Rotational Symmetry Breaking Research Articles

Computing light-front wave functions without light-front quantization: A large-momentum effective theory approach

Light-front wave functions play a fundamental role in the light-front quantization approach to QCD and hadron structure. However, a naive implementation of the light-front quantization suffers from various subtleties including the well-known zero-mode problem, the associated rapidity divergences which mixes ultraviolet divergences with infrared physics, as well as breaking of spatial rotational symmetry. We advocate that the light-front quantization should be viewed as an effective theory in which small ${k}^{+}$ modes have been effectively ``integrated out,'' with an infinite number of renormalization constants. Instead of solving light-front quantized field theories directly, we make the large momentum expansion of the equal-time Euclidean correlation functions in instant quantization as an effective way to systematically calculate light-front correlations, including the light-front wave function amplitudes. This large-momentum effective theory accomplishes an effective light-front quantization through lattice QCD calculations. We demonstrate our approach using an example of a pseudoscalar meson wave function.

Nonperturbative light-front effective potential for static sources in quenched scalar Yukawa theory

We compute an effective potential between two fixed sources in light-front quantization of a quenched scalar Yukawa theory that models the interaction of complex scalar fields through the exchange of a neutral scalar. Despite the breaking of explicit rotational symmetry by the use of light-front coordinates, the effective potential is rotationally symmetric and matches the standard Yukawa potential for scalar exchange. The neutral scalar field is represented by a coherent state, which is obtained nonperturbatively as an eigenstate of our model Hamiltonian, with the eigenenergy determining the effective potential. The sources are represented by wave packets that are fixed with respect to ordinary time, but move in light-front coordinates. The theory is quenched, to remove pair-production processes that would otherwise cause the spectrum to be unbounded from below.

Nematic superconductivity in the topological semimetal CaSn3

The superconducting behavior of the topological semimetal $\mathrm{Ca}{\mathrm{Sn}}_{3}$ was investigated by means of magnetotransport and muon spectroscopy ($\ensuremath{\mu}\mathrm{S}\mathrm{R}$) measurements, both providing strong evidence of nematic behavior. Magnetotransport detects an anisotropic upper critical field, characterized by a twofold symmetry about ${C}_{4}$ axis, thus breaking the rotational symmetry of the underlying cubic lattice. Transverse-field $\ensuremath{\mu}\mathrm{S}\mathrm{R}$ data support such picture, with the muon depolarization rate depending strongly on the magnetic field direction, here applied along the [110] or [001] crystal directions. In the former case, the absence of any additional muon depolarization suggests an unconventional vortex lattice. In the latter case, a vortex lattice encompassing a sample volume of at least 52% indicates the bulk nature of $\mathrm{Ca}{\mathrm{Sn}}_{3}$ superconductivity. The resulting superfluid density in the (001) planes shows a gapped low-temperature behavior, with a superconducting gap value $\mathrm{\ensuremath{\Delta}}(0)\ensuremath{\simeq}0.61(7)$ meV. Additional zero-field $\ensuremath{\mu}\mathrm{S}\mathrm{R}$ results indicate that the superconducting state is time-reversal invariant. This fact and the breaking of rotational symmetry in a fully gapped superconductor are consistent with an unconventional pairing state in a multidimensional representation, thus making $\mathrm{Ca}{\mathrm{Sn}}_{3}$ an important example of nematic superconductor.

Correlated second-order Dirac semimetals with Coulomb interactions

We investigate the effects of long range Coulomb interactions on the low-temperature properties of a second-order Dirac semimetal in terms of the renormalization group. In contrast to the first-order Dirac semimetal, the full rotation symmetry is broken even in the continuum limit, and thus the low-energy physics is controlled by two dimensionless parameters: the dimensionless coupling constant and the ratio of the anisotropy parameters. We show that the former flows to zero and the latter flows to a fixed value at low energies. Thus, one may calculate physical quantities in terms of the renormalized perturbation theory. As an application, we determine the temperature dependence of the specific heat by solving the renormalization-group equations. Following from the breaking of the full rotation symmetry, there exists a crossover temperature scale $T_c$ (and a length scale $L_c$). Physical quantities approach the values for the first-order Dirac semimetal only when the temperature is much smaller than $T_c$. Similarly, the screened Coulomb potential will become anisotropic when the distance is smaller than $L_c$, while the unscreened form is recovered at its tail.

The effect of elastic anisotropy on the symmetry selection of irradiation-induced void superlattices in cubic metals

Self-organized microstructures and patterns have been widely observed in non-equilibrium physical systems. In particular, irradiation in metals creates far-from-equilibrium environments, in which the competing dynamics of defect production and annihilation can lead to unique self-organized superlattice structures, e.g., void and gas bubble superlattices. From a physical point of view, the superlattice structures are dictated by the intrinsic symmetry breaking in the metals, i.e., anisotropy caused by the breaking of continuous rotational symmetry. In the literature, two distinctive anisotropies, elastic anisotropy and diffusion anisotropy of interstitials, have been proposed to be the origins of superlattice formation. However, it is still unclear which anisotropy dominates the symmetry selection of superlattice structures. In this paper, we study elastic anisotropy and its effect on the symmetry of void superlattices. By using theoretical analyses and phase field simulations, we show that elastic anisotropy in cubic metals can lead to either face-centered cubic or simple cubic superlattices depending on the Zener anisotropy ratio. The superlattices formed under this elastic anisotropy mechanism must form under the influence of spinodal decomposition, as the mechanism requires perturbations in the vacancy concentration field to develop into spatially-static concentration waves. We compare to existing work on symmetry selection in superlattices via diffusion anisotropy and to experimental observations, and we suggest that concentration wave development under the influence of elastic anisotropy is not the mechanism for symmetry selection during the formation of irradiation-induced void superlattices, but that diffusion anisotropy could be the dominant mechanism.

Rotation symmetry breaking in the normal state of a kagome superconductor KV3Sb5

Recently discovered kagome superconductors AV3Sb5 (A=K, Rb, Cs) provide a fresh opportunity to realize and study correlation-driven electronic phenomena on a kagome lattice. The observation of a 2a0 by 2a0 charge density wave (CDW) in the normal state of all members of AV3Sb5 kagome family has generated an enormous amount of interest, in an effort to uncover the nature of this CDW state, and identify any "hidden" broken symmetries. We use spectroscopic-imaging scanning tunneling microscopy to reveal a pronounced intensity anisotropy between different 2a0 CDW directions in KV3Sb5. In particular, by examining the strength of ordering wave vectors as a function of energy in Fourier transforms of differential conductance maps, we find that one of the CDW directions is distinctly different compared to the other two. This observation points towards an intrinsic rotation symmetry broken electronic ground state, where the symmetry is reduced from C6 to C2. Furthermore, in contrast to previous reports, we find that the CDW phase is insensitive to magnetic field direction, regardless of the presence or absence of atomic defects. Our experiments, combined with earlier observations of a stripe 4a0 charge ordering in CsV3Sb5, establish correlation-driven rotation symmetry breaking as a unifying feature of AV3Sb5 kagome superconductors.

Endpoint symmetries of helicity amplitudes

We investigate helicity amplitudes (HAs) of A→BC-type decays for arbitrary spin towards the kinematic endpoint. We show that HAs are proportional to product of Clebsch-Gordan coefficients (CGC) and the velocity to a non-negative power. The latter can be zero in which case the HA is non-vanishing at the endpoint. At the kinematic endpoint the explicit breaking of rotational symmetry, through the external momenta, is restored and the findings can be interpreted as a special case of the Wigner-Eckart theorem. Our findings are useful for i) checking theoretical computations and ii) the case where there is a sequence of decays, say B→B1B2 with the pair (B1B2) not interacting (significantly) with the C-particle. Angular observables, which are ratios of HAs, are given by ratios of CGC at the endpoint. We briefly discuss power corrections in the velocity to the leading order.

Moiré nematic phase in twisted double bilayer graphene

Graphene moir\'e superlattices display electronic flat bands. At integer fillings of these flat bands, energy gaps due to strong electron-electron interactions are generally observed. However, the presence of other correlation-driven phases in twisted graphitic systems at non-integer fillings is unclear. Here, we report scanning tunneling microscopy (STM) measurements that reveal the existence of threefold rotational (C3) symmetry breaking in twisted double bilayer graphene (tDBG). Using spectroscopic imaging over large and uniform areas to characterize the direction and degree of C3 symmetry breaking, we find it to be prominent only at energies corresponding to the flat bands and nearly absent in the remote bands. We demonstrate that the C3 symmetry breaking cannot be explained by heterostrain or the displacement field, and is instead a manifestation of an interaction-driven electronic nematic phase, which emerges even away from integer fillings. Comparing our experimental data with a combination of microscopic and phenomenological modeling, we show that the nematic instability is not associated with the local scale of the graphene lattice, but is an emergent phenomenon at the scale of the moir\'e lattice, pointing to the universal character of this ordered state in flat band moir\'e materials.

Arc-shaped structure factor in the J1−J2−J3 classical Heisenberg model on the triangular lattice

We study the $J_1$-$J_2$-$J_3$ classical Heisenberg model with ferromagnetic $J_1$ on the triangular lattice using the nematic bond theory. For parameters where the momentum space coupling function $J_{\vec{q}}$ shows a discrete set of minima, we find that the system in general exhibits a single first-order phase transition between the high-temperature ring liquid and the low-temperature single-$\vec{q}$ planar spiral state. Close to where $J_{\vec{q}}$ shows a continuous minimum, we on the other hand find several phase transitions upon lowering the temperature. Most interestingly, we find an intermediate temperature "arc" regime, where the structure factor breaks rotational symmetry and shows a broad arc-shaped maximum. We map out the parameter region over which this arc regime exists and characterize details of its static structure factor over the same region.

Spontaneous symmetry breaking in persistent currents of spinor polaritons

We predict the spontaneous symmetry breaking in a spinor Bose–Einstein condensate of exciton-polaritons (polaritons) caused by the coupling of its spin and orbital degrees of freedom. We study a polariton condensate trapped in a ring-shaped effective potential with a broken rotational symmetry. We propose a realistic scheme of generating controllable spinor azimuthal persistent currents of polaritons in the trap under the continuous wave optical pump. We propose a new type of half-quantum circulating states in a spinor system characterized by azimuthal currents in both circular polarizations and a vortex in only one of the polarizations. The spontaneous symmetry breaking in the spinor polariton condensate that consists in the switching from co-winding to opposite-winding currents in opposite spin states is revealed. It is characterized by the change of the average orbital angular momentum of the condensate from zero to non-zero values. The radial displacement of the pump spot and the polarization of the pump act as the control parameters. The considered system exhibits a fundamental similarity to a superconducting flux qubit, which makes it highly promising for applications in quantum computing.

Ferromagnetic Weyl metal in EuAgP

The combination of band topology with magnetic ordering provides an excellent platform to realize various magnetic topological phases. Based on first-principle calculations and symmetry analysis, we predict that two distinct topological phases can be switched in the ferromagnetic material EuAgP by tuning the direction of magnetic moment. In the absence of spin-orbit coupling (SOC), the material is half-metallic with only one spin-up channel around the Fermi level, giving rise to a pair of triple points (TPs) along C6 axis, protected by the point group symmetry. As the magnetic moment is oriented along the z direction (with SOC included), the emergent TP in the absence of SOC splits into two Weyl points (WPs), featuring the nontrivial Fermi arcs on the side surface; however, when the magnetic moment is rotated to the x direction, a tiny band gap (<3.0 meV) appears around the TP due to the breaking of rotation symmetry, which can be regarded as the nearly TP. The intrinsic anomalous Hall conductivity of EuAgP is calculated for the different ferromagnetic states, which is sensitive to the magnetic ordering. Furthermore, we propose to realize the ideal Weyl semimetal with a single pair of WPs close to the Fermi level via partially substituting Eu by Ba.

D- and p-wave Quantum Liquid Crystal Orders in Cuprate Superconductors, κ-(BEDT-TTF)2X, and Coupled Chain Hubbard Models: Functional-renormalization-group Analysis

Unconventional symmetry breaking without spin order,such as the rotational symmetry breaking (=nematic or smectic) orders as well as the spontaneous loop-current orders, have been recently reported in cuprate superconductors and their related materials.They are theoretically represented by non-$A_{1g}$ symmetry breaking in self-energy, which we call the form factor $f_{k,q}$.In this paper, we analyze typical Hubbard models by applying the renormalization-group (RG) method, and find that various unconventional ordering emerges due to the quantum interference among spin fluctuations. Due to this mechanism,nematic ($q=0$) and smectic ($q \ne 0$)bond orders with $d$-wave form factor appear $f_{k,q}\propto \cos k_x - \cos k_y$ in both cuprates and $\kappa$-(BEDT-TTF)$_2$X. The derived bond orders naturally explain the pseudogap behaviors in these compounds. The quantum interference also induces various current orders with odd-parity form factor. For example, we find the emergence of the charge and spin loop-current orders with $p$-wave form factor in geometrically frustrated Hubbard models. Thus, rich quantum phase transitions with $d$- and $p$-wave form factors are driven by the paramagnon interference in many low-dimensional Hubbard models.

A Modular Design of Continuously Tunable Full Color Plasmonic Pixels with Broken Rotational Symmetry

AbstractColor tuning is a fascinating and indispensable property in various applications. Thus far, a variety of reconfigurable approaches have been implemented to achieve color change. However, it is still a challenge to enable continuous color tuning over the entire hue range in a simple, stable, and rapid manner without changes in configuration and material properties. Here, an all‐optical continuously tunable plasmonic pixel scheme is demonstrated via a modular design approach to realize polarization‐controlled full color tuning by breaking the intrinsic symmetry of the unit cell layout. The polarization‐controlled full color tunable plasmonic pixels consist of three different types of color modules corresponding to three subtractive primary colors. Without changing the structural properties or surrounding environment, the structural colors can be continuously and precisely tuned across all hues by illuminating linearly polarized light with different polarization directions. Meanwhile, the plasmonic pixels can be flexibly customized for various color tuning processes through the appropriate choice of component modules and the elaborate design of module layouts. Furthermore, the color tuning is extended to achromatic colors with the utilization of a single module or the introduction of a black module. The proposed plasmonic pixels hold considerable potential to function as next‐generation color pixels integrated with liquid‐crystal polarizers.

Rotational symmetry breaking on the Rydberg energy spectrum of indirect excitons in diamond studied by terahertz time-domain spectroscopy

We investigated the $1S\text{\ensuremath{-}}2P$ transitions of the indirect excitons in diamond around 70 meV in the high-frequency terahertz region via time-resolved Lyman spectroscopy. We discovered significant splitting of the $2P$ levels and attributed it to the rotational-symmetry-breaking effect owing to the cubic crystal environment. The maximum energy separation of 14.9 meV reached 18% of the excitonic Rydberg constant---83.5 \ifmmode\pm\else\textpm\fi{} 2.9 meV---which deviated from the binding energy of the $1S$ ground state: 93.3 \ifmmode\pm\else\textpm\fi{} 2.0 meV. In addition to the anisotropy of the valence bands, we found the impact of the rotational symmetry breaking of the conduction band valleys, which leads to a significant deviation from the case with direct excitons. Detailed knowledge of the ground and excited states of long-lifetime excitons provides an unprecedented opportunity to develop the study of quantum many-body physics and quantum chaos.

Revealing the competition between charge density wave and superconductivity in CsV3Sb5 through uniaxial strain

In this paper we report the impact of uniaxial strain $\varepsilon$ applied along the crystalline $a$ axis on the newly discovered kagome superconductor CsV$_3$Sb$_5$. At ambient conditions, CsV$_3$Sb$_5$ shows a charge-density wave (CDW) transition at $T_{\rm CDW}=94.5$ K and superconducts below $T_C = 3.34$ K. In our study, when the uniaxial strain $\varepsilon$ is varied from $-0.90\%$ to $0.90\%$, $T_C$ monotonically increases by $\sim 33\%$ from 3.0 K to 4.0 K, giving rise to the empirical relation $T_C (\varepsilon)=3.4+0.56\varepsilon+0.12\varepsilon^2$. On the other hand, for $\varepsilon$ changing from $-0.76\%$ to $1.26\%$, $T_{\rm CDW}$ decreases monotonically by $\sim 10\%$ from 97.5 K to 87.5 K with $T_{\rm CDW}(\varepsilon)=94.5-4.72\varepsilon-0.60\varepsilon^2$. The opposite response of $T_C$ and $T_{\rm CDW}$ to the uniaxial strain suggests strong competition between these two orders. Comparison with hydrostatic pressure measurements indicate that it is the change in the $c$-axis that is responsible for these behaviors of the CDW and superconducting transitions, and that the explicit breaking of the sixfold rotational symmetry by strain has a negligible effect. Combined with our first-principles calculations and phenomenological analysis, we conclude that the enhancement in $T_C$ with decreasing $c$ is caused primarily by the suppression of $T_{\rm CDW}$, rather than strain-induced modifications in the bare superconducting parameters. We propose that the sensitivity of $T_{\rm CDW}$ with respect to the changes in the $c$-axis arises from the impact of the latter on the trilinear coupling between the $M_1^+$ and $L_2^-$ phonon modes associated with the CDW. Overall, our work reveals that the $c$-axis lattice parameter, which can be controlled by both pressure and uniaxial strain, is a powerful tuning knob for the phase diagram of CsV$_3$Sb$_5$.

Supersolidity in Two-Dimensional Trapped Dipolar Droplet Arrays.

We theoretically investigate the ground states and the spectrum of elementary excitations across the superfluid to droplet crystallization transition of an oblate dipolar Bose-Einstein condensate. We systematically identify regimes where spontaneous rotational symmetry breaking leads to the emergence of a supersolid phase with characteristic collective excitations, such as the Higgs amplitude mode. Furthermore, we study the dynamics across the transition and show how these supersolids can be realized with standard protocols in state-of-the-art experiments.

Nematicity in a cuprate superconductor revealed by angle-resolved photoemission spectroscopy under uniaxial strain

The nature of the pseudogap and its relationship with superconductivity are one of the central issues of cuprate superconductors. Recently, a possible scenario has been proposed that the pseudogap state is a distinct phase characterized by spontaneous rotational symmetry breaking called “nematicity” based on transport and magnetic susceptibility measurements, where the symmetry breaking was observed below the pseudogap temperature T∗. Here, we report a temperature-dependent ARPES study of nematicity in slightly overdoped Bi1.7Pb0.5Sr1.9CaCu2O8+δ triggered by a uniaxial strain applied along one of the Cu–O bond directions. While the nematicity was enhanced in the pseudogap state as in the previous studies, it was suppressed in the superconducting state. These results indicate that the pseudogap state is characterized by spontaneous rotational symmetry breaking and that the nematicity may compete with superconductivity. Relationship between the nematicity and charge-density waves, both of which are observed in the pseudogap state, is discussed.

Fundamental challenges induced by phase modulation inaccuracy and optimization guidelines of geometric phase metasurfaces with broken rotation symmetry.

Geometric phase metasurfaces feature complete phase manipulation of light at the nanoscale. While a majority of prior works assume the structure rotation in a fixed lattice of unit cells as equivalent to the element rotation required by the geometric phase principle, we argue that this assumption is fundamentally challenged for many current schematics which induce phase modulation inaccuracy. Here we take the dielectric nanobar type geometric phase metasurfaces as an example and perform an in-depth analysis about the physical origins of the phase modulation inaccuracy: imperfect structure rotation, resonance, tilted incidence and aperiodic arrays. We clarify the trade-off in phase modulation accuracy, efficiency, broadband property and wide angle acceptance. Furthermore, we present several examples of geometric phase metasurface devices to evaluate the performance degradation under different applications. Finally, based on the research, we provide a set of practical design and optimization guidelines to outperform the present devices of geometric phase metasurface.

Cascade of correlated electron states in the kagome superconductor CsV3Sb5.

The kagome lattice of transition metal atoms provides an exciting platform to study electronic correlations in the presence of geometric frustration and nontrivial band topology1-18, which continues to bear surprises. Here, using spectroscopic imaging scanning tunnelling microscopy, we discover a temperature-dependentcascade of different symmetry-broken electronic states in a new kagome superconductor, CsV3Sb5. We reveal, at a temperature far above the superconducting transition temperature Tc ~ 2.5 K, a tri-directional charge order with a 2a0 period that breaks the translation symmetry of the lattice. As the system is cooled down towards Tc, we observe a prominent V-shaped spectral gap opening at the Fermi level and an additional breaking of the six-fold rotational symmetry, which persists through the superconducting transition. This rotational symmetry breaking is observed as the emergence of an additional 4a0 unidirectional charge order and strongly anisotropic scattering in differential conductance maps. The latter can be directly attributed to the orbital-selective renormalization of the vanadium kagome bands. Our experiments reveal a complex landscape of electronic states that can coexist on a kagome lattice, and highlight intriguing parallels to high-Tc superconductors and twisted bilayer graphene.

Discovery of mesoscopic nematicity wave in iron-based superconductors

Patterned nematics Electrons in solids can break rotational symmetry, resulting in electronic nematicity. This phenomenon has been observed in both cuprate-based and iron-based high-temperature superconductors, and its relationship to superconductivity remains a subject of debate. Shimojima et al . used linear dichroism measurements to image nematicity in two iron-based superconductors. Unexpectedly, the researchers found periodic patterns with very long wavelengths. The findings could be described with a phenomenological model assuming a train of nematic domain walls. —JS