Peierls Insulator Research Articles

The topological soliton in Peierls semimetal Sb

Sb is a three-dimensional Peierls insulator. The Peierls instability gives rise to doubling of the translational period along the [111] direction and alternating van der Waals and covalent bonding between (111) atomic planes. At the (111) surface of Sb, the Peierls condition is violated, which in theory can give rise to properties differing from the bulk. The atomic and electronic structure of the (111) surface of Sb have been simulated by density functional theory calculations. We have considered the two possible (111) surfaces, containing van der Waals dangling bonds or containing covalent dangling bonds. In the models, the surfaces are infinite and the structure is defect free. Structural optimization of the model containing covalent dangling bonds results in strong deformation, which is well described by a topological soliton within the Su–Schrieffer–Heeger model centered about 25 Å below the surface. The electronic states associated with the soliton see an increase in the density of states (DOS) at the Fermi level by around an order of magnitude at the soliton center. Scanning tunneling microscopy and spectroscopy (STM/STS) measurements reveal two distinct surface regions, indicating that there are different surface regions cleaving van der Waals and covalent bonds. The DFT is in good agreement with the STM/STS experiments.

Emergence of exotic electronic and magnetic phases upon electron filling in Na2BO3 (B = Ta, Ir, Pt, and Tl): a first-principles study.

Competition between spin-orbit interaction and electron correlations can stabilize a variety of non-trivial electronic and magnetic ground states. Using density functional theory calculations, here we show that different exotic electronic and magnetic ground states can be obtained by electron filling of the B-site cation in the Na2BO3 family of compounds (B = Ta, Ir, Pt and Tl). Electron filling leads to a Peierls insulator state with a direct band gap to j = 1/2 spin-orbit assisted Mott-insulator to band insulator and then to negative charge-transfer half-metal transition. The magnetic ground state also undergoes a transition from a non-magnetic state to a zigzag antiferromagnetic state, a re-entrant non-magnetic state and finally to a ferromagnetic state. The electron localization function shows a ladder type dimerization or Peierls instability in Na2TaO3. Maximally localized Wannier function calculations reveal delocalization of electrons through the eg orbitals, which form a π bond, and localization of electrons through the t2g orbitals, which form a σ bond, between the neighbouring tantalum ions. Na2TlO3 shows Stoner or band ferromagnetism due to the localized moments with up-spin on oxygen ligands created by the negative charge-transfer character, interacting via the down-spin itinerant electrons of the Tl 5d-O 2p hybridized band. These findings are significant for practical applications; for instance the direct band gap insulator Na2TaO3 shows potential for utilisation in solar cells, while Na2TlO3, which exhibits ferromagnetic half metallicity, holds promise for spintronic device applications.

Higher-Order Topological Peierls Insulator in a Two-Dimensional Atom-Cavity System.

In this work, we investigate a two-dimensional system of ultracold bosonic atoms inside an optical cavity, and show how photon-mediated interactions give rise to a plaquette-ordered bond pattern in the atomic ground state. The latter corresponds to a 2D Peierls transition, generalizing the spontaneous bond dimerization driven by phonon-electron interactions in the 1D Su-Schrieffer-Heeger (SSH) model. Here the bosonic nature of the atoms plays a crucial role to generate the phase, as similar generalizations with fermionic matter do not lead to a plaquette structure. Similar to the SSH model, we show how this pattern opens a nontrivial topological gap in 2D, resulting in a higher-order topological phase hosting corner states, that we characterize by means of a many-body topological invariant and through its entanglement structure. Finally, we demonstrate how this higher-order topological Peierls insulator can be readily prepared in atomic experiments through adiabatic protocols. Our work thus shows how atomic quantum simulators can be harnessed to investigate novel strongly correlated topological phenomena beyond those observed in natural materials.

Devil's staircase of topological Peierls insulators and Peierls supersolids

We consider a mixture of ultracold bosonic atoms on a one-dimensional lattice described by the XXZ-Bose-Hubbard model, where the tunneling of one species depends on the spin state of a second deeply trapped species. We show how the inclusion of antiferromagnetic interactions among the spin degrees of freedom generates a Devil's staircase of symmetry-protected topological phases for a wide parameter regime via a bosonic analog of the Peierls mechanism in electron-phonon systems. These topological Peierls insulators are examples of symmetry-breaking topological phases, where long-range order due to spontaneous symmetry breaking coexists with topological properties such as fractionalized edge states. Moreover, we identify a region of supersolid phases that do not require long-range interactions. They appear instead due to a Peierls incommensurability mechanism, where competing orders modify the underlying crystalline structure of Peierls insulators, becoming superfluid. Our work show the possibilities that ultracold atomic systems offer to investigate strongly-correlated topological phenomena beyond those found in natural materials.

Mott-Insulator to Peierls Insulator Transition in the Two-Dimensional Holstein-Hubbard Model

We propose a variational study of the two dimensional square lattice to study the phase transition from an antiferromagnetic SDW Mott insulator to the bipolaronic CDW Peierls insulator for the half-filled Holstein Hubbard model. The correlated system is dealt analytically in two different regimes according to the renormalized Coulomb correlation strength. Different unitary transformations are performed to obtain an effective electronic Hamiltonian which is solved by using the mean-field Hartree-Fock approximation for the weakly correlated electrons. For the strong interaction case, the Zuberev’s Green function technique is used to solve the effective t-J model at the mean field limit. The variations of the effective Hubbard hopping parameter and the effective Coulomb interaction strength for different electron–electron and electron–phonon interaction coefficients have been studied. We have found a transition from the Mott-insulator to a Peierls insulator analytically for the two dimensional Holstein Hubbard model.

A semi exact solution for a metallic phase in a Holstein-Hubbard chain at half filling with Gaussian anharmonic phonons

The nature of phase transition from an antiferromagnetic SDW polaronic Mott insulator to the paramagnetic bipolaronic CDW Peierls insulator is studied for the half-filled Holstein-Hubbard model in one dimension in the presence of Gaussian phonon anharmonicity. A number of unitary transformations performed in succession on the Hamiltonian followed by a general many-phonon averaging leads to an effective electronic Hamiltonian which is then treated exactly by using the Bethe-Ansatz technique of Lieb and Wu to determine the energy of the ground state of the system. Next using the Mott–Hubbard metallicity condition, local spin-moment calculation, and the concept of quantum entanglement entropy and double occupancy, it is shown that in a plane spanned by the electron–phonon coupling coefficient and onsite Coulomb correlation energy, there exists a window in which the SDW and CDW phases are separated by an intermediate phase that is metallic.

First-order kinetics bottleneck during photoinduced ultrafast insulator–metal transition in 3D orbitally-driven Peierls insulator CuIr2S4

The spinel-structure CuIr2S4 compound displays a rather unusual orbitally-driven three-dimensional Peierls-like insulator–metal transition. The low-T symmetry-broken insulating state is especially interesting due to the existence of a metastable irradiation-induced disordered weakly conducting state. Here we study intense femtosecond optical pulse irradiation effects by means of the all-optical ultrafast multi-pulse time-resolved spectroscopy. We show that the structural coherence of the low-T broken symmetry state is strongly suppressed on a sub-picosecond timescale above a threshold excitation fluence resulting in a structurally inhomogeneous transient state which persists for several-tens of picoseconds before reverting to the low-T disordered weakly conducting state. The electronic order shows a transient gap filling at a significantly lower fluence threshold. The data suggest that the photoinduced-transition dynamics to the high-T metallic phase is governed by first-order-transition nucleation kinetics that prevents the complete ultrafast structural transition even when the absorbed energy significantly exceeds the equilibrium enthalpy difference to the high-T metallic phase.

Density-Matrix Embedding Theory Study of the One-Dimensional Hubbard-Holstein Model.

We present a density-matrix embedding theory (DMET) study of the one-dimensional Hubbard–Holstein model, which is paradigmatic for the interplay of electron–electron and electron–phonon interactions. Analyzing the single-particle excitation gap, we find a direct Peierls insulator to Mott insulator phase transition in the adiabatic regime of slow phonons in contrast to a rather large intervening metallic phase in the anti-adiabatic regime of fast phonons. We benchmark the DMET results for both on-site energies and excitation gaps against density-matrix renormalization group (DMRG) results and find good agreement of the resulting phase boundaries. We also compare the full quantum treatment of phonons against the standard Born–Oppenheimer (BO) approximation. The BO approximation gives qualitatively similar results to DMET in the adiabatic regime but fails entirely in the anti-adiabatic regime, where BO predicts a sharp direct transition from Mott to Peierls insulator, whereas DMET correctly shows a large intervening metallic phase. This highlights the importance of quantum fluctuations in the phononic degrees of freedom for metallicity in the one-dimensional Hubbard–Holstein model.

Ground-state phases and quantum criticality of a one-dimensional Peierls model with spin-dependent sign-alternating potentials

We consider a one-dimensional commensurate Peierls insulator in the presence of spin-dependent sign-alternating potentials. In a continuum description, the latter supply the fermions with spin-dependent "relativistic" masses $m_{\uparrow,\downarrow}$. The ground-state phase diagram describes three gapped phases: the CDW and SDW-like band insulator phases sandwiched by a "mixed" phase in which the CDW and SDW superstructures coexist with a nonzero spontaneous dimerization (SD). The critical lines separating the massive phases belong to the Ising universality class. The Ising criticality is accompanied by the Kohn anomaly in the renormalized phonon spectrum. We derive a Ginzburg criterion which specifies a narrow region around the critical point where quantum fluctuations play a dominant role, rendering the adiabatic (or mean-field) approximation inapplicable. A full account of quantum effects is achieved in the anti-adiabatic limit where the effective low-energy theory represents a massive version the N=4 Gross-Neveu model. Using Abelian bosonization we demonstrate that the description of the SD phase, including its critical boundaries, is well approximated by a sum of two effective double-frequency sine-Gordon (DSG) models subject to self-consistency conditions that couple the charge and spin sectors. Using the well-known critical properties of the DSG model we obtain the singular parts of the dimerization order parameter and staggered charge and spin susceptibilities near the Ising critical lines. We show that, in the anti-adiabatic limit, on the line $m_{\downarrow} = 0$ there exists of a Berezinskii-Kosterlitz-Thouless critical point separating a Luttinger-liquid gapless phase from the spontaneously dimerized one. We also discuss topological excitations of the model carrying fractional charge and spin. \pacs{71.10.Pm; 71.27.+a; 71.45.Lr; 75.40.Kb}

Electronic correlations and competing orders in multiorbital dimers: A cluster DMFT study

We investigate the violation of the first Hund's rule in 4$d$ and 5$d$ transition metal oxides that form solids of dimers. Bonding states within these dimers reduce the magnetization of such materials. We parametrize the dimer formation with realistic hopping parameters and find not only regimes, where the system behaves as a Fermi liquid or as a Peierls insulator, but also strongly correlated regions due to Hund's coupling and its competition with the dimer formation. The electronic structure is investigated using the cluster dynamical mean-field theory for a dimer in the two-plane Bethe lattice with two orbitals per site and $3/8$-filling, that is three electrons per dimer. It reveals dimer-antiferromagnetic order of a high-spin (double exchange) state and a low-spin (molecular orbital) state. At the crossover region we observe the suppression of long-range magnetic order, fluctuation enhancement and renormalization of electron masses. At certain interaction strengths the system becomes an incoherent antiferromagnetic metal with well defined local moments.

Influence of electron-phonon coupling on the low-temperature phases of metallic single-wall carbon nanotubes

We investigate the effect of electron-phonon coupling on low temperature phases in metallic single-wall carbon nanotubes. We obtain low-temperature phase diagrams of armchair and zigzag type nanotubes with screened interactions with a weak-coupling renormalization group approach. In the absence of electron-phonon coupling, two types of nanotubes have similar phase diagrams. A $D$-Mott phase or $d$-wave superconductivity appears when the on-site interaction is dominant, while a charge-density wave or an excitonic insulator phase emerges when the nearest neighbor interaction becomes comparable to the on-site interaction. The electron-phonon coupling, treated by a two-cutoff scaling scheme, leads to different behavior in two types of nanotubes. For strong electron-phonon interactions, phonon softening is induced and a Peierls insulator phase appears in armchair nanotubes. We find that this softening of phonons may occur for any intraband scattering phonon mode. On the other hand, the effect of electron-phonon coupling is negligible for zigzag nanotubes. The distinct behavior of armchair and zigzag nanotubes against lattice distortion is explained by analysis of the renormalization group equations.

Long-lived photoinduced response observed under extreme photoexcitation densities in a one-dimensional Peierls insulator

One-dimensional metal-halide compounds provide model systems to investigate the manner in which coupling between elementary degrees of freedom---here, electronic and vibrational---result in instabilities that give rise to both chemical and structural rearrangements. Here, we employ ``single-shot'' pump-probe spectroscopy to examine a one-dimensional platinum iodide compound (PtI(en)) under far-from-equilibrium conditions where repeated photoexcitation results in sample damage. It presents evidence for a distinct collective excited state lasting more than 100 ps upon self-trapped exciton generation at high densities, as measured by electronic signal amplitudes and phonon properties.

Doping dependence of ordered phases and emergent quasiparticles in the doped Hubbard-Holstein model

We present determinant quantum Monte Carlo simulations of the hole-doped single-band Hubbard-Holstein model on a square lattice, to investigate how quasiparticles emerge when doping a Mott insulator (MI) or a Peierls insulator (PI). The MI regime at large Hubbard interaction $U$ and small relative electron-phonon coupling strength $\lambda$ is quickly suppressed upon doping, by drawing spectral weight from the upper Hubbard band and shifting the lower Hubbard band towards the Fermi level, leading to a metallic state with emergent quasiparticles at the Fermi level. On the other hand, the PI regime at large $\lambda$ and small $U$ persists out to relatively high doping levels. We study the evolution of the $d$-wave superconducting susceptibility with doping, and find that it increases with lowering temperature in a regime of intermediate values of $U$ and $\lambda$.

Direct observation of the M2 phase with its Mott transition in a VO2 film

In VO2, the explicit origin of the insulator-to-metal transition is still disputable between Peierls and Mott insulators. Along with the controversy, its second monoclinic (M2) phase has received considerable attention due to the presence of electron correlation in undimerized vanadium ions. However, the origin of the M2 phase is still obscure. Here, we study a granular VO2 film using conductive atomic force microscopy and Raman scattering. Upon the structural transition from monoclinic to rutile, we observe directly an intermediate state showing the coexistence of monoclinic M1 and M2 phases. The conductivity near the grain boundary in this regime is six times larger than that of the grain core, producing a donut-like landscape. Our results reveal an intra-grain percolation process, indicating that VO2 with the M2 phase is a Mott insulator.

Interplay of Site and Bond Electron-Phonon Coupling in One Dimension.

The interplay of bond and charge correlations is studied in a one-dimensional model with both Holstein and Su-Schrieffer-Heeger (SSH) couplings to quantum phonons. The problem is solved exactly by quantum MonteCarlo simulations. If one of the couplings dominates, the ground state is a Peierls insulator with long-range bond or charge order. At weak coupling, the results suggest a spin-gapped and repulsive metallic phase arising from the competing order parameters and lattice fluctuations. Such a phase is absent from the pure SSH model even for quantum phonons. At strong coupling, evidence for a continuous transition between the two Peierls states is presented.

Charge Carrier Doping into the Peierls Insulator of the TCNQ Anion Radical Salt (TCNQ = 7,7,8,8-Tetracyanoquinodimethane)

Hole-doping into K–TCNQ (TCNQ = 7,7,8,8-tetracyanoquinodimethane) crystals with segregated TCNQ anion radical columns with dimeric deformation (Peierls state) has been performed by a contact doping method using F4TCNQ (F4TCNQ = 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane) crystals or powder. The sheet resistance of the K–TCNQ surface has been found to decrease by the F4TCNQ contact. Formation of K–F4TCNQ nanocrystals at the contact interface has been observed, but conductive AFM images indicate that current paths form along the hole-doped K–TCNQ surface. Interestingly, hole-doping into K–TCNQ suppresses the phase transition to the high-temperature phase (Mott insulator). This is considered to result from the energy gain by the delocalization of the doped carriers.

Finite-size effects in Luther-Emery phases of Holstein and Hubbard models

The one-dimensional Holstein model and its generalizations have been studied extensively to understand the effects of electron-phonon interaction. The half-filled case is of particular interest, as it describes a transition from a metallic phase with a spin gap due to attractive backscattering to a Peierls insulator with charge-density-wave (CDW) order. Our quantum Monte Carlo results support the existence of a metallic phase with dominant power-law charge correlations, as described by the Luther-Emery fixed point. We demonstrate that for Holstein and also for purely fermionic models the spin gap significantly complicates finite-size numerical studies, and explains inconsistent previous results for Luttinger parameters and phase boundaries. On the other hand, no such complications arise in spinless models. The correct low-energy theory of the spinful Holstein model is argued to be that of singlet bipolarons with a repulsive, mutual interaction. This picture naturally explains the existence of a metallic phase, but also implies that gapless Luttinger liquid theory is not applicable.

STM/STS Study of the Sb (111) Surface

An Sb crystal is a Peierls insulator. Formation of double layers in the Sb structure is due to the shift of atomic planes (111) next but one along the C3 axis. Atomic layers inside the double layer are connected by covalent bonds. The interaction between double layers is determined mainly by Van der Waals forces. The cleave of an Sb single crystal used to be via break of Van der Waals bonds. However, using scanning tunneling microscopy (STM) and spectroscopy (STS) we demonstrated that apart from islands equal in thickness to the double layer, steps of one atomic layer in height also exist on the cleaved Sb (111) surface. Formation of “unpaired” (111) planes on the surface leads to a local break of conditions of Peierls transition. STS experiment reveals higher local density of states (LDOS) measured for “unpaired” (111) planes in comparison with those for the double layer.

Phonon-assisted crossover from a nonmagnetic Peierls insulator to a magnetic Stoner metal.

We report a unique temperature-induced insulator-metal transition in MnB4 that is accompanied by a simultaneous magnetostructural change from a nonmagnetic monoclinic mP20 phase to a magnetic orthorhombic oP10 phase. Such a concurring magnetostructural and insulator-metal transformation is a manifestation of a strong competition between Peierls and Stoner mechanisms that governs a crossover from an electron-pairing to an electron-localization scenario in this system. Therefore, the phase stability of MnB4 is controlled by a subtle interplay among the Peierls mechanism, Stoner mechanism, and phonon free energy. Our findings not only resolve the longstanding magnetostructural puzzle of MnB4 but also provide a realistic system for the Peierls-Hubbard model.

Charge and spin correlations of a Peierls insulator after a quench

Electron-phonon coupling plays a central role for time-dependent phenomena in condensed matter, for example, in photoexcitation experiments. We use the continuous-time quantum Monte Carlo method to study the real-time evolution of charge and spin correlation functions of a Peierls insulator after a quench to a noninteracting Hamiltonian. This approach gives exact results, and fully takes into account quantum phonon effects without relying on a Hilbert space truncation. It is also free from a dynamical sign problem. The observed time dependence is compared to free-fermion time evolution starting from a dimerized state. Our exact results provide a benchmark for more realistic calculations and may be directly applicable to experiments with cold atoms or trapped ions.