Rotational Symmetry Breaking Research Articles

Shaping the Plasmonic Response: Hollow Gold Elliptical Nanotubes

AbstractHighly tunable localized surface plasmon (LSP) resonances in metal nanostructures are of great importance for manipulating light waves and enhancing light–matter interactions at the nanoscale. Here, a new type of plasmonic resonators based on hollow elliptical nanotubes, which can generate highly tunable LSP resonances in the visible frequencies, are reported. High‐quality hollow gold (Au) elliptical nanotubes with fine controllable size and morphology are experimentally fabricated. Dark‐field scattering measurements reveal the presence of multiple plasmon resonances including longitudinal Fabry–Pérot resonances and transverse hybridized LSP resonances due to rotational symmetry breaking. Upon varying the ellipticity, the hybridized LSP resonances exhibit continuously spectral evolution behaviors, such as the hybridized modes shifting and crossing. The experimental results show good agreement with the rigorous electromagnetic modeling and Raman spectroscopic measurements. The hollow anisotropic geometries provide highly tunable plasmonic responses together with homogeneous field distributions and high surface‐to‐volume ratio, which hold great potential for practical applications in sensing, nonlinear optics, surface‐enhanced spectroscopies, and bio‐medicine.

Symmetry-based requirement for the measurement of electrical and thermal Hall conductivity under an in-plane magnetic field

The in-plane (thermal) Hall effect is an unconventional transverse response when the applied magnetic field is in the (heat) current plane. In contrast to the normal Hall effect, the in-plane Hall effect requires the absence of certain crystal symmetries, and possibly manifests a non-trivial topology of quantum materials. An accurate estimation of the intrinsic in-plane (thermal) Hall conductivity is crucial to identify the underlying mechanisms as in the case of the Kitaev spin-liquid candidate alpha-RuCl3. Here, we give the symmetry conditions for the in-plane Hall effect and discuss the implications that may impede the experimental evaluation of the in-plane (thermal) Hall conductivity within the single-device measurement. First, the lack of symmetry in crystals can create merohedral twin domains that cancel the total Hall signal. Second, even in a twin-free crystal, the intrinsic response is potentially contaminated by the out-of-plane conduction in three-dimensional systems, which is systematically unavoidable in the in-plane Hall systems. Third, even in a quasi-two-dimensional system, the conversion of (thermal) resistivity, rho (lambda), to (thermal) conductivity, sigma (kappa) requires protocols beyond the widely-used simplified formula due to the lack of in-plane-rotational symmetry. In principle, two independent sample devices are necessary to accurately estimate the s_xy (k_xy). As a case study, we discuss the half-integer quantization of the in-plane thermal Hall effect in the spin-disordered state of alpha-RuCl3. For an accurate measurement of the thermal Hall effect, it is necessary to avoid crystals with the merohedral twins contributing oppositely to k_xy, while the out-of-plane transport may have a negligible effect. To deal with the field-induced rotational-symmetry breaking, we propose two symmetry-based protocols, improved single-device and two-device methods.

Spontaneous rotational symmetry breaking in KTaO3 heterointerface superconductors

Broken symmetries play a fundamental role in superconductivity and influence many of its properties in a profound way. Understanding these symmetry breaking states is essential to elucidate the various exotic quantum behaviors in non-trivial superconductors. Here, we report an experimental observation of spontaneous rotational symmetry breaking of superconductivity at the heterointerface of amorphous (a)-YAlO3/KTaO3(111) with a superconducting transition temperature of 1.86 K. Both the magnetoresistance and superconducting critical field in an in-plane field manifest striking twofold symmetric oscillations deep inside the superconducting state, whereas the anisotropy vanishes in the normal state, demonstrating that it is an intrinsic property of the superconducting phase. We attribute this behavior to the mixed-parity superconducting state, which is an admixture of s-wave and p-wave pairing components induced by strong spin-orbit coupling inherent to inversion symmetry breaking at the heterointerface of a-YAlO3/KTaO3. Our work suggests an unconventional nature of the underlying pairing interaction in the KTaO3 heterointerface superconductors, and brings a new broad of perspective on understanding non-trivial superconducting properties at the artificial heterointerfaces.

Strain-tuned quantum criticality in electronic Potts-nematic systems

Motivated by recent observations of threefold rotational symmetry breaking in twisted moir\'e systems, cold-atom optical lattices, quantum Hall systems, and triangular antiferromagnets, we phenomenologically investigate the strain-temperature phase diagram of the electronic 3-state Potts-nematic order. While in the absence of strain the quantum Potts-nematic transition is first order, quantum critical points (QCP) emerge when uniaxial strain is applied, whose nature depends on whether the strain is compressive or tensile. In one case, the nematic amplitude jumps between two nonzero values while the nematic director remains pinned, leading to a symmetry-preserving metanematic transition that terminates at a quantum critical end point. For the other type of strain, the nematic director unlocks from the strain direction and spontaneously breaks an in-plane twofold rotational symmetry, which in twisted moir\'e superlattices triggers an electric polarization. Such a piezoelectric transition changes from first to second order upon increasing strain, resulting in a quantum tricritical point. Using a Hertz-Millis approach, we show that these QCPs share interesting similarities with the widely studied Ising-nematic QCP. The existence of three minima in the nematic action also leaves fingerprints in the strain-nematic hysteresis curves, which display multiple loops. At nonzero temperatures, because the upper critical dimension of the 3-state Potts model is smaller than three, the Potts-nematic transition is expected to remain first order in three dimensions, but to change to second order in two dimensions (2D). As a result, the 2D strain-temperature phase diagram displays two first-order transition wings bounded by lines of critical end points or tricritical points, reminiscent of the phase diagram of metallic ferromagnets. We discuss how our results can be used to unambiguously identify spontaneous Potts-nematic order.

Periodic Atomic Displacements and Visualization of the Electron-Lattice Interaction in the Cuprate

Traditionally, X-ray scattering techniques have been used to detect the breaking of the structural symmetry of the lattice, which accompanies a periodic displacement of the atoms associated with charge density wave (CDW) formation in the cuprate pseudogap states. Similarly, the Spectroscopic Imaging Scanning Tunneling Microscopy (SI-STM) has visualized the short-range CDW. However, local coupling of electrons to the lattice in the form of a short-range CDW has been a challenge to visualize, thus a link between these measurements has been missing. Here, we introduce a novel STM-based technique to visualize the local bond length variations obtained from topographic imaging with picometer precision. Application of this technique to the high-Tc cuprate superconductor Bi2Sr2CaCu2O8+{\delta} revealed a high-fidelity local lattice distortion of the BiO lattice as large as 2%. In addition, analysis of local breaking of rotational symmetry associated with the bond lengths reveals modulations around four-unit-cell periodicity in both B1 and E representations in the C4v group of the lattice, which coincides with the uni-directional d-symmetry CDW (dCDW) previously identified within the CuO2 planes, thus providing direct evidence of electron-lattice coupling in the pseudogap state and a link between the X-ray scattering and STM measurements. Overall, our results suggest that the periodic lattice displacements in E representations correspond to a locally-frozen version of the soft phonons identified by the X-ray scattering measurements, and a fluctuation of the bond length is reflected by the fluctuation of the dCDW formation near the quantum critical point.

Nematicity-enhanced superconductivity in systems with a non-Fermi liquid behavior

We explore the interplay between nematicity (spontaneous breaking of the sixfold rotational symmetry), superconductivity, and non-Fermi liquid behavior in partially flat-band (PFB) models on the triangular lattice. A key result is that the nematicity (Pomeranchuk instability), which is driven by many-body effect and stronger in flat-band systems, enhances superconducting transition temperature in a systematic manner on the T c dome. There, a plausible -wave symmetry, in place of the conventional -wave, governs the nematicity-enhanced pairing with a sharp rise in the T c dome on the filling axis. When the sixfold symmetry is spontaneously broken, the pairing interaction is shown to become stronger with more compact pairs in real space than when the symmetry is enforced. These are accompanied by a non-Fermi character of electrons in the PFBs with many-body interactions.

Moiré engineering in 2D heterostructures with process-induced strain

We report deterministic control over a moiré superlattice interference pattern in twisted bilayer graphene by implementing designable device-level heterostrain with process-induced strain engineering, a widely used technique in industrial silicon nanofabrication processes. By depositing stressed thin films onto our twisted bilayer graphene samples, heterostrain magnitude and strain directionality can be controlled by stressor film force (film stress × film thickness) and patterned stressor geometry, respectively. We examine strain and moiré interference with Raman spectroscopy through in-plane and moiré-activated phonon mode shifts. Results support systematic C3 rotational symmetry breaking and tunable periodicity in moiré superlattices under the application of uniaxial or biaxial heterostrain. Experimental results are validated by molecular statics simulations and density functional theory based first principles calculations. This provides a method not only to tune moiré interference without additional twisting but also to allow for a systematic pathway to explore different van der Waals based moiré superlattice symmetries by deterministic design.

Manipulating the nematic director by magnetic fields in the spin-triplet superconducting state of CuxBi2Se3

Electronic nematicity, a consequence of rotational symmetry breaking, is an emergent phenomenon in various new materials. In order to fully utilize the functions of these materials, ability of tuning them through a knob, the nematic director, is desired. Here we report a successful manipulation of the nematic director, the vector order-parameter (d-vector), in the spin-triplet superconducting state of CuxBi2Se3 by magnetic fields. At H = 0.5 T, the ac susceptibility related to the upper critical field shows a two-fold symmetry in the basal plane. At H = 1.5 T, however, the susceptibility shows a six-fold symmetry, which has never been reported before in any superconductor. These results indicate that the d-vector initially pinned to a certain direction is unlocked by a threshold field to respect the trigonal crystal symmetry. We further reveal that the superconducting gap in different crystals converges to p_x symmetry at high fields, although it differs at low fields.

Direct observation of a superconducting vortex diode

The interplay between magnetism and superconductivity can lead to unconventional proximity and Josephson effects. A related phenomenon that has recently attracted considerable attention is the superconducting diode effect, in which a nonreciprocal critical current emerges. Although superconducting diodes based on superconductor/ferromagnet (S/F) bilayers were demonstrated more than a decade ago, the precise underlying mechanism remains unclear. While not formally linked to this effect, the Fulde–Ferrell–Larkin–Ovchinikov (FFLO) state is a plausible mechanism due to the twofold rotational symmetry breaking caused by the finite center-of-mass-momentum of the Cooper pairs. Here, we directly observe asymmetric vortex dynamics that uncover the mechanism behind the superconducting vortex diode effect in Nb/EuS (S/F) bilayers. Based on our nanoscale SQUID-on-tip (SOT) microscope and supported by in-situ transport measurements, we propose a theoretical model that captures our key results. The key conclusion of our model is that screening currents induced by the stray fields from the F layer are responsible for the measured nonreciprocal critical current. Thus, we determine the origin of the vortex diode effect, which builds a foundation for new device concepts.

Enhanced Superconducting Pairing Strength near a Pure Nematic Quantum Critical Point

The quest for high-temperature superconductivity at ambient pressure is a central issue in physics. In this regard, the relationship between unconventional superconductivity and the quantum critical point (QCP) associated with the suppression of some form of symmetry-breaking order to zero temperature has received particular attention. The key question is how the strength of the electron pairs changes near the QCP, and this can be verified by high-field experiments. However, such studies are limited mainly to superconductors with magnetic QCPs, and the possibility of unconventional mechanisms by which nonmagnetic QCP promotes strong pairing remains a nontrivial issue. Here, we report systematic measurements of the upper critical field $H_{{\rm c2}}$ in nonmagnetic FeSe$_{1-x}$Te$_{x}$ superconductors, which exhibit a QCP of electronic nematicity characterized by spontaneous rotational-symmetry breaking. As the magnetic field increases, the superconducting phase of FeSe$_{1-x}$Te$_{x}$ shrinks to a narrower dome surrounding the nematic QCP. The analysis of $H_{{\rm c2}}$ reveals that the Pauli-limiting field is enhanced toward the QCP, implying that the pairing interaction is significantly strengthened via nematic fluctuations emanated from the QCP. Remarkably, this nonmagnetic nematic QCP is not accompanied by a divergent effective mass, distinct from the magnetically mediated pairing. Our observation opens up a nonmagnetic route to high-temperature superconductivity.

Infinite critical boson non-Fermi liquid

We study a distinct type of non-Fermi liquid where there exists an infinite number of critical bosonic modes instead of finite number of bosonic modes for the conventional ones. We consider itinerant magnets with both conduction electrons and fluctuating magnetic moments in three dimensions. With Dzyaloshinskii–Moriya interaction, the moments fluctuate near a boson surface in the reciprocal space at low energies when the system approaches an ordering transition. The infinite number of critical modes on the boson surface strongly scatter the gapless electrons on the Fermi surface and convert the metallic sector into a non-Fermi liquid. We explain the physical properties of this non-Fermi liquid. On the ordered side, a conventional non-Fermi liquid emerges due to the scattering by the gapless Goldstone mode from the spontaneous breaking of the global rotational symmetry. We discuss the general structure of the phase diagram in the vicinity of the quantum phase transition and clarify various crossover behaviors.

Unidirectional coherent quasiparticles in the high-temperature rotational symmetry broken phase of AV3Sb5 kagome superconductors

Kagome metals AV3Sb51 (where the A can stand for K, Cs or Rb) display a rich phase diagram of correlated electron states, including superconductivity2–4 and density waves5–7. Within this landscape, recent experiments have revealed signs of a transition below approximately 35 K attributed to an electronic nematic phase that spontaneously breaks the rotational symmetry of the lattice8. Here we show that the rotational symmetry breaking initiates universally at a high temperature in these materials, towards the 2 × 2 charge density wave transition temperature. We do this via spectroscopic-imaging scanning tunnelling microscopy and study the atomic-scale signatures of the electronic symmetry breaking across several materials in the AV3Sb5 family: CsV3Sb5, KV3Sb5 and Sn-doped CsV3Sb5. Below a substantially lower temperature of about 30 K, we measure the quantum interference of quasiparticles, a key signature for the formation of a coherent electronic state. These quasiparticles display a pronounced unidirectional feature in reciprocal space that strengthens as the superconducting state is approached. Our experiments reveal that high-temperature rotation symmetry breaking and the charge ordering states are separated from the superconducting ground state by an intermediate-temperature regime with coherent unidirectional quasiparticles. This picture is phenomenologically different compared to that in high-temperature superconductors, shedding light on the complex nature of rotation symmetry breaking in AV3Sb5 kagome superconductors. The charge density wave state in kagome superconductors is not fully understood. Now, evidence suggests that the rotational symmetry of the lattice is broken before coherence of unidirectional quasiparticles is established at a lower temperature.

Bulk evidence of anisotropic s-wave pairing with no sign change in the kagome superconductor CsV3Sb5

The recently discovered kagome superconductors AV3Sb5 (A = K, Rb, Cs) exhibit unusual charge-density-wave (CDW) orders with time-reversal and rotational symmetry breaking. One of the most crucial unresolved issues is identifying the symmetry of the superconductivity that develops inside the CDW phase. Theory predicts a variety of unconventional superconducting symmetries with sign-changing and chiral order parameters. Experimentally, however, superconducting phase information in AV3Sb5 is still lacking. Here we report the impurity effects in CsV3Sb5 using electron irradiation as a phase-sensitive probe of superconductivity. Our magnetic penetration depth measurements reveal that with increasing impurities, an anisotropic fully-gapped state changes to an isotropic full-gap state without passing through a nodal state. Furthermore, transport measurements under pressure show that the double superconducting dome in the pressure-temperature phase diagram survives against sufficient impurities. These results support that CsV3Sb5 is a non-chiral, anisotropic s-wave superconductor with no sign change both at ambient and under pressure.

Impact of core polarity on smectic B-induced hydrogen bond liquid crystals.

The novel series of hydrogen bond liquid crystals were synthesized from the 2-methylglutaric acid (MGA) and 4-alkyloxybenzoic acid (nOBA) compounds. The induced smectic B phase with different texture (spine texture, needle texture, mosaic texture, natural mosaic texture and marble texture) were identified by polarizing optical microscope. Due to breaking of in-plane rotational symmetry within molecular layers, smectic B phase is tempted by suppressing other usual mesophases. The mesomorphic transition temperature, enthalpy and entropy values were calculated by differential scanning calorimeter which strongly proves the existence of mesomorphism. H-bond interaction and functional groups were confirmed by the observed peak between 2910 and 2954cm-1 in the FTIR spectra. Thermal stability and extended mesophase width (for MGA + 12OBA = 31.1) of Sm B mesophase were reported and it clearly reveals the existence of mono-phase variance in the MGA + nOBA HBLC complex. Due to the steric effect, and the increased molecular core polarity, the highly stabilized Sm B phase with different textures were observed while varying alkyloxy carbon number n = 7 to 12. Further, the origination of Sm B phase and its detailed characteristics were reported.

Rhombic skyrmion lattice coupled with orthorhombic structural distortion in EuAl4

The centrosymmetric tetragonal itinerant magnet EuAl$_{4}$ exhibits an intricate magnetic phase diagram including rhombic and square skyrmion-lattice (SkL) phases in the external magnetic field. Here, we report a multi-axis dilatometric investigation of EuAl$_{4}$ by means of a newly designed fiber-Bragg-grating technique complemented by a resonant x-ray scattering experiment, revealing anisotropic magnetostriction and magnetovolume effect associated with successive phase transitions. The rhombic and square SkL phases are found to possess $\sim$0.10% and $\sim$0.03% orthorhombic structural distortion within the $ab$ plane, respectively. We propose that the coupling between the spin system and the lattice deformation should be essential for the structural instability in EuAl$_{4}$, yielding a rich variety of topological spin textures with spontaneous rotational-symmetry breaking as well as a potential controllability of the SkL phases by uniaxial stress or pressure.

Quantum vacuum, rotation, and nonlinear fields

In this paper, we extend previous results on the quantum vacuum or Casimir energy, for a noninteracting rotating system and for an interacting nonrotating system, to the case where both rotation and interactions are present. Concretely, we first reconsider the noninteracting rotating case of a scalar field theory and propose an alternative and simpler method to compute the Casimir energy based on a replica trick and the Coleman-Weinberg effective potential. We then consider the simultaneous effect of rotation and interactions, including an explicit breaking of rotational symmetry. To study this problem, we develop a numerical implementation of zeta-function regularization. Our work recovers previous results as limiting cases and shows that the simultaneous inclusion of rotation and interactions produces nontrivial changes in the quantum vacuum energy. Besides expected changes (where, as the size of the ring increases for fixed interaction strength, the angular momentum grows with the angular velocity), we notice that the way rotation combines with the coupling constant amplifies the intensity of the interaction strength. Interestingly, we also observe a departure from the typical massless behavior where the Casimir energy is proportional to the inverse size of the ring.

Metastability of photonic spin meron lattices in the presence of perturbed spin-orbit coupling.

Photonic skyrmions and merons are topological quasiparticles characterized by nontrivial electromagnetic textures, which have received increasing research attention recently, providing novel degree of freedom to manipulate light-matter interactions and exhibiting excellent potential in deep-subwavelength imaging and nanometrology. Here, the topological stability of photonic spin meron lattices, which indicates the invariance of skyrmion number and robustness of spin texture under a continuous deformation of the field configuration, is demonstrated by inducing a perturbation to break the C4 symmetry in the presence spin-orbit coupling in an optical field. We revealed that amplitude perturbation would result in an amplitude-dependent shift of spin center, while phase perturbation leads to the deformation of domain walls, manifesting the metastability of photonic meron. Such spin topology is verified through the interference of plasmonic vortices with a broken rotational symmetry. The results provide new insights on optical topological quasiparticles, which may pave the way towards applications in topological photonics, optical information storage and transfer.

Holographic nonlocal rotating observables and their renormalization

We analyze nonlocal rotating observables in holography corresponding to spinning bound states. To renormalize their energies and momenta we suggest and discuss different holographic renormalization schemes motivated by the static nonlocal observables. Namely the holographic renormalization and the rotating color singlet mass subtraction scheme. In the holographic renormalization we identify the infinite boundary terms and subtract them. In the mass subtraction scheme we evaluate the energy of a spinning trailing string corresponding to the color charged singlet which experiences dragging phenomena and we subtract it from the energy of the bound state to obtain the renormalized finite energy. Then we apply our generic framework to certain strongly coupled thermal theories with broken rotational symmetry. We find numerical solutions corresponding to spinning bound states with a fixed size while varying their angular frequency. By applying numerically the renormalization schemes, we find that there is a critical frequency where the bound state ceases to exist or dissociates. We also note that bound states require lower angular frequencies to dissociate when the theory has less symmetry.

Enhanced symmetry-breaking tendencies in the S=1 pyrochlore antiferromagnet

We investigate the ground-state properties of the nearest-neighbor $S=1$ pyrochlore Heisenberg antiferromagnet using two complementary numerical methods, the density-matrix renormalization group (DMRG) and pseudofermion functional renormalization group (PFFRG). Within DMRG, we are able to reliably study clusters with up to 48 spins by keeping 20 000 SU(2) states. The investigated 32-site and 48-site clusters both show indications of a robust ${C}_{3}$ rotation symmetry breaking of the ground-state spin correlations and the 48-site cluster additionally features inversion symmetry breaking. Our PFFRG analysis of various symmetry-breaking perturbations corroborates the findings of either ${C}_{3}$ or a combined ${C}_{3}$/inversion symmetry breaking. Moreover, in both methods the symmetry-breaking tendencies appear to be more pronounced than in the $S=1/2$ system.

Coexistence of trihexagonal and star-of-David pattern in the charge density wave of the kagome superconductor AV3Sb5

The recently discovered layered kagome metals AV$_3$Sb$_5$(A=K, Rb, Cs) have attracted much attention because of their unique combination of superconductivity, charge density wave (CDW) order, and nontrivial band topology. The CDW order with an in-plane 2x2 reconstruction is found to exhibit exotic properties, such as time-reversal symmetry breaking and rotational symmetry breaking. However, the nature of the CDW, including its dimensionality, structural pattern, and effect on electronic structure, remains elusive despite intense research efforts. Here, using angle-resolved photoemission spectroscopy, we unveil for the first time characteristic double-band splittings and band reconstructions, as well as the band gap resulting from band folding, in the CDW phase. Supported by density functional theory calculations, we unambiguously show that the CDW in AV$_3$Sb$_5$ originates from the intrinsic coexistence of Star-of-David and Tri-Hexagonal distortions. The alternating stacking of these two distortions naturally leads to three-dimensional 2x2x2 or 2x2x4 CDW order. Our results provide crucial insights into the nature and distortion pattern of the CDW order, thereby laying down the basis for a substantiated understanding of the exotic properties in the family of AV$_3$Sb$_5$ kagome metals.