Degeneracy

Dirac Fermions with different helicities exist on the top and bottom surfaces of topological insulators, offering a rare opportunity to break the degeneracy protected by the no-go theorem. Through the application of Co clusters, quantum Hall plateaus were modulated for the topological insulator BiSbTeSe2, allowing an optimized surface transport. Here, using renormalization group flow diagrams, we show the extraction of two sets of converging points in the conductivity tensor space, revealing that the top surface exhibits an anomalous quantization trajectory, while the bottom surface retains the 1/2 quantization...

Topological insulators constitute a new phase of matter protected by symmetries. Time-reversal symmetry protects strong topological insulators of the Z2 class, which possess an odd number of metallic surface states with dispersion of a Dirac cone. Topological crystalline insulators are merely protected by individual crystal symmetries and exist for an even number of Dirac cones. Here, we demonstrate that Bi-doping of Pb1-x Sn x Se (111) epilayers induces a quantum phase transition from a topological crystalline insulator to a Z2 topological insulator...

We develop the theory of all-dielectric absorbers based on temporal coupled mode theory (TCMT), with parameters extracted from eigenfrequency simulations. An infinite square array of cylindrical resonators embedded in air is investigated, and we find that it supports two eigenmodes of opposite symmetry that are each responsible for half of the total absorption. The even and odd eigenmodes are found to be the hybrid electric (EH111) and hybrid magnetic (HE111) waveguide modes of a dielectric wire of circular cross section, respectively...

We experimentally demonstrate spatial mode multiplexing of optical beams using multiplexed volume holographic gratings (MVGHs) formed in phenanthrenquinone-poly (methyl methacrylate) (PQ-PMMA) photopolymer. Multiple spatial modes of Laguerre-Gaussian (LG) beams are recorded at the same pupil area of a volume hologram resulting in MVHGs, for simultaneous reconstruction of spatial modes. In addition, a helical phase beam, a non-diffracting beam with conical phase profile, and a parabolic non-diffracting beam with cubic phase profile have also been simultaneously recorded and reconstructed from MVHGs...

Magnetic honeycomb iridates are thought to show strongly spin-anisotropic exchange interactions which, when highly frustrated, lead to an exotic state of matter known as the Kitaev quantum spin liquid. However, in all known examples these materials magnetically order at finite temperatures, the scale of which may imply weak frustration. Here we show that the application of a relatively small magnetic field drives the three-dimensional magnet β-Li2IrO3 from its incommensurate ground state into a quantum correlated paramagnet...

The high magnetic field electronic structure of bilayer graphene is enhanced by the spin, valley isospin, and an accidental orbital degeneracy, leading to a complex phase diagram of broken symmetry states. Here, we present a technique for measuring the layer-resolved charge density, from which we directly determine the valley and orbital polarization within the zero energy Landau level. Layer polarization evolves in discrete steps across 32 electric field-tuned phase transitions between states of different valley, spin, and orbital order, including previously unobserved orbitally polarized states stabilized by skew interlayer hopping...

Colloidal semiconductor quantum dots are attractive materials for the realization of solution-processable lasers. However, their applications as optical-gain media are complicated by a non-unity degeneracy of band-edge states, because of which multiexcitons are required to achieve the lasing regime. This increases the lasing thresholds and leads to very short optical gain lifetimes limited by nonradiative Auger recombination. Here, we show that these problems can be at least partially resolved by employing not neutral but negatively charged quantum dots...

Symmetry degree is utilized to characterize the asymmetry of a physical system with respect to a symmetry group. The scalar form of symmetry degree (SSD) based on Frobenius-norm has been introduced recently to present a quantitative description of symmetry. Here we present the vector form of the symmetry degree (VSD) which possesses more advantages than the SSD. Mathematically, the dimension of VSD is defined as the conjugacy class number of the symmetry group, the square length of the VSD gives rise to the SSD and the direction of VSD is determined by the orders of the conjugacy classes...

Inbreeding depression is widely hypothesised to drive adaptive evolution of pre-copulatory and post-copulatory mechanisms of inbreeding avoidance, which in turn are hypothesised to affect evolution of polyandry (i.e., female multiple mating). However, surprisingly little theory or modelling critically examines selection for pre-copulatory or post-copulatory inbreeding avoidance, or both strategies, given evolutionary constraints and direct costs, or examines how evolution of inbreeding avoidance strategies might feed back to affect evolution of polyandry...

Atomically thin monolayer transition metal dichalcogenides possess coupling of spin and valley degrees of freedom. The chirality is locked to identical valleys as a consequence of spin-orbit coupling and inversion symmetry breaking, leading to a valley analog of the Zeeman effect in presence of an out-of-plane magnetic field. Owing to the inversion symmetry in bilayers, the photoluminescence helicity should no longer be locked to the valleys. Here we show that the Zeeman splitting, however, persists in 2H-MoTe2 bilayers, as a result of an additional degree of freedom, namely the layer pseudospin, and spin-valley-layer locking...

The orbital effect on the Fulde-Ferrell (FF) phase is investigated in superconducting core/shell nanowires subjected to the axial magnetic field. The confinement in the radial direction results in the quantization of the electron motion with energies determined by the radial $j$ and orbital $m$ quantum numbers. In the external magnetic field the twofold degeneracy with respect to the orbital magnetic quantum number $m$ is lifted which leads to the Fermi wave vector mismatch between the paired electrons $(k, j,m,\uparrow) \leftrightarrow (-k, j,-m,\downarrow)$...

Strong spin-orbit coupling lifts the degeneracy of t 2g orbitals in 5d transition-metal systems, leaving a Kramers doublet and quartet with effective angular momentum of J eff = 1/2 and 3/2, respectively. These spin-orbit entangled states can host exotic quantum phases such as topological Mott state, unconventional superconductivity, and quantum spin liquid. The lacunar spinel GaTa4Se8 was theoretically predicted to form the molecular J eff = 3/2 ground state. Experimental verification of its existence is an important first step to exploring the consequences of the J eff = 3/2 state...

Mechanical properties of biological cells play a role in cell locomotion, embryonic tissue formation, and tumor migration among many other processes. Cells exhibit a complex nonlinear response to mechanical cues that is not understood. Cells may stiffen as well as soften, depending on the exact type of stimulus. Here we apply large-amplitude oscillatory shear to a monolayer of separated fibroblast cells suspended between two plates. Although we apply identical steady-state excitations, in response we observe different typical regimes that exhibit cell softening or cell stiffening to varying degrees...

Charge ordering (CO) is a phenomenon in which electrons in solids crystallize into a periodic pattern of charge-rich and charge-poor sites owing to strong electron correlations. This usually results in long-range order. In geometrically frustrated systems, however, a glassy electronic state without long-range CO has been observed. We found that a charge-ordered organic material with an isosceles triangular lattice shows charge dynamics associated with crystallization and vitrification of electrons, which can be understood in the context of an energy landscape arising from the degeneracy of various CO patterns...

In this Letter, we explore the dispersion of spoof surface plasmons supported by a single-layer glide-symmetric structure. This structure consists of an infinitely long double-notched slot perforated in a metal layer. The presence of a degeneracy of the two lowest-order modes at the Brillouin zone boundary, which have non-zero group velocity is explained and experimentally demonstrated. Further, the dependence of the band structure when glide-symmetric configuration is broken is also explored.

Energy or quasienergy (QE) band spectra depending on two parameters may have a nontrivial topological characterization by Chern integers. Band spectra of one-dimensional (1D) systems that are spanned by just one parameter, a Bloch phase, are topologically trivial. Recently, an ensemble of 1D Floquet (time-periodic) systems, double-kicked rotors (DKRs) that are classically nonintegrable and depend on an external parameter, has been studied. It was shown that a QE band spanned by both the Bloch phase and the external parameter is characterized by a Chern integer...

We report on combined measurements of heat and charge transport through a single-electron transistor. The device acts as a heat switch actuated by the voltage applied on the gate. The Wiedemann-Franz law for the ratio of heat and charge conductances is found to be systematically violated away from the charge degeneracy points. The observed deviation agrees well with the theoretical expectation. With a large temperature drop between the source and drain, the heat current away from degeneracy deviates from the standard quadratic dependence in the two temperatures...

A central requirement for any quantum error correction scheme is the ability to perform quantum nondemolition measurements of an error syndrome, corresponding to a special symmetry property of the encoding scheme. It is in particular important that such a measurement does not introduce extra error mechanisms, not included in the error model of the correction scheme. In this Letter, we ensure such a robustness by designing an interaction with a measurement device that preserves the degeneracy of the measured observable...

The current work presents a new single-reference method for capturing at the same time the static and dynamic electron correlation. The starting point is a determinant wave function formed with natural orbitals obtained from a new interacting-pair model. The latter leads to a natural orbital functional (NOF) capable of recovering the complete intrapair, but only the static interpair correlation. Using the solution of the NOF, two new energy functionals are defined for both dynamic (E^{dyn}) and static (E^{sta}) correlation...

We provide an experimental framework where periodically driven PT-symmetric systems can be investigated. The setup, consisting of two ultra high frequency oscillators coupled by a time-dependent capacitance, demonstrates a cascade of PT-symmetric broken domains bounded by exceptional point degeneracies. These domains are analyzed and understood using an equivalent Floquet frequency lattice with local PT symmetry. Management of these PT-phase transition domains is achieved through the amplitude and frequency of the drive...