Probing topological signatures in an optically driven α−T3 lattice (original) (raw)
Related papers
2019
The role of disorder, interactions and temperature on topological phases of matter is subtle and often presents dichotomic features. Understanding these effects is however essential to predict the topological properties and their stability in real-world materials. This is particularly relevant for 2D materials, where the low dimensionality typically enhances these effects. As an example of dichotomic behavior, topological phases are suppressed in the presence of strong local interactions [1], while some studies showed that interactions themselves could induce a topological phase on a trivial band [2,3]. The role of disorder is also subtle. For topological insulators with broken time-reversal symmetry, disorder effects localize every eigenstate except two bulk extended states that carry opposite topological numbers [4,5]. The merging of these states, for a sufficiently large disorder strength, is associated with the destruction of the topological phase. Interestingly, a disorder-induced transition into a new topologically nontrivial phase-the topological Anderson insulator-was also shown to be possible [6,7]. To unbiasedly characterize the interplay of all these ingredients we introduce a model system that combines the topological features of the Haldane model with an interaction term of the Falicov-Kimball type. The Haldane-Falicov-Kimball model can be seen as a limiting case of the Hubbard model on an hexagonal lattice, for which one of the spin species is infinitely massive and the other has the hopping matrix elements of the Haldane model. The ability to employ numerically exact methods, renders our model an excellent testbed to unveil the subtle and often contradictory role of interactions and disorder. Moreover, the model can be studied at finite temperatures, where the behavior of topological matter have been much less explored. By performing a careful numerical and analytic analysis, we obtain the phase diagram on the temperatureinteraction plane, displaying a rich set of phases. One of our main results is to show that the thermal fluctuations, that affect the spatial charge ordering, induce a temperature-driven topological phase transition into gapped and gapless topological insulators, present for a wide range of interaction strengths. We also find an insulating charge ordered state with gapless excitations where spectral regions of extended and localized states seem to coexist due to the long range nature of the interaction-induced disorder potential [8]. Recent technological advances in ultracold atoms in optical lattices, in particular, the ability of having fermionic systems with a large mass unbalance and the possibility of realizing topologically non-trivial band structures such as the one of the Haldane model, render this model easily realizable with current experimental setups.
Physical Review B, 2018
We consider α-T3 lattice illuminated by intense circularly polarized radiation in terahertz regime. We present quasienergy band structure, time-averaged energy spectrum and time-averaged density of states of α-T3 lattice by solving the Floquet Hamiltonian numerically. We obtain exact analytical expressions of the quasienergies at the Dirac points for all values of α and field strength. We find that the quasienergy band gaps at the Dirac point decrease with increase of α. Approximate forms of quasienergy and band gaps at single and multi-photon resonant points are derived using rotating wave approximation. The expressions reveal a stark dependence of quasienergy on the Berry phase of the charge carrier. The quasi energy flat band remains unaltered in presence of radiation for dice lattice (α = 1). However, it acquires a dispersion in and around the Dirac and even-photon resonant points when 0 < α < 1. The valley degeneracy and electron-hole symmetry in the quasienergy spectrum are broken for 0 < α < 1. Unlike graphene, the mean energy follows closely the linear dispersion of the Dirac cones till near the single-photon resonant point in dice lattice. There are additional peaks in the time-averaged density of states at the Dirac point for 0 < α ≤ 1.
Floquet topological phase transition in the α−T3 lattice
Physical Review B
We investigate topological characteristics of the photon-dressed band structure of α-T3 lattice on being driven by off-resonant circularly polarized radiation. We obtain exact analytical expressions of the quasienergy bands over the first Brillouin zone. The broken time-reversal symmetry caused by the circularly polarized light lifts the triple point degeneracy completely at both the Dirac points. The gaps become unequal at K and K (except at α = 0 and 1), which reveals the absence of inversion symmetry in the system. At α = 1/ √ 2, the gap between flat and valence bands closes at K, while that between conduction and flat bands closes at K , thereby restoring a semimetalic phase. At the gap closing point (α = 1/ √ 2) which is independent of the radiation amplitude, there is a reappearance of low-energy Dirac cones around K and K points. Under the influence of the circularly polarized radiation, the α-T3 lattice is transformed from semimetal to a Haldane-like Chern insulator characterized by non-zero Chern number. The system undergoes a topological phase transition from C = 1(−1) to C = 2(−2) at α = 1/ √ 2, where C is the Chern number of the valence (conduction) band. This sets an example of a multiband system having larger Chern number. These results are supported by the appearance of chiral edge states in irradiated α-T3 nanoribbon.
Berry-phase-mediated topological thermoelectric transport in gapped single and bilayer graphene
Physical Review B, 2009
We consider the anomalous thermoelectric transport in gapped single and bilayer graphene where the gap may be due to broken inversion symmetry. In the presence of the gap, non-trivial Berry phase effects can be shown to mediate a transverse thermoelectric voltage in response to an applied temperature gradient even in the absence of a perpendicular magnetic field. This spontaneous, anomalous Nernst effect is nonzero for non-uniform chemical potential in the two inequivalent valleys in the graphene band structure. Conversely, the Nernst response can be used to create a valley-index polarization between the two transverse sample edges as in the analogous valley Hall effect.
Measurement of topological Berry phase in highly disordered graphene
Physical Review B, 2015
We have observed the quantum Hall effect (QHE) and Shubnikov-de Haas (SdH) oscillations in highly disordered graphene at magnetic fields up to 65 T. Disorder was introduced by hydrogenation of graphene up to a ratio H/C ≈ 0.1%. The analysis of SdH oscillations and QHE indicates that the topological part of the Berry phase, proportional to the pseudo-spin winding number, is robust against introduction of disorder by hydrogenation in large scale graphene.
Chern mosaic and Berry-curvature magnetism in magic-angle graphene
Nature Physics
Charge carriers in magic angle graphene come in eight flavors described by a combination of their spin, valley, and sublattice polarizations [1-4]. When the inversion and time reversal symmetries are broken by the substrate or by strong interactions, the degeneracy of the flavors can be lifted and their corresponding bands can be filled sequentially [5-7]. Due to their non-trivial band topology and Berry curvature, each of the bands is classified by a topological Chern number [8-12], leading to the quantum anomalous Hall [13-15] and Chern insulator states [7,8,16-19] at integer fillings of the bands. It has been recently predicted, however, that depending on the local atomic-scale arrangements of the graphene and the encapsulating hBN lattices, rather than being a global topological invariant, the Chern number may become position dependent, altering transport and magnetic properties of the itinerant electrons [20-23]. Using scanning superconducting quantum interference device on a tip (SQUID-on-tip) [24], we directly image the nanoscale Berry-curvatureinduced equilibrium orbital magnetism, the polarity of which is governed by the local Chern number, and detect its two constituent components associated with the drift and the self-rotation of the electronic wave packets [25]. At = 1, we observe local zero-field valley-polarized Chern insulators forming a mosaic of microscopic patches of = −1, 0, or 1. Upon further filling, we find a first-order phase transition due to recondensation of electrons from valley to ′, which leads to irreversible flips of the local Chern number and the magnetization, and to the formation of valley domain walls giving rise to hysteretic global anomalous Hall resistance. The findings shed new light on the structure and dynamics of topological phases and call for exploration of the controllable formation of flavor domain walls and their utilization in twistronic devices.
Magnetoelectric control of topological phases in graphene
Physical Review B, 2019
Topological antiferromagnetic (AFM) spintronics is an emerging field of research, which involves the topological electronic states coupled to the AFM order parameter known as the Néel vector. The control of these states is envisioned through manipulation of the Néel vector by spin-orbit torques driven by electric currents. Here we propose a different approach favorable for low-power AFM spintronics, where the control of the topological states in a two-dimensional material, such as graphene, is performed via the proximity effect by the voltage induced switching of the Néel vector in an adjacent magnetoelectric AFM insulator, such as chromia. Mediated by the symmetry protected boundary magnetization and the induced Rashba-type spin-orbit coupling at the interface between graphene and chromia, the emergent topological phases in graphene can be controlled by the Néel vector. Using density functional theory and tightbinding Hamiltonian approaches, we model a graphene/Cr2O3 (0001) interface and demonstrate non-trivial band gap openings in the graphene Dirac bands asymmetric between the K and K′ valleys. This gives rise to an unconventional quantum anomalous Hall effect (QAHE) with a quantized value of 2e 2 /h and an additional step-like feature at a value close to e 2 /2h, and the emergence of the spin-polarized valley Hall effect (VHE). Furthermore, depending on the Néel vector orientation, we predict the appearance and transformation of different topological phases in graphene across the 180° AFM domain wall, involving the QAHE, the valley-polarized QAHE and the quantum VHE (QVHE), and the emergence of the chiral edge state along the domain wall. These topological properties are controlled by voltage through magnetoelectric switching of the AFM insulator with no need for spin-orbit torques.
Topological phase transition induced by band structure modulation in a Chern insulator
2021
We study a systematic evolution of the topological properties of a Chern insulator upon smooth variation of a hopping parameter (t 1) of the electrons among a pair of nearest neighbour sites on a honeycomb lattice, while keeping the other two hopping terms (t) fixed. In the absence of a Haldane flux, the tuning of t 1 results in gradual shifting of the Dirac cones which eventually merge into one at the M point in the Brillouin zone (BZ) at t 1 = 2t with a gapless semi-Dirac dispersion at low energies. In the presence of a Haldane flux, the system becomes a Chern insulator for t 1 < 2t, but turns gapless at t 1 = 2t with the semi-Dirac dispersion being transformed to an anisotropic Dirac one. The spectrum eventually gaps out and transforms into a trivial insulator for t 1 > 2t. The Chern number phase diagram obtained via integrating the Berry curvature over the BZ shows a gradual shrinking of the ‘topological’ lobes, and vanishes just beyond t 1 = 2t, where a small but a finite...
Photoinduced valley and electron-hole symmetry breaking in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">mml:mrowmml:miαmml:mo−mml:msubmml:miTmml:mn3 lattice: The role of a variable Berry phase
Physical review, 2018
We consider α-T3 lattice illuminated by intense circularly polarized radiation in terahertz regime. We present quasienergy band structure, time-averaged energy spectrum and time-averaged density of states of α-T3 lattice by solving the Floquet Hamiltonian numerically. We obtain exact analytical expressions of the quasienergies at the Dirac points for all values of α and field strength. We find that the quasienergy band gaps at the Dirac point decrease with increase of α. Approximate forms of quasienergy and band gaps at single and multi-photon resonant points are derived using rotating wave approximation. The expressions reveal a stark dependence of quasienergy on the Berry phase of the charge carrier. The quasi energy flat band remains unaltered in presence of radiation for dice lattice (α = 1). However, it acquires a dispersion in and around the Dirac and even-photon resonant points when 0 < α < 1. The valley degeneracy and electron-hole symmetry in the quasienergy spectrum are broken for 0 < α < 1. Unlike graphene, the mean energy follows closely the linear dispersion of the Dirac cones till near the single-photon resonant point in dice lattice. There are additional peaks in the time-averaged density of states at the Dirac point for 0 < α ≤ 1.
Lattice symmetries, spectral topology and opto-electronic properties of graphene-like materials
EPL (Europhysics Letters), 2017
The topology of the band structure, which is determined by the lattice symmetries, has a strong influence on the transport properties. Here we consider an anisotropic honeycomb lattice and study the effect of a continuously deformed band structure on the optical conductivity and on diffusion due to quantum fluctuations. In contrast to the behavior at an isotropic node we find super-and subdiffusion for the anisotropic node. The spectral saddle points create van Hove singularities in the optical conductivity, which could be used to characterize the spectral properties experimentally.