Broken Spin-rotation Symmetry Research Articles

Spontaneous dimerization, spin-nematic order, and deconfined quantum critical point in a spin-1 Kitaev chain with tunable single-ion anisotropy

Kitaev-type spin chains have been demonstrated to be fertile playgrounds in which exotic phases and unconventional phase transitions are ready to appear. In this work, we use the density-matrix renormalization-group method to study the quantum phase diagram of a spin-1 Kitaev chain with a tunable negative single-ion anisotropy (SIA). When the strength of the SIA is small, the ground state is revealed to be a spin-nematic phase, which escapes conventional magnetic order but is characterized by a finite spin-nematic correlation because of the breaking spin-rotational symmetry. As the SIA increases, the spin-nematic phase is taken over by either a dimerized phase or an antiferromagnetic phase through an Ising-type phase transition, depending on the direction of the easy axis. For large enough SIA, the dimerized phase and the antiferromagnetic phase undergo a ``Landau-forbidden'' continuous phase transition, suggesting new platform of deconfined quantum critical point in spin-1 Kitaev chain.

Coupling of lattice, spin, and intraconfigurational excitations of Eu3+ in Eu2ZnIrO6

In Eu2ZnIrO6, effectively two atoms are active i.e. Ir is magnetically active, which results in complex magnetic ordering within the Ir sublattice at low temperature. On the other hand, although Eu is a van-vleck paramagnet, it is active in the electronic channels involving 4f 6 crystal-field split levels. Phonons, quanta of lattice vibration, involving vibration of atoms in the unit cell, are intimately coupled with both magnetic and electronic degrees of freedom (DoF). Here, we report a comprehensive study focusing on the phonons as well as intra-configurational excitations in double-perovskite Eu2ZnIrO6. Our studies reveal strong coupling of phonons with the underlying magnetic DoF reflected in the renormalization of the phonon self-energy parameters well above the spin-solid phase (TN ~ 12 K) till temperature as high as ~ 3TN, evidences broken spin rotational symmetry deep into the paramagnetic phase. In particular, all the observed first-order phonon modes show softening of varying degree below ~3TN, and low-frequency phonons become sharper, while the high-frequency phonons show broadening attributed to the additional available magnetic damping channels. We also observed a large number of high-energy modes, 39 in total, attributed to the electronic transitions between 4f-levels of the rare-earth Eu3+ ion and these modes shows anomalous temperature evolution as well as mixing of the crystal-field split levels attributed to the strong coupling of electronic and lattice DoF.

Strain-Induced Spin-Nematic State and Nematic Susceptibility Arising from 2×2 Fe Clusters in KFe_{0.8}Ag_{1.2}Te_{2}.

Spin nematics break spin-rotational symmetry while maintaining time-reversal symmetry, analogous to liquid crystal nematics that break spatial rotational symmetry while maintaining translational symmetry. Although several candidate spin nematics have been proposed, the identification and characterization of such a state remain challenging because the spin-nematic order parameter does not couple directly to experimental probes. KFe_{0.8}Ag_{1.2}Te_{2} (K_{5}Fe_{4}Ag_{6}Te_{10}, KFAT) is a local-moment magnet consisting of well-separated 2×2 Fe clusters, and in its ground state the clusters order magnetically, breaking both spin-rotational and time-reversal symmetries. Using uniform magnetic susceptibility and neutron scattering measurements, we find a small strain induces sizable spin anisotropy in the paramagnetic state of KFAT, manifestly breaking spin-rotational symmetry while retaining time-reversal symmetry, resulting in a strain-induced spin-nematic state in which the 2×2 clusters act as the spin analog of molecules in a liquid crystal nematic. The strain-induced spin anisotropy in KFAT allows us to probe its nematic susceptibility, revealing a divergentlike increase upon cooling, indicating the ordered ground state is driven by a spin-orbital entangled nematic order parameter.

Correlated paramagnetism and interplay of magnetic and phononic degrees of freedom in 3d-5d coupled La2CuIrO6

Conventional paramagnetism–a state with finite magnetic moment per ion sans long range magnetic ordering, but with lowering temperature the moment each ion picks up a particular direction, breaking spin rotational symmetry, and results into long-range magnetic ordering. However, in systems with competing multiple degrees of freedom this conventional notion may easily break and results into short range correlation much above the global magnetic transition temperature. La2CuIrO6 with complex interplay of spins (s = 1/2) on Cu site and pseudo-spin (j = 1/2) on Ir site owing to strong spin–orbit coupling provides fertile ground to observe such correlated phenomena. By a comprehensive temperature dependent Raman study, we have shown the presence of such a correlated paramagnetic state in La2CuIrO6 much above the long-range magnetic ordering temperature (TN). Our observation of strong interactions of phonons, associated with Cu/Ir octahedra, with underlying magnetic degrees of freedom mirrored in the observed Fano asymmetry, which remarkably persists as high as ~3.5TN clearly signals the existence of correlated paramagnetism hence broken spin rotational symmetry. Our detailed analysis also reveals anomalous changes in the self-energy parameters of the phonon modes, i.e. mode frequencies and linewidth, below TN, providing a useful gauge for monitoring the strong coupling between phonons and magnetic degrees of freedom.

Spin-mediated particle transport in the disordered Hubbard model

Motivated by the recent experiments that reported signatures of many-body localization of ultracold atoms in optical lattices [M. Schreiber {\it et al.}, Science {\bf 349}, 842 (2015)], we study dynamics of highly excited states in the strongly disordered Hubbard model in one dimension. Owing to the $SU(2)$ spin symmetry, spin degrees of freedom form a delocalized thermal bath with a narrow bandwidth. The spin bath mediates slow particle transport, eventually leading to delocalization of particles. The particle hopping rate is exponentially small in $t/W$ ($t$, $W$ being hopping and disorder scales) owing to the narrow bandwidth of the spin bath. We find the optimal lenghtscale for particle hopping, and show that the particle transport rate depends strongly on the density of singly occupied sites in the initial state. The delocalization rate is zero for initial states with only doubly occupied or empty sites, suggesting that such states are truly many-body localized, and therefore the Hubbard model may host both localized and delocalized states. Full many-body localization can be induced by breaking spin rotational symmetry.

Nematic superconductivity in CuxBi2Se3 : Surface Andreev bound states

We study theoretically the topological surface states (TSSs) and the possible surface Andreev bound states (SABSs) of Cu$_{x}$Bi$_{2}$Se$_{3}$ which is known to be a topological insulator at $x=0$. The superconductivity (SC) pairing of this compound is assumed to have the broken spin-rotation symmetry, similar to that of the A-phase of $^{3}$He as suggested by recent nuclear-magnetic resonance experiments. For both spheroidal and corrugated cylindrical Fermi surfaces with the hexagonal warping terms, we show that the bulk SC gap is rather anisotropic; the minimum of the gap is negligibly small as comparing to the maximum of the gap. This would make the fully-gapped pairing effectively nodal. For a clean system, our results indicate the bulk of this compound to be a topological superconductor with the SABSs appearing inside the bulk SC gap. The zero-energy SABSs which are Majorana fermions, together with the TSSs not gapped by the pairing, produce a zero-energy peak in the surface density of states (SDOS). The SABSs are expected to be stable against short-range nonmagnetic impurities, and the local SDOS is calculated around a nonmagnetic impurity. The relevance of our results to experiments is discussed.

Coulomb drag between helical Luttinger liquids

We theoretically study Coulomb drag between two helical edges with broken spin-rotational symmetry, such as would occur in two capacitively coupled quantum spin Hall insulators. For the helical edges, Coulomb drag is particularly interesting because it specifically probes the inelastic interactions that break the conductance quantization for a single edge. Using the kinetic equation formalism, supplemented by bosonization, we find that the drag resistivity $\rho_D$ exhibits a nonmonotonic dependence on the temperature $T$. In the limit of low $T$, $\rho_D$ vanishes with decreasing $T$ as a power law if intraedge interactions are not too strong. This is in stark contrast to Coulomb drag in conventional quantum wires, where $\rho_D$ diverges at $T\to 0$ irrespective of the strength of repulsive interactions. Another unusual property of Coulomb drag between the helical edges concerns higher $T$ for which, unlike in the Luttinger liquid model, drag is mediated by plasmons. The special type of plasmon-mediated drag can be viewed as a distinguishing feature of the helical liquid---because it requires peculiar Umklapp scattering only available in the presence of a Dirac point in the electron spectrum.

Superconductor-insulator transitions: Phase diagram and magnetoresistance

Influence of disorder-induced Anderson localization and of electron-electron interaction on superconductivity in two-dimensional systems is explored. We determine the superconducting transition temperature $T_c$, the temperature dependence of the resistivity, the phase diagram, as well as the magnetoresistance. The analysis is based on the renormalization group (RG) for a nonlinear sigma model. Derived RG equations are valid to the lowest order in disorder but for arbitrary electron-electron interaction strength in particle-hole and Cooper channels. Systems with preserved and broken spin-rotational symmetry are considered, both with short-range and with long-range (Coulomb) interaction. In the cases of short-range interaction, we identify parameter regions where the superconductivity is enhanced by localization effects. Our RG analysis indicates that the superconductor-insulator transition is controlled by a fixed point with a resistivity $R_c$ of the order of the quantum resistance $R_q = h/ 4e^2$. When a transverse magnetic field is applied, we find a strong nonmonotonous magnetoresistance for temperatures below $T_c$.

Spin fragmentation of Bose–Einstein condensates with antiferromagnetic interactions

We study spin fragmentation of an antiferromagnetic spin 1 condensate in the presence of a quadratic Zeeman (QZ) effect breaking spin rotational symmetry. We describe how the QZ effect turns a fragmented spin state, with large fluctuations of the Zeeman populations, into a regular polar condensate, where the atoms all condense in the m = 0 state along the field direction. We calculate the average value and variance of the population of the Zeeman state m = 0 to illustrate clearly the crossover from a fragmented to an unfragmented state. The typical width of this crossover is q ∼ kBT/N, where q is the QZ energy, T the spin temperature and N the atom number. This shows that the spin fluctuations are a mesoscopic effect that will not survive in the thermodynamic limit N → ∞, but are observable for a sufficiently small atom number.

Renormalization group flow for fermions into antiferromagnetically ordered phases: Method and mean-field models

We present a functional renormalization group (fRG) flow for many-fermion lattice models into phases with broken spin-rotational symmetry. The flow is expressed purely in terms of fermionic vertex functions. The symmetry breaking is seeded by a small initial anomalous self-energy which grows at the transition scale and which prevents a runaway flow at nonzero scales. Focusing on the case of commensurate antiferromagnetism, we discuss how the interaction vertex can be parametrized efficiently. For reduced models with long-range bare interactions, we show the results of standard mean-field theory are reproduced by the fRG and how anisotropies in the spin sector change the flows. We then describe a more efficient decomposition of the interaction vertex that should allow for the treatment of more general models.

Photoinduced spin Chern number change in a two-dimensional quantum spin Hall insulator with broken spin rotational symmetry

We propose a scheme by which the spin Chern number of two-dimensional insulators with generic spin-orbit interaction can be externally controlled by optical methods. When submitting the system to a circularly polarized laser field, and then adiabatically sweeping the amplitude of the latter, the various hopping integrals associated with an electron system effectively turn into tunable variables. This in turn transforms the spin Chern number, which governs the topological properties of the system into a function of the laser amplitude. This scheme can steer a conventional insulator into the quantum spin Hall state, and vice versa. We anticipate that our findings, which provide a firmly grounded connection between optical techniques and spin transport, will open up the possibility of developing spintronics devices that build on the physics of the photosteering of spin currents.

Broken Time Translation Symmetry as a Model for Quantum State Reduction

The symmetries that govern the laws of nature can be spontaneously broken, enabling the occurrence of ordered states. Crystals arise from the breaking of translation symmetry, magnets from broken spin rotation symmetry and massive particles break a phase rotation symmetry. Time translation symmetry can be spontaneously broken in exactly the same way. The order associated with this form of spontaneous symmetry breaking is characterised by the emergence of quantum state reduction: systems which spontaneously break time translation symmetry act as ideal measurement machines. In this review the breaking of time translation symmetry is first compared to that of other symmetries such as spatial translations and rotations. It is then discussed how broken time translation symmetry gives rise to the process of quantum state reduction and how it generates a pointer basis, Born’s rule, etc. After a comparison between this model and alternative approaches to the problem of quantum state reduction, the experimental implications and possible tests of broken time translation symmetry in realistic experimental settings are discussed.

Average shot-noise power via a diagrammatic method

In this work we use a diagrammatic method for integration over the unitary group to obtain a quantum correction to the average shot-noise power of a chaotic cavity with non-ideal contacts. We present maximally crossed diagrams representing the physical modes of the system responsible for the dominant quantum correction. We demonstrate with explicit calculations that the suppression–amplification effect reported in Ramos et al (2008 Phys. Rev. B 78 235305) occurs both for systems in the presence of time-reversal (TR) and spin-rotation (SR) symmetries and for systems with broken SR symmetry but in the presence of TR symmetry.

Single‐wall carbon nanotubes: spintronics in the Luttinger liquid phase

AbstractWe study the electron spin resonance (ESR) intensity in the Luttinger liquid phase of carbon nanotubes. The ESR measurables such as the signal intensity and the line‐width are calculated in the framework of Luttinger liquid theory with broken spin rotational symmetry as a function of magnetic field and temperature. The linewidth is broadened significantly at high temperatures, and the intensity is well describes by Lorentzians. At very low temperatures, however, the ESR lineshape becomes asymmetric around the resonance, and is characterized by threshold behavior. These observables are of special importance for the spintronics applications of carbon nanotubes.

Electron Spin Resonance Signal of Luttinger Liquids and Single-Wall Carbon Nanotubes

A comprehensive theory of electron spin resonance (ESR) for a Luttinger liquid state of correlated metals is presented. The ESR measurables such as the signal intensity and the linewidth are calculated in the framework of Luttinger liquid theory with broken spin rotational symmetry as a function of magnetic field and temperature. We obtain a significant temperature dependent homogeneous line broadening which is related to the spin-symmetry breaking and the electron-electron interaction. The result crosses over smoothly to the ESR of itinerant electrons in the noninteracting limit. These findings explain the absence of the long-sought ESR signal of itinerant electrons in single-wall carbon nanotubes when considering realistic experimental conditions.

Triplet supercurrents in clean and disordered half-metallic ferromagnets

Interfaces between materials with differently ordered phases present unique opportunities to study fundamental problems in physics. One example is the interface between a singlet superconductor and a half-metallic ferromagnet, where Cooper pairing occurs between electrons with opposite spin on one side, while the other displays 100% spin polarisation. The recent surprising observation of a supercurrent through half-metallic CrO_2 therefore requires a mechanism for conversion between unpolarised and completely spin polarised supercurrents. Here we suggest a conversion mechanism based on electron spin precession together with triplet pair rotation at interfaces with broken spin-rotation symmetry. In the diffusive limit the triplet supercurrent is dominated by inter-related odd-frequency s-wave and even-frequency p-wave pairs. In the crossover to the ballistic limit additional symmetry components become relevant. The interface region exhibits a superconducting state of mixed-spin pairs with highly unusual symmetry properties that opens up new perspectives for exotic Josephson devices.

Localization in disordered superconducting wires with broken spin-rotation symmetry

Localization and delocalization of noninteracting quasiparticle states in a superconducting wire are reconsidered, for the cases in which spin-rotation symmetry is absent, and time-reversal symmetry is either broken or unbroken; these are referred to as symmetry classes BD and DIII, respectively. We show that, if a continuum limit is taken to obtain a Fokker-Planck (FP) equation for the transfer matrix, as in some previous work, then when there are more than two scattering channels, all terms that break a certain symmetry are lost. It was already known that the resulting FP equation exhibits critical behavior. The additional symmetry is not required by the definition of the symmetry classes; terms that break it arise from non-Gaussian probability distributions, and may be kept in a generalized FP equation. We show that they lead to localization in a long wire. When the wire has more than two scattering channels, these terms are irrelevant at the short distance (diffusive or ballistic) fixed point, but as they are relevant at the long-distance critical fixed point, they are termed dangerously irrelevant. We confirm the results in a supersymmetry approach for class BD, where the additional terms correspond to jumps between the two components of the sigma model target space. We consider the effect of random $\ensuremath{\pi}$ fluxes, which prevent the system localizing. We show that in one dimension the transitions in these two symmetry classes, and also those in the three chiral symmetry classes, all lie in the same universality class.

Gapped anisotropic spin chains in a field

We consider the fully anisotropic Heisenberg spin-1/2 antiferromagnet in a uniform magnetic field, whose ground-state is characterized by broken spin rotation symmetry and gapped spinon excitations. We expand on a recent mean-field approach to the problem by incorporating fluctuations in a loop expansion. Quantitative results for the magnetization, excitation gap and specific heat are obtained. We compare our predictions with new DMRG and exact diagonalization data and, for zero field, with the exact solution of the ${XYZ}$ spin chain from the Bethe Ansatz.

Universality of delocalization in unconventional dirty superconducting wires with broken spin-rotation symmetry

In dirty superconducting wires, quasiparticle states at the Fermi level need not be exponentially localized if spin-rotation symmetry is broken [Brouwer et al., Phys. Rev. Lett. 85, 1064 (2000)]. Here we present evidence that not-localized states are generic in the thick-wire limit, while for wires of finite thickness delocalization requires fine tuning of the disorder, consistent with earlier results of Motrunich et al. [Phys. Rev. B 63, 224204 (2001)]. The thick-wire limit is defined as the simultaneous limit where the length L of the wire and the number N of propagating channels at the Fermi energy are both taken to infinity with their ratio held fixed.

Observation of Zeeman splitting in universal conductance fluctuations.

We provide experimental evidence for a transition from a random-matrix ensemble with broken timereversal symmetry to an ensemble with partially broken spin-rotation symmetry. The transition from a Gaussian unitary ensemble to the ensemble in which the Zeeman degeneracy of electrons is lifted is accompanied by a factor of 2 change in 1/f noise fluctuations measured in a mesoscopic Li wire at low temperature. The magnetic-field scale characterizing the Zeeman crossover is determined by kBT , rather than by the Thouless energy.