Broken Time-reversal Invariance Research Articles

Resonances in a single-lead reflection from a disordered medium: [formula omitted]-model approach

Using the framework of supersymmetric non-linear σ-model we develop a general non-perturbative characterization of universal features of the density ρ(Γ) of the imaginary parts (“width”) for S-matrix poles (“resonances”) describing waves incident and reflected from a disordered medium via M-channel waveguide/lead. Explicit expressions for ρ(Γ) are derived for several instances of systems with broken time-reversal invariance, in particular for quasi-1D and 3D media. In the case of perfectly coupled lead with a few channels (M∼1) the most salient features are tails ρ(Γ)∼Γ−1 for narrow resonances reflecting exponential localization and ρ(Γ)∼Γ−2 for broad resonances reflecting states located in the vicinity of the attached wire. For multimode quasi 1D wires with M≫1, an intermediate asymptotics ρ(Γ)∼Γ−3/2 is shown to emerge reflecting diffusive nature of decay into wide enough contacts.

Intensity statistics inside an open wave-chaotic cavity with broken time-reversal invariance.

Using the supersymmetric method of random matrix theory within the Heidelberg approach framework we provide statistical description of stationary intensity sampled in locations inside an open wave-chaotic cavity, assuming that the time-reversal invariance inside the cavity is fully broken. In particular, we show that when incoming waves are fed via a finite number M of open channels the probability density P(I) for the single-point intensity I decays as a power law for large intensities: P(I)∼I^{-(M+2)}, provided there is no internal losses. This behavior is in marked difference with the Rayleigh law P(I)∼exp(-I/I[over ¯]), which turns out to be valid only in the limit M→∞. We also find the joint probability density of intensities I_{1},...,I_{L} in L>1 observation points, and then we extract the corresponding statistics for the maximal intensity in the observation pattern. For L→∞ the resulting limiting extreme value statistics (EVS) turns out to be different from the classical EVS distributions.

Simple fluid with broken time-reversal invariance.

We characterize a system of hard spheres with a simple collision rule that breaks time-reversal symmetry but conserves energy. The collisions lead to an achiral, isotropic, and homogeneous stationary state whose properties are determined in simulations and compared to an approximate theory originally developed for elastic hard spheres. In the nonequilibrium fluid state, velocities are correlated, a phenomenon known from other nonequilibrium stationary states. The correlations are long-ranged decaying like 1/r^{D} in D dimensions. Such correlations are expected on general grounds far from equilibrium and had previously been observed in driven or nonstationary systems.

Confirming the trilinear form of the optical magnetoelectric effect in the polar honeycomb antiferromagnet Co2Mo3O8

Magnetoelectric phenomena are intimately linked to relativistic effects and also require the material to break spatial inversion symmetry and time-reversal invariance. Magnetoelectric coupling can substantially affect light–matter interaction and lead to non-reciprocal light propagation. Here, we confirm on a fully experimental basis, without invoking either symmetry-based or material-specific assumptions, that the optical magnetoelectric effect in materials with non-parallel magnetization (M) and electric polarization (P) generates a trilinear term in the refractive index, δn ∝ k ⋅ (P × M), where k is the propagation vector of light. Its sharp magnetoelectric resonances in the terahertz regime, which are simultaneously electric and magnetic dipole active excitations, make Co2Mo3O8 an ideal compound to demonstrate this fundamental relation via independent variation of M, P, and k. Remarkably, the material shows almost perfect one-way transparency in moderate magnetic fields for one of these magnetoelectric resonances.

Skyrme pseudopotentials at next-to-next-to-leading order: Construction of local densities and first symmetry-breaking calculations

There is an ongoing quest to improve on the spectroscopic quality of nuclear energy density functionals (EDFs) of the Skyrme type through extensions of its traditional form. One direction for such activities is the inclusion of terms of higher order in gradients in the EDF. We report on exploratory symmetry-breaking calculations performed for an extension of the Skyrme EDF that includes central terms with four gradients at next-to-next-to-leading order (N2LO) and for which the high-quality parametrization SN2LO1 has been constructed recently [P. Becker et al, Phys. Rev. C 96, 044330 (2017)]. Up to now, the investigation of such functionals with higher-order terms was limited to infinite matter and spherically symmetric configurations of singly- and doubly-magic nuclei. We address here nuclei and phenomena that require us to consider axial and non-axial deformation, both for reflection-symmetric and also reflection-asymmetric shapes, as well as the breaking of time-reversal invariance. Achieving these calculations demanded a number of formal developments. These all resulted from the formulation of the N2LO EDF requiring the introduction of new local densities with additional gradients that are not present in the EDF at NLO. Their choice is not unique, but can differ in the way the gradients are coupled. While designing a numerical implementation of N2LO EDFs in Cartesian 3d coordinate-space representation, we have developed a novel definition and a new unifying notation for normal and pair densities that contain gradients at arbitrary order. The resulting scheme resolves several issues with some of the choices that have been made for local densities in the past, in particular when breaking time-reversal symmetry. Guided by general practical considerations, we propose an alternative form of the N2LO contribution to the Skyrme EDF that is built from a different set of densities.

Chaotic scattering with localized losses: S-matrix zeros and reflection time difference for systems with broken time-reversal invariance.

Motivated by recent studies of the phenomenon of coherent perfect absorption, we develop the random matrix theory framework for understanding statistics of the zeros of the (subunitary) scattering matrices in the complex energy plane, as well as of the recently introduced reflection time difference (RTD). The latter plays the same role for S-matrix zeros as the Wigner time delay does for its poles. For systems with broken time-reversal invariance, we derive the n-point correlation functions of the zeros in a closed determinantal form, and we study various asymptotics and special cases of the associated kernel. The time-correlation function of the RTD is then evaluated and compared with numerical simulations. This allows us to identify a cubic tail in the distribution of RTD, which we conjecture to be a superuniversal characteristic valid for all symmetry classes. We also discuss two methods for possible extraction of S-matrix zeros from scattering data by harmonic inversion.

Microscopic Features of Bosonic Quantum Transport and Entropy Production

AbstractThe microscopic features of bosonic quantum transport in a nonequilibrium steady state, which breaks time reversal invariance spontaneously, are investigated. The analysis is based on the probability distributions, generated by the correlation functions of the particle current and the entropy production operator. The general approach is applied to an exactly solvable model with a point‐like interaction driving the system away from equilibrium. The quantum fluctuations of the particle current and the entropy production are explicitly evaluated in the zero frequency limit. It is shown that all moments of the entropy production distribution are non‐negative, which provides a microscopic version of the second law of thermodynamics. On this basis a concept of efficiency, taking into account all quantum fluctuations, is proposed and analyzed. The role of the quantum statistics in this context is also discussed.

Nonlinear anomalous photocurrents in Weyl semimetals

We study the second-order nonlinear optical response of a Weyl semimetal (WSM), i.e. a three-dimensional metal with linear band touchings acting as point-like sources of Berry curvature in momentum space, termed "Weyl-Berry monopoles". We first show that the anomalous second-order photocurrent of WSMs can be elegantly parametrized in terms of Weyl-Berry dipole and quadrupole moments. We then calculate the corresponding charge and node conductivities of WSMs with either broken time-reversal invariance or inversion symmetry. In particular, we predict a universal dissipationless second-order anomalous node conductivity for WSMs belonging to the TaAs family.

Topologically Protected Photonic Edge States in the Visible in Plasmo‐Gyroelectric Metamaterials

AbstractGyroelectric materials can be used to realize nontrivial photonic topological states. The usual strategy to maximize this effect is to increase the strength of the typically very small, off‐diagonal dielectric permittivity tensor components. This is a very difficult task, in particular at high frequencies. Here, an alternative method is proposed: reducing the strength of the diagonal permittivity tensor components. It is shown that this can be achieved by employing a layered plasmo‐gyroelectric metamaterial as the background medium of a 2D photonic crystal. It is demonstrated that by applying magnetic field, which breaks time reversal invariance, a topologically nontrivial photonic gap opens in the band structure of square and hexagonal photonic crystals. This is confirmed by detecting the presence of a topologically protected edge state at the boundary of this structure. This state is a photonic analog of the edge state in the conventional integer quantum Hall effect, also characterized by suppressed backscattering.

Punchets: nonlinear transport in Hamiltonian pump-ratchet hybrids

‘Punchets’ are hybrids between ratchets and pumps, combining a spatially periodic static potential, typically asymmetric under space inversion, with a local driving that breaks time-reversal invariance, and are intended to model metal or semiconductor surfaces irradiated by a collimated laser beam. Their crucial feature is irregular driven scattering between asymptotic regions supporting periodic (as opposed to free) motion. With all binary spatio-temporal symmetries broken, scattering in punchets typically generates directed currents. We here study the underlying nonlinear transport mechanisms, from chaotic scattering to the parameter dependence of the currents, in three types of Hamiltonian models, (i) with spatially periodic potentials where only in the driven scattering region, spatial and temporal symmetries are broken, and (ii), spatially asymmetric (ratchet) potentials with a driving that only breaks time-reversal invariance. As more realistic models of laser-irradiated surfaces, we consider (iii), a driving in the form of a running wave confined to a compact region by a static envelope. In this case, the induced current can even run against the direction of wave propagation, drastically evidencing its nonlinear nature. Quantizing punchets is indicated as a viable research perspective.

Quasiparticle interference and strong electron–mode coupling in the quasi-one-dimensional bands of Sr2RuO4

The single-layered ruthenate Sr$_2$RuO$_4$ has attracted a great deal of interest as a spin-triplet superconductor with an order parameter that may potentially break time reversal invariance and host half-quantized vortices with Majorana zero modes. While the actual nature of the superconducting state is still a matter of controversy, it has long been believed that it condenses from a metallic state that is well described by a conventional Fermi liquid. In this work we use a combination of Fourier transform scanning tunneling spectroscopy (FT-STS) and momentum resolved electron energy loss spectroscopy (M-EELS) to probe interaction effects in the normal state of Sr$_2$RuO$_4$. Our high-resolution FT-STS data show signatures of the \beta-band with a distinctly quasi-one-dimensional (1D) character. The band dispersion reveals surprisingly strong interaction effects that dramatically renormalize the Fermi velocity, suggesting that the normal state of Sr$_2$RuO$_4$ is that of a 'correlated metal' where correlations are strengthened by the quasi 1D nature of the bands. In addition, kinks at energies of approximately 10meV, 38meV and 70meV are observed. By comparing STM and M-EELS data we show that the two higher energy features arise from coupling with collective modes. The strong correlation effects and the kinks in the quasi 1D bands may provide important information for understanding the superconducting state. This work opens up a unique approach to revealing the superconducting order parameter in this compound.

Feedback-controlled heat transport in quantum devices: theory and solid-state experimental proposal

A theory of feedback-controlled heat transport in quantum systems is presented. It is based on modelling heat engines as driven multipartite systems subject to projective quantum measurements and measurement-conditioned unitary evolutions. The theory unifies various results presented previously in the literature. Feedback control breaks time reversal invariance. This in turn results in the fluctuation relation not being obeyed. Its restoration occurs through appropriate accounting of the gain and use of information via measurements and feedback. We further illustrate an experimental proposal for the realisation of a Maxwell demon using superconducting circuits and single-photon on-chip calorimetry. A two-level qubit acts as a trap-door, which, conditioned on its state, is coupled to either a hot resistor or a cold one. The feedback mechanism alters the temperatures felt by the qubit and can result in an effective inversion of temperature gradient, where heat flows from cold to hot thanks to the gain and use of information.

Exciting reflectionless unidirectional edge modes in a reciprocal photonic topological insulator medium

Photonic topological insulators are an interesting class of materials whose photonic band structure can have a band gap in the bulk while supporting topologically protected unidirectional edge modes. Recent studies on bianisotropic metamaterials that emulate the electronic quantum spin Hall effect using its electromagnetic analog are examples of such systems with a relatively simple and elegant design. In this paper, we present a rotating magnetic dipole antenna, composed of two perpendicularly oriented coils, that can efficiently excite the unidirectional topologically protected surface waves in the bianisotropic metawaveguide (BMW) structure recently realized by T. Ma et al. [Phys. Rev. Lett. 114, 127401 (2015)] despite the fact that the BMW medium does not break time-reversal invariance. In addition to achieving a high directivity, the antenna can be tuned continuously to excite reflectionless edge modes in the two opposite directions at various amplitude ratios. We demonstrate its performance through experiments and compare the results to simulation results.

Lift force due to odd Hall viscosity

We study the problem of flow of a neutral gas past an infinite cylinder at right angle to its axis at low Reynolds number when the fluid is characterized by broken time-reversal invariance, and hence by odd viscosity in addition to the normal even one. We solve the Oseen approximation to Navier-Stokes equation and calculate the lift force which appears due to the odd viscosity.

Spin-nematic order in antiferromagnetic spinor condensates

Large spin systems can exhibit unconventional types of magnetic ordering different from the ferromagnetic or N\'eel-like antiferromagnetic order commonly found in spin 1/2 systems. Spin-nematic phases, for instance, do not break time-reversal invariance and their magnetic order parameter is characterized by a second rank tensor with the symmetry of an ellipsoid. Here we show direct experimental evidence for spin-nematic ordering in a spin-1 Bose-Einstein condensate of sodium atoms with antiferromagnetic interactions. In a mean field description this order is enforced by locking the relative phase between spin components. We reveal this mechanism by studying the spin noise after a spin rotation, which is shown to contain information hidden when looking only at averages. The method should be applicable to high spin systems in order to reveal complex magnetic phases.

Nonlocal topological magnetoelectric effect by Coulomb interaction at a topological insulator-ferromagnet interface

The interface between a topological insulator and a ferromagnetic insulator exhibits an interesting interplay of topological Dirac electrons and magnetism. As has been shown recently, the breaking of time-reversal invariance by magnetic order generates a Chern-Simons term in the action, that in turn leads to a Berry phase and a magnetoelectric effect of topological origin. Here, we consider the system in the presence of long-range Coulomb interaction between the Dirac electrons, and find that the magnetoelectric effect of the fluctuating electric field becomes non-local. We derive a Landau-Lifshitz equation for the fluctuation-induced magnetization dynamics and the Euler-Lagrange equation of the Coulomb field by explicit one-loop calculations. Via the Coulomb interaction, divergences in the in-plane magnetization affect the magnetization dynamics over large distances in a topologically protected way.

Time asymmetric extensions of general relativity

We describe a class of modified gravity theories that deform general relativity in a way that breaks time reversal invariance and, very mildly, locality. The algebra of constraints, local physical degrees of freedom, and their linearized equations of motion, are unchanged, yet observable effects may be present on cosmological scales, which have implications for the early history of the universe. This is achieved in the Hamiltonian framework, in a way that requires the constant mean curvature gauge conditions and is, hence, inspired by shape dynamics.

Logarithmic correlations in quantum Hall plateau transitions

The critical behavior of quantum Hall transitions in two-dimensional disordered electronic systems can be described by a class of complicated, non-unitary conformal field theories with logarithmic correlations. The nature and the physical origin of these logarithmic correlation functions remain however mysterious. Using the replica trick and the underlying symmetries of these quantum critical points, we show here how to construct non-perturbatively disorder-averaged observables in terms of Green's functions that scale logarithmically at criticality. In the case of the spin quantum Hall transition, which may occur in disordered superconductors with spin-rotation symmetry and broken time reversal invariance, we argue that our results are compatible with an alternative approach based on supersymmetry. The generalization to the Integer quantum Hall plateau transition is also discussed.

Time reversal symmetry broken fractional topological phases at zero magnetic field

We extend the coupled-wire construction of quantum Hall phases, and search for fractional topological insulating states in models of weakly coupled wires at zero external magnetic field. Focusing on systems beyond double copies of fractional quantum Hall states at opposite fields, we find that spin-spin interactions can stabilize a large family of fractional topological phases with broken time reversal invariance. The latter is manifested by spontaneous spin polarization, by a finite Hall conductivity, or by both. This suggests the possibility that fractional topological insulators may be unstable to spontaneous symmetry breaking.

Topological transitions in multi-band superconductors

The search for Majorana fermions has been concentrated in topological insulators or superconductors. In general, the existence of these modes requires the presence of spin–orbit interactions and of an external magnetic field. The former implies in having systems with broken inversion symmetry, while the latter breaks time reversal invariance. In a recent paper, we have shown that a two-band metal with an attractive inter-band interaction has non-trivial superconducting properties, if the k-dependent hybridization is anti-symmetric in the wave-vector. This is the case, if the crystalline potential mixes states with different parities as for orbitals with angular momentum l and l+1. In this paper we take into account the effect of an external magnetic field, not considered in the previous investigation, in a two-band metal and show how it modifies the topological properties of its superconducting state. We also discuss the conditions for the appearance of Majorana fermions in this system.