantum Hall ferromagnetism. Using Hartree-Fock theory and exact diagonalization, we show that excitations of the quantum Hall ferromagnet are topological textures known as skyrmions.

Coherent Magnetization Dynamics in Ni80Fe20 Thin Films Incorporated in Fe/Au Spintronic Terahertz Emitters

Coherent magnetization dynamics at terahertz (THz) frequencies is achieved by directly incorporating ferromagnetic Ni <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">80</sub> Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20</sub> thin films into Fe/Au bilayer spintronic THz emitters. Electrooptical (EO) sampling demonstrates a generation of THz pulses centered near ~2.8 THz with a bandwidth in the 1-4 THz range. Ni <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">80</sub> Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20</sub> magnetization is directly coupled to the magnetic component of the THz wave, in which the large-amplitude magnetization precession is found phase locked with the THz pulse. The THz-induced magnetization dynamics can be controlled by external bias magnetic fields. The micromagnetic and analytical models based on the Landau-Lifshitz-Gilbert (LLG) equation are in good agreement with experimental findings and verify that the underlying mechanism of the THz-induced magnetization dynamics is the Zeeman coupling between the magnetic component of the THz field and Ni <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">80</sub> Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20</sub> magnetization. Our results open the opportunities for the use of low-cost metallic spintronic THz emitters in the studies of THz-induced magnetization dynamics in magnetic thin films.

Critical temperature Tc and Pauli limited critical field of Sr2RuO4 : Uniaxial strain dependence

Variations of critical temperature $T_c$ and in-plane critical field $H_{c2}$ of $\text{Sr}_2\text{Ru}\text{O}_4$ under uniaxial stress have recently been reported. We compare the strain dependence of $T_c$ and $H_{c2}$ in various pairing channels ($d$-wave, extended s-wave and $p$-wave) with the experimental observations, by studying a three-band tight-binding model that includes effects of spin-orbit and Zeeman couplings and a separable pairing interaction. Our study helps narrow down the possibility of pairing channels. The importance of the multi-band nature of $\text{Sr}_2\text{Ru}\text{O}_4$ is also highlighted.

Emergent flat band lattices in spatially periodic magnetic fields

Motivated by the recent discovery of Mott insulating phase and unconventional superconductivity due to the flat bands in twisted bilayer graphene, we propose more generic ways of getting two-dimensional (2D) emergent flat band lattices using either 2D Dirac materials or ordinary electron gas (2DEG) subject to moderate periodic orbital magnetic fields with zero spatial average. Employing both momentum-space and real-space numerical methods to solve the eigenvalue problems, we find stark contrast between Schr\"{o}dinger and Dirac electrons, i.e., the former show recurring "magic" values of the magnetic field when the lowest band becomes flat, while for the latter the zero-energy bands are asymptotically flat without magicness. By examining the Wannier functions localized by the smooth periodic magnetic fields, we are able to explain these nontrivial behaviors using minimal tight-binding models on a square lattice. The two cases can be interpolated by varying the $g$-factor or effective mass of a 2DEG and by taking into account the Zeeman coupling, which also leads to flat bands with nonzero Chern numbers for each spin. Our work provides flexible platforms for exploring interaction-driven phases in 2D systems with on-demand superlattice symmetries.

1H spin-lattice NMR relaxation in the presence of residual dipolar interactions – Dipolar relaxation enhancement

A model of spin-lattice relaxation for spin-1/2 nuclei in the presence of a residual dipole-dipole coupling has been presented. For slow dynamics the model predicts a bi-exponential relaxation at low frequencies, when the residual dipole-dipole interaction dominates the Zeeman coupling. Moreover, according to the model a frequency-specific relaxation enhancement, referred to as Dipolar Relaxation Enhancement (DRE) in analogy to the Quadrupole Relaxation Enhancement (QRE) is expected. The frequency position of the relaxation maximum is determined by the amplitude of the residual dipole-dipole interaction. Experimental examples of relaxation properties that might be attributed to the DRE are presented. The DRE effect has the potential to be exploited, in analogy to QRE, as a unique source of information about molecular dynamics and structure.

Nonuniform superconductivity in wires with strong spin-orbit coupling

We study theoretically the onset of nonuniform superconductivity in a one-dimensional single wire in presence of Zeeman (or exchange field) and spin-orbit coupling. Using the Green's function formalism, we show that the spin-orbit coupling stabilizes modulated superconductivity in a broad range of temperatures and Zeeman fields. We investigate the anisotropy of the temperature-Zeeman field phase diagram, which is related to the orientation of the Zeeman field. In particular, the inhomogeneous superconducting state disappears if this latter field is aligned or perpendicular to the wire direction. We identify two regimes corresponding to weak and strong spin-orbit coupling respectively. The wave-vector of the modulated phase is evaluated in both regimes. The results also pertain for quasi-1D superconductors made of weakly coupled 1D chains.

Terahertz excitation of spin dynamics in ferromagnetic thin films incorporated in metallic spintronic-THz-emitter

An experimental approach to trigger ultrafast spin dynamics at frequencies of the terahertz (THz) regime is explored by directly incorporating ferromagnetic Ni80Fe20 films to a Fe/Au spintronic-THz-emitter. It is found that Ni80Fe20 magnetization is directly coupled to the terahertz magnetic fields, in which the magnetic responses of Ni80Fe20 are phase-locked with terahertz pulses. High efficiency of metallic spintronic-terahertz emitters in driving terahertz-induced magnetization dynamics is observed; the maximum precession amplitude of the out-of-plane component of the Ni80Fe20 magnetization reaches over 10% of its saturation magnetization. Analytical integrations of THz magnetic field pulses reproduce the experimental results, confirming that the underlying mechanism of the observed spin dynamics is the Zeeman coupling between the terahertz magnetic field and magnetization in the Ni80Fe20 film. Our results open up possibilities for the studies of terahertz spin dynamics by integrating highly efficient low-cost metallic spintronic-THz-emitters into magnetic thin film elements.

Quantum Anomalous Hall Effects in Graphene from Proximity-Induced Uniform and Staggered Spin-Orbit and Exchange Coupling.

We investigate an effective model of proximity modified graphene (or symmetrylike materials) with broken time-reversal symmetry. We predict the appearance of quantum anomalous Hall phases by computing bulk band gap and Chern numbers for benchmark combinations of system parameters. Allowing for staggered exchange field enables quantum anomalous Hall effect in flat graphene with Chern number C=1. We explicitly show edge states in zigzag and armchair nanoribbons and explore their localization behavior. Remarkably, the combination of staggered intrinsic spin-orbit and uniform exchange coupling gives topologically protected (unlike in time-reversal systems) pseudohelical states, whose spin is opposite in opposite zigzag edges. Rotating the magnetization from out of plane to in plane makes the system trivial, allowing us to control topological phase transitions. We also propose, using density functional theory, a material platform-graphene on Ising antiferromagnet MnPSe_{3}-to realize staggered exchange (pseudospin Zeeman) coupling.

Vector-boson condensates, spin-triplet superfluidity of paired neutral and charged fermions, and 3P2 pairing of nucleons

After reminding of properties of the condensate of the complex scalar field in the external uniform magnetic field $H$ focus is made on the study of phases of the complex neutral vector boson fields coupled with magnetic field by the Zeeman coupling and phases of the charged vector boson fields. These systems may behave as nonmagnetic and ferromagnetic superfluids and ordinary and ferromagnetic superconductors. Response of the ferromagnetic superfluid and superconducting systems occupying half of space on the external uniform static magnetic field $H$ is thoroughly studied. Then the spin-triplet pairing of neutral fermions at conserved spin is considered. Novel phases are found. In external magnetic field the phase with zero mean spin proves to be unstable to the formation of a phase with a non-zero spin. For $H>H_{\rm cr 2}$ the spin-triplet pairing and ferromagnetic superfluidity continue to exist above the "old" phase transition critical temperature $T_{\rm cr}$. For a certain parameter choice ferromagnetic superfluid phases are formed already for $H=0$, characterized by an own magnetic field $h$. Formation of domains is discussed. Next, spin-triplet pairing of charged fermions is studied. Novel phases are found with a ferromagnetic superconductivity. Then, the 3P$_2$ $nn$ pairing in neutron star matter is studied. Also a 3P$_2$ $pp$ pairing is considered. Numerical estimates are performed in the BCS weak coupling limit and beyond it for the $3P_2$ $nn$ and $pp$ pairings, as well as for the 3S$_1$ $np$ pairing.