Peierls Phase Research Articles

Flat-band conditions influenced by spin-orbit interaction in the presence of external magnetic field

We deduct conditions for the Hamiltonian coupling strengths necessary to achieve flat bands in polymers (i.e. a pentagon chain) considering many-body spin-orbit coupling and external magnetic field. We consider itinerant electrons on pentagon chains with first neighbour hoppings, on-site electron potentials and spin-flip first neighbour hoppings representing the Rashba type spin-orbit interaction (SOI). The external magnetic field is also present in the system via the Peierls phase factors. The band structure is obtained by solving the secular equation of the diagonalized one particle part of the Hamiltonian in k-space (momentum-space). The flat band conditions make the bands k-independent, providing a highly a degenerate state, which gives broad possibilities for applications. In our work we have shown how the SOI is able to relax the strict, rigid flat band conditions given by the Hamiltonian coupling strengths. The role of the external magnetic field was also investigated.

Reconstruction of the Fermi surface induced by high magnetic field in the quasi-two-dimensional charge density wave conductor η−Mo4O11

Low-dimensional charge density wave (CDW) systems, which undergo successive so-called Peierls phase transitions at characteristic temperatures associated with corresponding changes in electronic structure, are of great importance for exploring novel quantum physics. Here, we report systematic research of the magnetotransport properties for the quasi-two-dimensional CDW conductor $\ensuremath{\eta}\text{\ensuremath{-}}\mathrm{M}{\mathrm{o}}_{4}{\mathrm{O}}_{11}$ under high magnetic fields up to 59 T. Measurements of in-plane and out-of-plane magnetoresistance and Hall resistance have been carried out to determine the Fermi surface (FS) structure at low temperatures and high magnetic fields. Beyond the quantum limit (QL), fast quantum oscillations (QOs) with complex periods have been found in both MR and Hall resistance, representing a direct measurement of the area of the FS. In addition, we observe a conspicuous phase transition at 45 T. The QO frequency and carrier density successively increase above the QL and phase transition fields. Consequently, we propose that such remarkable feature of the magnetic field dependence of the fast QOs for $\ensuremath{\eta}\text{\ensuremath{-}}\mathrm{M}{\mathrm{o}}_{4}{\mathrm{O}}_{11}$ arises from the field-induced density wave transition and FS reconstruction. We have further discussed the mechanism and provided the evolution on the geometry of the FS with magnetic field in the second CDW state based on the field-dependent FS model.

Observation of gauge invariance in a 71-site Bose-Hubbard quantum simulator.

The modern description of elementary particles, as formulated in the standard model of particle physics, is built on gauge theories1. Gauge theories implement fundamental laws of physics by local symmetry constraints. For example, in quantum electrodynamics Gauss's law introduces an intrinsic local relation between charged matter and electromagnetic fields, which protects many salient physical properties, including massless photons and a long-ranged Coulomb law. Solving gauge theories using classical computers is an extremely arduous task2, which has stimulated an effort to simulate gauge-theory dynamics in microscopically engineered quantum devices3-6. Previous achievements implemented density-dependent Peierls phases without defining a local symmetry7,8, realized mappings onto effective models to integrate out either matter or electric fields9-12, or were limited to very small systems13-16. However, the essential gauge symmetry has not been observed experimentally. Here we reportthe quantum simulation of an extended U(1) lattice gauge theory, and experimentally quantify the gauge invariance in a many-body system comprising matter and gauge fields. Thesefields are realized in defect-free arrays of bosonic atoms in an optical superlattice of 71 sites. We demonstrate full tunability of the model parameters and benchmark the matter-gauge interactions by sweeping across a quantum phase transition. Using high-fidelity manipulation techniques, we measure the degree to which Gauss's law is violated by extracting probabilities of locally gauge-invariant states from correlated atom occupations. Our work provides a way to explore gauge symmetry in the interplay of fundamental particles using controllable large-scale quantum simulators.

Peierls-phase-induced topological semimetals in an optical lattice: Moving of Dirac points, anisotropy of Dirac cones, and hidden symmetry protection

We propose a square optical lattice in which some of neighbor hoppings have a Peierls phase. The Peierls phase makes the lattice have a special band structure and induces the existence of Dirac points in the Brillouin zone, which means that topological semimetals exist in the system. The Dirac points move with the change of the Peierls phase and the Dirac cones are anisotropic for some vales of the Peierls phase. The lattice has a novel hidden symmetry, which is a composite antiunitary symmetry composed of a translation operation, a sublattice exchange, a complex conjugation, and a local U(1) gauge transformation. We prove that the Dirac points are protected by the hidden symmetry and perfectly explain the moving of Dirac points with the change of the Peierls phase based on the hidden symmetry protection.

Photoinduced η -pairing at finite temperatures

We numerically prove photoinduced $\eta$-pairing in a half-filled fermionic Hubbard chain at both zero and finite temperature. The result, obtained by combining the matrix-product-state based infinite time-evolving block decimation technique and the purification method, applies to the thermodynamic limit. Exciting the Mott insulator by a laser electric field docked on via the Peierls phase, we track the time-evolution of the correlated many-body system and determine the optimal parameter set for which the nonlocal part of the $\eta$-pair correlation function becomes dominant during the laser pump at zero and low temperatures. These correlations vanish at higher temperatures and long times after pulse irradiation. In the high laser frequency strong Coulomb coupling regime we observe a remnant enhancement of the Brillouin-zone boundary pair-correlation function also at high temperatures, if the Hubbard interaction is about a multiple of the laser frequency, which can be attributed to an enhanced double occupancy in the virtual Floquet state.

Light splitting and stopping and their combination via controllable Bloch oscillation in a lattice

We study controllable Bloch oscillation and its potential applications in a one-dimensional lattice with partly phase-modulated hopping rates. Under proper conditions, such a system can be built by using a quasi-one-dimensional sawtooth lattice with Peierls phases induced by a synthetic magnetic field. The amplitude of the Bloch oscillation can be adjusted precisely and continuously by adjusting the phase, and hence we realize tunable light splitting in the presence of a V-type potential. Moreover, we construct two distinct sandwich structures to realize tunable light stopping and delayed splitting, respectively, of which the stopping and delay durations are tunable. Our proposal may imply exciting opportunities for potential applications in optical communications and photonic device fabrication involving unconventional light transports.

Spinless Fulde–Ferrell superfluid in Haldane model with nearest-neighbor interaction

Fulde–Ferrell (FF) state is an exotic superconducting or superfluid state, characterized by Cooper pairs with a finite center-of-mass momentum, and it has been intensively investigated in spinful systems, but the spin population imbalance is usually necessary. Here we propose a model to realize and modulate the spinless FF superfluid, namely, Haldane model with nearest-neighbor interaction. The FF state appears when the space-inversion and time-reversal symmetries are broken simultaneously, and there exists the first order phase transition. A higher Berezinskii–Kosterlitz–Thouless transition temperature is obtained at larger absolute value of Peierls phase and smaller energy offset of the sublattices. Our proposal provides a feasible option for experimental researchers to detect the FF superfluid.

Electromagnetic coupling in tight-binding models for strongly correlated light and matter

We discuss the construction of low-energy tight-binding Hamiltonians for condensed matter systems with a strong coupling to the quantum electromagnetic field. Such Hamiltonians can be obtained by projecting the continuum theory on a given set of Wannier orbitals. However, different representations of the continuum theory lead to different low-energy formulations, because different representations may entangle light and matter, transforming orbitals into light-matter hybrid states before the projection. In particular, a multi-center Power-Zienau-Woolley transformation yields a dipolar Hamiltonian which incorporates the light-matter coupling via both Peierls phases and a polarization density. We compare this dipolar gauge Hamiltonian and the straightforward Coulomb gauge Hamiltonian for a one-dimensional solid, to describe sub-cycle light-driven electronic motion in the semiclassical limit, and a coupling of the solid to a quantized cavity mode which renormalizes the band-structure into electron-polariton bands. Both descriptions yield the same result when many bands are taken into account, but the dipolar Hamiltonian is more accurate when the model is restricted to few electronic bands, while the Coulomb Hamiltonian requires fewer electromagnetic modes.

Realization of a Density-Dependent Peierls Phase in a Synthetic, Spin-Orbit Coupled Rydberg System

We experimentally realize a Peierls phase in the hopping amplitude of excitations carried by Rydberg atoms, and observe the resulting characteristic chiral motion in a minimal setup of three sites. Our demonstration relies on the intrinsic spin-orbit coupling of the dipolar exchange interaction combined with time-reversal symmetry breaking by a homogeneous external magnetic field. Remarkably, the phase of the hopping amplitude between two sites strongly depends on the occupancy of the third site, thus leading to a correlated hopping associated to a density-dependent Peierls phase. We experimentally observe this density-dependent hopping and show that the excitations behave as anyonic particles with a non-trivial phase under exchange. Finally, we confirm the dependence of the Peierls phase on the geometrical arrangement of the Rydberg atoms.

Controllable unidirectional transport and light trapping using a one-dimensional lattice with non-Hermitian coupling

We propose a one-dimensional tight-binding lattice with special non-Hermitian coupling, the imaginary part of which is modulated by an effective Peierls phase arising from the synthetic magnetic field. Such a non-Hermitian lattice supports robust unidirectional transport that is reflectionless and immune to defects; it thus can serve as a frequency-selectable light filter. To achieve more applications, we further construct two well-designed structures involving this lattice, namely a heterostructure and a sandwich structure. An optical diode can be realized using the heterostructure, while tunable light trapping and reversal can be realized through phase modulations on the sandwich structure. The results in this paper may not only open up a new path for unconventional light transport but also have potential applications for optical communication.

Bose–Einstein condensates in rotating ring-shaped lattices: a multimode model

We develop a multimode model that describes the dynamics on a rotating Bose–Einstein condensate confined by a ring-shaped optical lattice with large filling numbers. The parameters of the model are obtained as a function of the rotation frequency using full 3D Gross–Pitaevskii simulations. From such numerical calculations, we extract the velocity field induced at each site and analyze the relation and the differences between the phase of the hopping parameter of our model and the Peierls phase. To this end, a detailed discussion of such phases is presented in geometrical terms which takes into account the position of the junctions for different configurations. For circularly symmetric onsite densities a simple analytical relation between the hopping phase and the angular momentum is found for arbitrary number of sites. Finally, we confront the results of the rotating multimode model dynamics with Gross–Pitaevskii simulations finding a perfect agreement.

Angular momentum supercontinuum from fibre rings

Broadband, coherent light carrying optical angular momentum (AM) is of potential utility for a variety of classical and quantum communication applications, but at present few such sources exist. We study the theory of generation of supercontinua in a ring array of coupled optical fibres. Short pulses carrying discrete AM undergo soliton fission, spontaneously breaking azimuthal symmetry. This results in a train of pulses with a broadband frequency spectrum as well as a non-trivial AM distribution. These spatio-temporal solitary waves, localised around a single fibre core, emit an unusual form of resonant radiation which can be present even in the absence of intrinsic higher order dispersion, being induced by the lattice dispersion of the ring array. We explore how the coupling properties between fibre cores affect the resulting supercontinuum, in particular how mildly twisting the array can effectively manipulate its AM content and resonant frequencies through the induced Peierls phase.

Sequential insulating-metal-insulating phase transition of NbO2 by doping photoexcited carrier

A large number of free carriers are introduced in the photoexcitation process and the complex interaction between photoexcited carriers and lattice can lead to an ultrafast phase transition in the solid. Niobium dioxide is an important optical material, which exhibiting a threshold switching phenomenon that can be explained by insulating-metal phase transition. It can be used as an ultrafast optical switches for telecommunication and optoelectronic devices. Here, we investigated the effects of injecting photoexcited carriers on consecutive insulator-metal-insulator phase transition of NbO2 by applying the GGA and GGA + U energy functions on the basis of density functional theory (DFT). Compared with electron injection, the effect of hole doping on phase transition in NbO2 is significantly more effective. The length of Nb-Nb dimer (long or short) is nearly unchanged upon electron doping, while the length of Nb-Nb_l is gradual shortened from 3.366 to 3.039 Å and the Nb-Nb_s is gradual stretched from 2.733 to 3.035 Å upon hole doping below a critical level of doping 12 holes per conventional cell. The structure phase changed from a body-center tetragonal (bct) to a rutile. Upon a higher hole doping, the structure kept the rutile structure until the number of doping holes reached 28 and it began to change to bct structure. We studied the electronic properties of NbO2 at a certain carriers concentration and reported a controlled and reversible insulator-metal-insulator phase transition by carries doping. The coexistence of the strong electron correlation and the Nb-Nb dimerization due to lattice distortion obscures the nature of the phase transition in NbO2. By analyzing the evolutions of lattice parameters and electronic properties of NbO2 at different charge carrier concentration, we got a conclusion that this sequential phase transition of NbO2 is not just a Mott phase transition or Peierls phase transition, but a collaborative of Peierls-Mott phase transition. Our work confirms that the observed structural transformations are driven primarily by hole doping, and the dominant lattice distortion caused by hole doping is the off-centering of Nb atoms in NbO6 octahedral.

Floquet-Engineered Vibrational Dynamics in a Two-Dimensional Array of Trapped Ions

We demonstrate Floquet engineering in a basic yet scalable 2D architecture of individually trapped and controlled ions. Local parametric modulations of detuned trapping potentials steer the strength of long-range interion couplings and the related Peierls phase of the motional state. In our proof of principle, we initialize large coherent states and tune modulation parameters to control trajectories, directions, and interferences of the phonon flow. Our findings open a new pathway for future Floquet-based trapped-ion quantum simulators targeting correlated topological phenomena and dynamical gauge fields.

Time-Dependent Coupled Cluster Theory on the Keldysh Contour for Nonequilibrium Systems.

We leverage the Keldysh formalism to extend our implementation of finite temperature coupled cluster theory [J. Chem. Theory Comput. 2018, 14, 5690-5700] to thermal systems that have been driven out of equilibrium. The resulting Keldysh coupled cluster theory is discussed in detail. We describe the implementation of the equations necessary to perform Keldysh coupled cluster singles and doubles calculations of finite-temperature dynamics, and we apply the method to some simple systems including a Hubbard model with a Peierls phase and an ab initio model of warm-dense silicon subject to an ultrafast XUV pulse.

Orbital magnetic field effects in Mott insulators with strong spin-orbit coupling

We study the effect of a magnetic field on the low energy description of Mott insulators with strong spin-orbit (SO) coupling. In contrast to the standard case of the Hubbard model without SO coupling, we show that Peierls phases can modulate the magnetic exchange at leading order in the interaction. Our mechanism crucially depends on the existence of distinct exchange paths between neighboring magnetic ions enclosing a well-defined area. Thus it will generically be present in any solid state realisation of the Kitaev model and its extensions. We explicitly calculate the variation of the exchange constants of the so-called $JK\Gamma$ model as a function of the magnetic flux. We discuss experimental implications of our findings for various settings of candidate Kitaev spin liquids.

Realization of density-dependent Peierls phases to engineer quantized gauge fields coupled to ultracold matter

Gauge fields that appear in models of high-energy and condensed matter physics are dynamical quantum degrees of freedom due to their coupling to matter fields. Since the dynamics of these strongly correlated systems is hard to compute, it was proposed to implement this basic coupling mechanism in quantum simulation platforms with the ultimate goal to emulate lattice gauge theories. Here, we realize the fundamental ingredient for a density-dependent gauge field acting on ultracold fermions in an optical lattice by engineering non-trivial Peierls phases that depend on the site occupations. We propose and implement a Floquet scheme that relies on breaking time-reversal symmetry (TRS) by driving the lattice simultaneously at two frequencies which are resonant with the onsite interactions. This induces density-assisted tunnelling processes that are controllable in amplitude and phase. We demonstrate techniques in a Hubbard dimer to quantify the amplitude and to directly measure the Peierls phase with respect to the single-particle hopping. The tunnel coupling features two distinct regimes as a function of the modulation amplitudes, which can be characterised by a $\mathbb{Z}_2$-invariant. Moreover, we provide a full tomography of the winding structure of the Peierls phase around a Dirac point that appears in the driving parameter space.

Phase-dependent topological interface state and spatial adiabatic passage in a generalized Su-Schrieffer-Heeger model

We extend the Su-Schrieffer-Heeger model to include both an additional real intercell coupling and a complex intracell coupling whose phase can be interpreted as the Peierls phase associated with a synthetic gauge field. Using different Peierls phases, we can realize a heterostructure supporting a topologically protected interface state, depending on the existence of one trivial and two nontrivial phases of distinct winding numbers. The spatial adiabatic passage of this localized state from the inner interface to either open boundary can be attained simply by modulating the corresponding Peierls phase, while its decay or growth rate is controlled by the on-site parity-time symmetric loss and gain terms. Our results provide a scheme to achieve dynamical control of topologically protected states while being of potential interest to topological lasers with an adjustable spatial profile.

Modulation instability of discrete angular momentum in coupled fiber rings

We present an analysis of temporal modulation instability in a ring array of coupled optical fibers. Continuous-wave signals are shown to be unstable to perturbations carrying discrete angular momenta, both for normal and anomalous group velocity dispersion. We find the frequency spectrum of modulation instability is different for each perturbation angular momentum and depends strongly on the coupling strength between fibers in the ring. Twisting the ring array also allows the frequency spectra to be tuned through the induced tunnelling Peierls phase.

Perubahan Panjang Lokalisasi dan Kerapatan Keadaan Elektron pada Molekul DNA Poli(dA)-Poli(dT) Karena Medan Magnet

The localization length and the Density Of State (DOS) of electron in a Poly(dA)-Poly(dT) DNA molecule at two temperatures have been calculated for several values of magnetic field. The calculation are carried out on a DNA molecule model that consists of adenine (A) and Thymine (T) nucleobases and sugar-phosphate backbone . The DNA molecule is modeled in tight binding Hamiltonian approach with semi empiri cal Slater-Koster theory and Peierls phase factor for introducing the effect of temperature and magnetic field, respectively . In the model, electron is allowed to move between nucleobase sites, backbode sites, and between backbone site and nucleobase site. The localization length is obtained from the smallest Lyapunov exponent which is calculated using transfer matri x method along with Gram-Schmidt ort h onormali zation procedure . The DOS is calculated using Green ’s function method by taking into account the presence of metallic electrode at both ends of the DNA molecule . The localization length and the DOS change as a result of the change in electron wave phase due to magnetic field. The change is observed at both temperature used in the study, but the change at lower temperature is larger than the one at higher temperature. Thermally agitated vibrational twisting motion perturbs electron motion in the DNA molecule such that the influence of magnetic field on the localization length and the DOS of electron at higher temperature becomes smaller.