Spin Imbalance Research Articles

Wilson Ratio of Fermi Gases in One Dimension

We calculate the Wilson ratio of the one-dimensional Fermi gas with spin imbalance. The Wilson ratio of attractively interacting fermions is solely determined by the density stiffness and sound velocity of pairs and of excess fermions for the two-component Tomonaga-Luttinger liquid phase. The ratio exhibits anomalous enhancement at the two critical points due to the sudden change in the density of states. Despite a breakdown of the quasiparticle description in one dimension, two important features of the Fermi liquid are retained; namely, the specific heat is linearly proportional to temperature, whereas the susceptibility is independent of temperature. In contrast to the phenomenological Tomonaga-Luttinger liquid parameter, the Wilson ratio provides a powerful parameter for testing universal quantum liquids of interacting fermions in one, two, and three dimensions.

Quantum phase transitions in 1/3 plateau of the quantum spin tube

We study quantum phase transitions in the 1/3 plateau state of the three-leg spin-1/2 tube, where the low-energy effective chirality degree of freedom plays an essential role. Using the density matrix renormalization group and the effective chirality model, we find that, as the leg coupling increases, the chirality liquid, a novel spin imbalance phase and the vector-spin-chirality ordered phase emerge without closing the plateau spin gap. We also clarify the role of the S 3-symmetry of the spin tube, behind these quantum phase transitions.

Highly polarized Fermi gases in two dimensions

We investigate the highly polarized limit of a two-dimensional (2D) Fermi gas, where we effectively have a single spin-down impurity atom immersed in a spin-up Fermi sea. By constructing variational wave functions for the impurity, we map out the ground state phase diagram as a function of mass ratio M/m and interaction strength. In particular, we determine when it is favorable for the dressed impurity (polaron) to bind particles from the Fermi sea to form a dimer, trimer or even larger clusters. Similarly to 3D, we find that the Fermi sea favors the trimer state so that it exists for M/m less than the critical mass ratio for trimer formation in the vacuum. We also find a region where dimers have finite momentum in the ground state, a scenario which corresponds to the Fulde-Ferrell-Larkin-Ovchinnikov superfluid state in the limit of large spin imbalance. For equal masses (M=m), we compute rigorous bounds on the polaron-dimer transition, and we show that the polaron energy and residue is well captured by the variational approach, with the former quantity being in good agreement with experiment. When there is a finite density of impurities, we find that this polaron-dimer transition is preempted by a first-order superfluid-normal transition at zero temperature, but it remains an open question what happens at finite temperature.

Spin injection from a normal metal into a mesoscopic superconductor

We report on nonlocal transport in superconductor hybrid structures, with ferromagnetic as well as normal-metal tunnel junctions attached to the superconductor. In the presence of a strong Zeeman splitting of the density of states, both charge and spin imbalance is injected into the superconductor. While previous experiments demonstrated spin injection from ferromagnetic electrodes, we show that spin imbalance is also created for normal-metal injector contacts. Using the combination of ferromagnetic and normal-metal detectors allows us to directly discriminate between charge and spin injection, and demonstrate a complete separation of charge and spin imbalance. The relaxation length of the spin imbalance is of the order of several $\mu$m and is found to increase with a magnetic field, but is independent of temperature. We further discuss possible relaxation mechanisms for the explanation of the spin relaxation length.

Spin imbalance and spin-charge separation in a mesoscopic superconductor

What happens to spin-polarised electrons when they enter a superconductor? Superconductors at equilibrium and at finite temperature contain both paired particles (of opposite spin) in the condensate phase as well as unpaired, spin-randomised quasiparticles. Injecting spin-polarised electrons into a superconductor thus creates both spin and charge imbalances [1, 2, 3, 4, 5, 6, 7] (respectively Q* and S*, cf. Ref. [4]). These must relax when the injection stops, but not necessarily over the same time (or length) scale as spin relaxation requires spin-dependent interactions while charge relaxation does not. These different relaxation times can be probed by creating a dynamic equilibrium between continuous injection and relaxation, which leads to constant-in-time spin and charge imbalances. These scale with their respective relaxation times and with the injection current. While charge imbalances in superconductors have been studied in great detail both theoretically [8] and experimentally [9], spin imbalances have not received much experimental attention [6, 10] despite intriguing theoretical predictions of spin-charge separation effects [11, 12]. These could occur e.g. if the spin relaxation time is longer than the charge relaxation time, i.e. Q* relaxes faster than S*. Fundamentally, spin-charge decoupling in superconductors is possible because quasiparticles can have any charge between e and -e, and also because the condensate acts as a particle reservoir [13, 11, 12]. Here we present evidence for an almost-chargeless spin imbalance in a mesoscopic superconductor.

Gate controlled spin-density wave and chiral FFLO superconducting phases in interacting helical liquids

We explore the phases exhibited by an interacting helical liquid in the presence of finite chemical potential (applied gate voltage) and spin imbalance (applied magnetic field). We find that the helical nature gives rise to quantum orders that are expected to be absent in nonchiral one-dimensional electronic systems. For repulsive interactions, the ordered state has an oscillatory spin texture whose ordering wave vector is controlled by the chemical potential. We analyze the manner in which a magnetic impurity provides signatures of such oscillations. We find that finite spin imbalance favors a finite current carrying ground state that is not condensed in the absence of interactions and is superconducting for attractive interactions. This state is characterized by Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-type oscillations where the Cooper pairs obtain a finite center-of-mass momentum. These phases can be realized on the edge of two-dimensional systems exhibiting the quantum spin Hall effect or on dislocation lines in weak topological insulators.

Spin Imbalance Effect on Josephson Junction and Grey Soliton

We study spin imbalance effects on the Josephson junction of superconductors under a strong magnetic field and the grey soliton in spin-polarized ultracold Fermi gas. We obtain the exact solution for the condensates with arbitrary spin imbalance and the fermion spectrum perturbatively in the presence of small spin imbalance.

Entangled states of trapped ions allow measuring the magnetic field gradient produced by a single atomic spin

We propose detecting the magnetic field gradient produced by the magnetic dipole moment of a single atom by using ions in an entangled state trapped a few μm from the dipole. This requires measuring magnetic field gradients of order 10−13 tesla/μm. We discuss applications in determining magnetic moments of a wide variety of ion species, for investigating the magnetic substructure of ions with level structures that are not suitable for laser cooling and detection, and for studying exotic or rare ions, and molecular ions. The scheme may also be used for measuring spin imbalances of neutral atoms or atomic ensembles trapped by optical dipole forces. As the proposed method relies on techniques that are well established in ion trap quantum information processing, it is within reach of current technology.

Oscillatory pairing amplitude and magnetic compressible-incompressible transitions in imbalanced fermionic superfluids in optical lattices of elongated tubes

We study two-species fermion gases with attractive interaction in two-dimensional optical lattices producing an array of elongated tube confinements. Focusing on the interplay of Cooper pairing, spin imbalance (or magnetization) and intertube tunneling, we find the pairing gap can exhibit oscillatory behavior both along and across the tubes, reminiscent of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We obtain a Bose-Hubbard-like phase diagram that shows that the magnetization of the system undergoes an incompressible-compressible transition as a function of magnetic field and intertube tunneling strength. We find the parity of tube-filling imbalance in incompressible states is protected by that of the oscillatory pairing gap. Finally, we discuss signatures of this transition and thus (indirectly) of the FFLO pairing in cold atom experiments.

Single magnetic impurity in a spin-imbalanced superfluid Fermi gas

A spin-imbalanced superfluid Fermi gas harmonically trapped in a two-dimensional optical lattice with a single classical magnetic impurity is investigated by Bogoliubov-de Gennes equations. In both the spin-balanced and weak spin-imbalanced cases, we show that a strong magnetic impurity can change the sign of the pairing order parameter. The amplitude of the sign-changed order parameter caused by impurity is affected by the strength of the impurity potential, temperature, and particle density. Compared to the spin-balanced case, we find that an additional in-gap bound state can be induced by a strong magnetic impurity in the weak spin-imbalanced case. In the strong spin-imbalanced case where the Fulde-Ferrell-Larkin-Ovchinnikov state is established as the ground state, the impurity induces wide spatial oscillations of pairing order parameters and can enhance the order parameters by suppressing the local spin imbalance.

On the Sarma-Type Phase Transitions in Ferromagnet/Superconductor/Ferromagnet Tunneling Junctions with Highly Spin-Polarized Ferromagnets

In the ferromagnet/superconductor/ferromagnet double tunneling junctions, the spin-polarized tunneling current in the antiparallel alignment of the magnetization induces spin imbalance in the superconductor, which has a pair breaking effect depressing superconductivity in the same way that the Zeeman effect does in the paramagnetic limit. In particular, it is shown that when the ferromagnets are highly spin polarized, the strong spin imbalance may lead to a first-order phase transition from the superconducting phase to the normal phase at low temperature and low bias voltage. This phase transition accompanies a large discontinuous drop in superconducting gap parameter bring in distinctive features in low energy transport.

Spin Hall Effect in Superconductors

Spin Hall effect in a superconductor is theoretically studied. The spin injection from a ferromagnet into a superconductor creates quasiparticle spin and charge currents in SC, which generate charge and spin currents in the transverse direction to accumulate spin and charge imbalance near the side edges of a superconductor. A giant enhancement of spin and charge accumulation signals in the side jump and skew scattering mechanisms of the spin Hall effect is predicted to occur at low temperatures in the superconducting state.

Expansion dynamics of the Fulde-Ferrell-Larkin-Ovchinnikov state

We consider a two-component Fermi gas in the presence of spin imbalance, modeling the system in terms of a one-dimensional attractive Hubbard Hamiltonian initially in the presence of a confining trap potential. With the aid of the time-evolving block decimation method, we investigate the dynamics of the initial state when the trap is switched off. We show that the dynamics of a gas initially in the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state is decomposed into the independent expansion of two fluids, namely the paired and the unpaired particles. In particular, the expansion velocity of the unpaired cloud is shown to be directly related to the FFLO momentum. This provides an unambiguous signature of the FFLO state in a remarkably simple way.

Spin imbalance effect on the Larkin-Ovchinnikov-Fulde-Ferrel state

We study spin imbalance effects on the Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) state relevant for superconductors under a strong magnetic field and spin polarized ultracold Fermi gas. We obtain the exact solution for the condensates with arbitrary spin imbalance and the fermion spectrum perturbatively in the presence of small spin imbalance. We also obtain fermion zero mode exactly without perturbation theory.

Stable Fulde-Ferrell-Larkin-Ovchinnikov pairing states in two-dimensional and three-dimensional optical lattices

We present the study of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing states in the $p$-orbital bands in both two and three-dimensional optical lattices. Due to the quasi one-dimensional band structure which arises from the unidirectional hopping of the orthogonal $p$-orbitals, the pairing phase space is not affected by spin imbalance. Furthermore, interactions build up high dimensional phase coherence which stabilizes the FFLO states in 2D and 3D optical lattices in a large parameter regime in phase diagram. These FFLO phases are stable with imposing the inhomogeneous trapping potential. Their entropies are comparable to those of the normal states at finite temperatures.

Competition between the Fulde–Ferrell–Larkin–Ovchinnikov phase and the Bardeen–Cooper– Schrieffer phase in the presence of an optical potential

In three-dimensional Fermi gases with spin imbalance, a competition exists between Cooper pairing with zero and finite momentum. The latter gives rise to the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) superfluid phase, which only exists in a restricted area of the phase diagram as a function of chemical potential imbalance and interaction strength. Applying an optical potential along one direction enhances the FFLO region in this phase diagram. In this paper, we construct the phase diagram as a function of polarization and interaction strength in order to study the competition between the FFLO phase and the spin balanced Bardeen–Cooper–Schrieffer (BCS) phase. This allows us to take into account the region of phase separation, and provides a more direct connection with experiment. Subsequently, we investigate the effects of the wavelength and the depth of the optical potential, which is applied along one direction, on the FFLO state. It is shown that the FFLO state can exist up to a higher level of spin imbalance if the wavelength of the optical potential becomes smaller. Our results give rise to an interesting effect: the maximal polarization at which the FFLO state can exist decreases when the interaction strength exceeds a certain critical value. This counterintuitive phenomenon is discussed and the connection to the optical potential is explained.

Origination of electron magnetic chiral dichroism in cobalt-doped ZnO dilute magnetic semiconductors

Electron magnetic chiral dichroism (EMCD) relates the microstructure of a single nanostructure with the magnetic property, indicating that the ferromagnetism observed in cobalt-doped ZnO dilute magnetic semiconductor is intrinsic. First-principles calculations were carried out and the electronic states contributing to the spin imbalance are identified. An exact model is developed, allowing one to visualize the origination of dichroism to be the difference of transition intensity from spin-polarized 2p states to Co-3d states in cobalt-doped ZnO nanostructures.

A Bogoliubov–de Gennes study of trapped spin-imbalanced unitary Fermi gases

It is quite common that several different phases exist simultaneously in a system of trapped quantum gases of ultra-cold atoms. One example is the strongly interacting Fermi gas with two imbalanced spin species, which has received a great deal of attention owing to the possible occurrence of exotic superfluid phases. By using novel numerical techniques and algorithms, we self-consistently solve the Bogoliubov–de Gennes equations, which describe Fermi superfluids in the mean-field framework. From this study, we investigate the novel phases of spin-imbalanced Fermi gases and examine the validity of local density approximation (LDA), which is often invoked in the extraction of bulk properties from experimental measurements within trapped systems. We show how the validity of the LDA is affected by the trapping geometry, the number of atoms and the spin imbalance.

Spin transport in polaronic and superfluid Fermi gases

We present measurements of spin transport in ultracold gases of fermionic 6Li in a mixture of two spin states at a Feshbach resonance. In particular, we study the spin-dipole mode, where the two spin components are displaced from each other against a harmonic restoring force. We prepare a highly imbalanced, or polaronic, spin mixture with a spin-dipole excitation and we observe strong, unitarity-limited damping of the spin-dipole mode. In gases with small spin imbalance, below the Pauli limit for superfluidity, we observe strongly damped spin flow even in the presence of a superfluid core. This indicates strong mutual friction between superfluid and polarized normal spins, possibly involving Andreev reflection at the superfluid–normal interface.

Influence of spin relaxation length on lateral double superconductor/ferromagnet/superconductor junctions

We study the spin dependent transport at the junctions between two superconducting Nb leads connected by two ferromagnetic NiFe bars in parallel, which have various separations. The separation distance l between NiFe bars was varied from 150 to 700 nm to study the spin relaxation effect in Nb. In small l (150 and 250 nm) samples, a spin-valve-like behavior related to the inverse proximity effect was observed, which manifest itself as charge accumulation due to spin imbalance near the interface. However, for samples with large l, the spin-valve behavior vanishes and the anisotropic magnetoresistance effect dominates.