Broken Time-reversal Symmetry Research Articles

Engineering Flat Bands in Twisted-Bilayer Graphene away from the Magic Angle with Chiral Optical Cavities.

Twisted bilayer graphene (TBG) is a recently discovered two-dimensional superlattice structure which exhibits strongly correlated quantum many-body physics, including strange metallic behavior and unconventional superconductivity. Most of TBG exotic properties are connected to the emergence of a pair of isolated and topological flat electronic bands at the so-called magic angle, θ≈1.05°, which are nevertheless very fragile. In this work, we show that, by employing chiral optical cavities, the topological flat bands can be stabilized away from the magic angle in an interval of approximately 0.8°<θ<1.3°. As highlighted by a simplified theoretical model, time reversal symmetry breaking (TRSB), induced by the chiral nature of the cavity, plays a fundamental role in flattening the isolated bands and gapping out the rest of the spectrum. Additionally, TRSB suppresses the Berry curvature and induces a topological phase transition, with a gap closing at the Γ point, towards a band structure with two isolated flat bands with Chern number equal to 0. The efficiency of the cavity is discussed as a function of the twisting angle, the light-matter coupling and the optical cavity characteristic frequency. Our results demonstrate the possibility of engineering flat bands in TBG using optical devices, extending the onset of strongly correlated topological electronic phases in moiré superlattices to a wider range in the twisting angle.

Dispersive nonreciprocity between a qubit and a cavity.

The dispersive interaction between a qubit and a cavity is ubiquitous in circuit and cavity quantum electrodynamics. It describes the frequency shift of one quantum mode in response to excitations in the other and, in closed systems, is necessarily bidirectional, i.e., reciprocal. Here, we present an experimental study of a nonreciprocal dispersive-type interaction between a transmon qubit and a superconducting cavity, arising from a common coupling to dissipative intermediary modes with broken time reversal symmetry. We characterize the qubit-cavity dynamics, including asymmetric frequency pulls and photon shot noise dephasing, under varying degrees of nonreciprocity by tuning the magnetic field bias of a ferrite component in situ. We introduce a general master equation model for nonreciprocal interactions in the dispersive regime, providing a compact description of the observed qubit-cavity dynamics agnostic to the intermediary system. Our result provides an example of quantum nonreciprocal phenomena beyond the typical paradigms of non-Hermitian Hamiltonians and cascaded systems.

Helicity-Sensitive Terahertz Detection in Monolayer 1T'-WTe2.

Valleytronics, identified as electronic properties of the energy band extrema in momentum space, has been intensively revived following the emergence of two-dimensional transition metal dichalcogenides (TMDCs) as their valley information can be controlled and probed through the spin angular momentum of light. Previous optical investigations of valleytronics have been limited to the visible/near-infrared spectral regime through which the carriers of most TMDCs can be excited. Monolayer 1T'-WTe2 with broken time-reversal symmetry provides a fertile platform to study the long-wavelength photonic properties in different valleys. Here, we employed a circularly polarized terahertz (THz) laser to selectively excite the valley of monolayer 1T'-WTe2 and demonstrate that the helicity-dependent photoresponse is generated via the photogalvanic effect (PGE). We also observed that the photocurrent is controlled by circular polarization and the external electric field. Because of the tunable Berry curvature dipole derived from the nontrivial wave functions near the inverted gap edge in monolayer WTe2, the bandgap can be tuned efficiently. Our results provide a versatile venue for controlling, detecting, and processing valleytronics and applications in on-chip THz imaging and quantum information processing.

Compensated Ferrimagnets with Colossal Spin Splitting in Organic Compounds.

The study of the magnetic order has recently been invigorated by the discovery of exotic collinear antiferromagnets with time-reversal symmetry breaking. Examples include altermagnets and compensated ferrimagnets, which show spin splittings of the electronic band structures even at zero net magnetization, leading to several unique transport phenomena, notably spin-current generation. Altermagnets demonstrate anisotropic spin splitting, such as d-wave, in momentum space, whereas compensated ferrimagnets exhibit isotropic spin splitting. However, methods to realize compensated ferrimagnets are limited. Here, we demonstrate a method to realize a fully compensated ferrimagnet with isotropic spin splitting utilizing the dimer structures inherent in organic compounds. Moreover, based on abinitio calculations, we find that this compensated ferrimagnet can be realized in the recently discovered organic compound (EDO-TTF-I)_{2}ClO_{4}. Our findings provide an unprecedented strategy for using the dimer degrees of freedom in organic compounds to realize fully compensated ferrimagnets with colossal spin splitting.

Charge transfer and spin-valley locking in 4Hb-TaS2

Abstract4Hb-TaS2 is a superconductor that exhibits unique characteristics such as time-reversal symmetry breaking, hidden magnetic memory, and topological edge modes. It is a naturally occurring heterostructure comprising of alternating layers of 1H-TaS2 and 1T-TaS2. The former is a well-known superconductor, while the latter is a correlated insulator with a possible non- trivial magnetic ground state. In this study, we use angle resolved photoemission spectroscopy to investigate the normal state electronic structure of this unconventional superconductor. Our findings reveal that the band structure of 4Hb-TaS2 fundamentally differs from that of its constituent materials. Specifically, we observe a significant charge transfer from the 1T layers to the 1H layers that drives the 1T layers away from half-filling. In addition, we find a substantial reduction in inter-layer coupling in 4Hb-TaS2 compared to the coupling in 2H-TaS2 that results in a pronounced spin-valley locking within 4Hb-TaS2.

Chirality Probe of Twisted Bilayer Graphene in the Linear Transport Regime.

We propose minimal transport experiments in the coherent regime that can probe the chirality of twisted moiré structures. We show that only with a third contact and in the presence of an in-plane magnetic field (or another time-reversal symmetry breaking effect) a chiral system may display nonreciprocal transport in the linear regime. We then propose to use the third lead as a voltage probe and show that opposite enantiomers give rise to different voltage drops on the third lead. Additionally, in the scenario of layer-discriminating contacts, the third lead can serve as a current probe capable of detecting different handedness even in the absence of a magnetic field. In a complementary configuration, applying opposite voltages on the two layers of the third lead gives rise to a chiral (super)current in the absence of a source-drain voltage whose direction is determined by its chirality.

Realization of a quadrupole topological insulator phase in a gyromagnetic photonic crystal

ABSTRACT The field of topological photonics was initiated with the realization of a Chern insulator phase in a gyromagnetic photonic crystal (PhC) with broken time-reversal symmetry (T), hosting chiral edge states that are topologically protected propagating modes. Along a separate line of research, a quadrupole topological insulator was the first higher-order topological phase supporting localized corner states, but has been so far limited to T-invariant systems, as T is a key ingredient in early models. Here we report the realization of a quadrupole topological insulator phase in a gyromagnetic PhC, as a consequence of topological phase transition from the previously demonstrated Chern insulator phase. The phase transition has been demonstrated with microwave measurements, which characterize the evolution from propagating chiral edge states to localized corner states. We also demonstrate the migration of topological boundary states into the continuum, when the gyromagnetic PhC is magnetically tuned. These results extend the quadrupole topological insulator phase into T-broken systems, and integrate topologically protected propagating and localized modes in a magnetically tunable photonic crystal platform.

Intertwined Van Hove Singularities as a Mechanism for Loop Current Order in Kagome Metals.

Recent experiments on kagome metals AV_{3}Sb_{5} (A=Cs,Rb,K) indicated spontaneous time-reversal symmetry breaking in the charge density wave state in the absence of static magnetization. The loop current order (LCO) is proposed as its cause, but a microscopic model explaining the emergence of LCO through electronic correlations has not been firmly established. We show that the coupling between van Hove singularities with distinct mirror symmetries is a key ingredient to generate LCO ground state. By constructing an effective model, we find that when multiple van Hove singularities with opposite mirror eigenvalues are close in energy, the nearest-neighbor electron repulsion favors a ground state with coexisting LCO and charge bond order. It is then demonstrated that this mechanism applies to the kagome metals AV_{3}Sb_{5}. Our findings provide an intriguing mechanism of LCO and pave the way for a deeper understanding of complex quantum phenomena in kagome systems.

Tunable Colossal Anomalous Hall Conductivity in Half-Metallic Material Induced by d-Wave-Like Spin-Orbit Gap.

The anomalous Hall conductivity (AHC) in magnetic materials, resulting from inverted band topology, has emerged as a key adjustable function in spin-torque devices and advanced magnetic sensors. Among systems with near-half-metallicity and broken time-reversal symmetry, cobalt disulfide (CoS2) has proven to be a material capable of significantly enhancing its AHC. In this study, the AHC of CoS2 is empirically assessed by manipulating the chemical potential through Fe- (hole) and Ni- (electron) doping. The primary mechanism underlying the colossal AHC is identified through the application of density functional theory and tight-binding analyses. The main source of this substantial AHC is traced to four spin-polarized massive Dirac dispersions in the kz = 0 plane of the Brillouin zone, located slightly below the Fermi level. In Co0.95Fe0.05S2, the AHC, which is directly proportional to the momentum-space integral of the Berry curvature (BC), reached a record-breaking value of 2507 Ω-1cm-1. This is because the BCs of the four Dirac dispersions all exhibit the same sign, a consequence of the d-wave-like spin-orbit coupling among spin-polarized egorbitals.

Electronic Raman response of a superconductor across a time reversal symmetry breaking phase transition

Electronic Raman response of a superconductor across a time reversal symmetry breaking phase transition

Large nonlinear optical magnetoelectric response in a noncentrosymmetric magnetic Weyl semimetal

Weyl semimetals resulting from either inversion (P) or time-reversal (T) symmetry breaking have been revealed to show the record-breaking large optical response due to intense Berry curvature of Weyl-node pairs. Different classes of Weyl semimetals with both P and T symmetry breaking potentially exhibit optical magnetoelectric (ME) responses, which are essentially distinct from the previously observed optical responses in conventional Weyl semimetals, leading to the versatile functions such as directional dependence for light propagation and gyrotropic effects. However, such optical ME phenomena of (semi)metallic systems have remained elusive so far. Here, we show the large nonlinear optical ME response in noncentrosymmetric magnetic Weyl semimetal PrAlGe, in which the polar structural asymmetry and ferromagnetic ordering break P and T symmetry. We observe the giant second harmonic generation (SHG) arising from the P symmetry breaking in the paramagnetic phase, being comparable to the largest SHG response reported in Weyl semimetal TaAs. In the ferromagnetically ordered phase, it is found that interference between this nonmagnetic SHG and the magnetically induced SHG emerging due to both P and T symmetry breaking results in the magnetic field switching of SHG intensity. Furthermore, such an interference effect critically depends on the light-propagating direction. The corresponding magnetically induced nonlinear susceptibility is significantly larger than the prototypical ME material, manifesting the existence of the strong nonlinear dynamical ME coupling. The present findings establish the unique optical functionality of P- and T-symmetry broken ME topological semimetals.

Absence of floating phase in superconductors with time-reversal symmetry breaking on any lattice

Absence of floating phase in superconductors with time-reversal symmetry breaking on any lattice

Nonequilibrium Casimir–Polder Force between Nanoparticles and Graphene-Coated Silica Plate: Combined Effect of the Chemical Potential and Mass Gap

The Casimir–Polder force between spherical nanoparticles and a graphene-coated silica plate is investigated in situations out of thermal equilibrium, i.e., with broken time-reversal symmetry. The response of the graphene coating to the electromagnetic field is described on the basis of first principles of quantum electrodynamics at nonzero temperature using the formalism of the polarization tensor in the framework of the Dirac model. The nonequilibrium Casimir–Polder force is calculated as a function of the mass-gap parameter, the chemical potential of graphene, and the temperature of the graphene-coated plate, which can be both higher or lower than that of the environment. It is shown that the force value increases with the increasing chemical potential, and this increase is more pronounced when the temperature of a graphene-coated plate is lower than that of the environment. The nonequilibrium force also increases with increasing temperature of the graphene-coated plate. This increase is larger when the plate is hotter than the environment. The effect is revealed that the combined impact of the chemical potential, μ, and mass gap, Δ, of the graphene coating depends on the relationship between Δ and 2μ. If 2μ&gt;Δ, the magnitude of the nonequilibrium force between nanoparticles and a cooled graphene-coated plate becomes much larger than for a graphene coating with μ=0. The physical reasons explaining this effect are elucidated. Possible applications of the obtained results are discussed.

Symmetry and magnetic direction dependent spin/valley splitting and anomalous Hall conductivity of antiferromagnetic monolayer MnPTe3

Due to the time reversal symmetry breaking or spin-valley coupling, there are intrinsic valley splittings in two-dimensional magnetic materials, which are closely related to the symmetry and magnetic order. Based on MnPTe3 monolayers with different symmetries, we present an understanding of direction dependent spin/valley splitting and anomalous Hall conductivity from the perspective of orbital interactions. Unlike T-MnPTe3 with central inversion symmetry, in-plane magnetization leads to further non-degeneracy of valley electrons of H–MnPTe3, and the splitted valley states are spin polarized, which is perpendicular to the in-plane magnetization direction. The model and first-principle calculations consistently indicate that the splitting of the valley states is almost proportional to sinθxz, which originates from the difference in spin-up and spin-down interactions introduced by the breaking of spatial inversion symmetry. Regardless of spin degeneracy, non-zero anomalous Hall conductivity occurs with out-of-plane magnetization, and this direction dependent anomalous Hall effect is caused by mirror symmetry breaking from the neighboring Te atoms and spin-orbit coupling. Magnetization direction is an important means of regulating valley/spin splittings and anomalous Hall effect, which has certain significance for realizing spin or valley polarized Hall effect and the research of spintronic or valleytronic devices.

Nonreciprocal superconducting transport and the spin Hall effect in gyrotropic structures

The search for superconducting systems exhibiting nonreciprocal transport and, specifically, the diode effect, has proliferated in recent years. This trend has encompassed a wide variety of systems, including planar hybrid structures, asymmetric SQUIDs, and certain noncentrosymmetric superconductors. A common feature of such systems is a gyrotropic symmetry, realized on different scales and characterized by a polar vector. Alongside time-reversal symmetry breaking, the presence of a polar axis allows for magnetoelectric effects, which, when combined with proximity-induced superconductivity, results in spontaneous non-dissipative currents that underpin the superconducting diode effect. With this symmetry established, we present a comprehensive theoretical study of transport in a lateral Josephson junction composed of a normal metal supporting the spin Hall effect, and attached to a ferromagnetic insulator. Due to the presence of the latter, magnetoelectric effects arise without requiring external magnetic fields. We determine the dependence of the anomalous currents on the spin relaxation length and the transport parameters commonly used in spintronics to characterize the interface between the metal and the ferromagnetic insulator. Therefore, our theory naturally unifies nonreciprocal transport in superconducting systems with classical spintronic effects, such as the spin Hall effect, spin galvanic effect, and spin Hall magnetoresistance. We propose an experiment involving measurements of magnetoresistance in the normal state and nonreciprocal transport in the superconducting state. Such experiment would, on the one hand, allow for determining the parameters of the model and thus verifying with a greater precision the theories of magnetoelectric effects in normal systems. On the other hand, it would contribute to a deeper understanding of the underlying microscopic origins that determine these parameters.

Vestigial singlet pairing in a fluctuating magnetic triplet superconductor and its implications for graphene superlattices

Stacking and twisting graphene layers allows to create and control a two-dimensional electron liquid with strong correlations. Experiments indicate that these systems exhibit strong tendencies towards both magnetism and triplet superconductivity. Motivated by this phenomenology, we study a 2D model of fluctuating triplet pairing and spin magnetism. Individually, their respective order parameters, d and N, cannot order at finite temperature. Nonetheless, the model exhibits a variety of vestigial phases, including charge-4e superconductivity and broken time-reversal symmetry. Our main focus is on a phase characterized by finite d ⋅ N, which has the same symmetries as the BCS state, a Meissner effect, and metastable supercurrents, yet rather different spectral properties: most notably, the suppression of the electronic density of states at the Fermi level can resemble that of either a fully gapped or nodal superconductor, depending on parameters. This provides a possible explanation for recent tunneling experiments in the superconducting phase of graphene moiré systems.

Angle-resolved transport non-reciprocity and spontaneous symmetry breaking in twisted trilayer graphene.

The identification and characterization of spontaneous symmetry breaking is central to our understanding of strongly correlated two-dimensional materials. In this work, we utilize the angle-resolved measurements of transport non-reciprocity to investigate spontaneous symmetry breaking in twisted trilayer graphene. By analysing the angular dependence of non-reciprocity in both longitudinal and transverse channels, we are able to identify the symmetry axis associated with the underlying electronic order. We report that a hysteretic rotation in the mirror axis can be induced by thermal cycles and a large current bias, supporting the spontaneous breaking of rotational symmetry. Moreover, the onset of non-reciprocity with decreasing temperature coincides with the emergence of orbital ferromagnetism. Combined with the angular dependence of the superconducting diode effect, our findings uncover a direct link between rotational and time-reversal symmetry breaking. These symmetry requirements point towards exchange-driven instabilities in momentum space as a possible origin for transport non-reciprocity in twisted trilayer graphene.

Tunable positions of Weyl nodes via magnetism and pressure in the ferromagnetic Weyl semimetal CeAlSi

The noncentrosymmetric ferromagnetic Weyl semimetal CeAlSi with simultaneous space-inversion and time-reversal symmetry breaking provides a unique platform for exploring novel topological states. Here, by employing multiple experimental techniques, we demonstrate that ferromagnetism and pressure can serve as efficient parameters to tune the positions of Weyl nodes in CeAlSi. At ambient pressure, a magnetism-facilitated anomalous Hall/Nernst effect (AHE/ANE) is uncovered. Angle-resolved photoemission spectroscopy (ARPES) measurements demonstrated that the Weyl nodes with opposite chirality are moving away from each other upon entering the ferromagnetic phase. Under pressure, by tracing the pressure evolution of AHE and band structure, we demonstrate that pressure could also serve as a pivotal knob to tune the positions of Weyl nodes. Moreover, multiple pressure-induced phase transitions are also revealed. These findings indicate that CeAlSi provides a unique and tunable platform for exploring exotic topological physics and electron correlations, as well as catering to potential applications, such as spintronics.

Chiral active particles are sensitive reporters to environmental geometry

Chiral active particles (CAPs) are self-propelling particles that break time-reversal symmetry by orbiting or spinning, leading to intriguing behaviors. Here, we examined the dynamics of CAPs moving in 2D lattices of disk obstacles through active Brownian dynamics simulations and granular experiments with grass seeds. We find that the effective diffusivity of the CAPs is sensitive to the structure of the obstacle lattice, a feature absent in achiral active particles. We further studied the transport of CAPs in obstacle arrays under an external field and found a reentrant directional locking effect, which can be used to sort CAPs with different activities. Finally, we demonstrated that parallelogram lattices of obstacles without mirror symmetry can separate clockwise and counter-clockwise CAPs. The mechanisms of the above three novel phenomena are qualitatively explained. As such, our work provides a basis for designing chirality-based tools for single-cell diagnosis and separation, and active particle-based environmental sensors.

Altermagnetic lifting of Kramers spin degeneracy

Lifted Kramers spin degeneracy (LKSD) has been among the central topics of condensed-matter physics since the dawn of the band theory of solids1,2. It underpins established practical applications as well as current frontier research, ranging from magnetic-memory technology3–7 to topological quantum matter8–14. Traditionally, LKSD has been considered to originate from two possible internal symmetry-breaking mechanisms. The first refers to time-reversal symmetry breaking by magnetization of ferromagnets and tends to be strong because of the non-relativistic exchange origin15. The second applies to crystals with broken inversion symmetry and tends to be comparatively weaker, as it originates from the relativistic spin–orbit coupling (SOC)16–19. A recent theory work based on spin-symmetry classification has identified an unconventional magnetic phase, dubbed altermagnetic20,21, that allows for LKSD without net magnetization and inversion-symmetry breaking. Here we provide the confirmation using photoemission spectroscopy and ab initio calculations. We identify two distinct unconventional mechanisms of LKSD generated by the altermagnetic phase of centrosymmetric MnTe with vanishing net magnetization20–23. Our observation of the altermagnetic LKSD can have broad consequences in magnetism. It motivates exploration and exploitation of the unconventional nature of this magnetic phase in an extended family of materials, ranging from insulators and semiconductors to metals and superconductors20,21, that have been either identified recently or perceived for many decades as conventional antiferromagnets21,24,25.