Tight-binding model for topological insulators: Analysis of helical surface modes over the whole Brillouin zone

Mao, Shijun; Yamakage, Ai; Kuramoto, Yoshio

doi:10.1103/physrevb.84.115413

Cited by 29 publications

(38 citation statements)

References 32 publications

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“…1(c) [18]. This parallels the appearance of the topologically nonprotected edge or surface states in certain systems, whose existence is not connected to topology but is accidental [1, 29,30].…”

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confidence: 81%

Topological classification of dynamical phase transitions

2015

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We study the nonequilibrium time evolution of a variety of one-dimensional (1D) and two-dimensional (2D) systems (including SSH model, Kitaev-chain, Haldane model, p + ip superconductor, etc.) following a sudden quench. We prove analytically that topology-changing quenches are always followed by nonanalytical temporal behavior of return rates (logarithm of the Loschmidt echo), referred to as dynamical phase transitions (DPTs) in the literature. Similarly to edge states in topological insulators, DPTs can be classified as being topologically protected or not. In 1D systems the number of topologically protected nonequilibrium time scales are determined by the difference between the initial and final winding numbers, while in 2D systems no such relation exists for the Chern numbers. The singularities of dynamical free energy in the 2D case are qualitatively different from those of the 1D case; the cusps appear only in the first time derivative. [3,4] are two vividly investigated fields of physics, with no strong bonds between them. The leading role played by topology in condensed matter has only been realized recently with the discovery of topological insulators, the descendants of quantum Hall states. Some of their correlation functions are universal and are not influenced by the microscopic details of the system, but are rather determined by the underlying topology. The analysis of nonequilibrium states, on the other hand, have emerged recently in a different field: in cold atomic systems. With the unprecedented control of preparing initial states and governing the time evolution, a number of interesting phenomena has been observed such as the Kibble Zurek scaling [5], the lack of thermalization in integrable systems [6], etc. In this paper, we connect these two, seemingly unrelated fields and show that topology can be used as an organizing principle to classify out-of-equilibrium systems.The most popular setups for nonequilibrium dynamics are quench experiments in which the quantum system initially sits in the ground state of a given Hamiltonian, but its time evolution is governed by another Hamiltonian. The quench protocol can conveniently be characterized by the dynamical partition function with no reference to any particular observables, defined asFor positive real values of z this gives the partition function of a field theory with boundaries |ψ separated by z [7]. For our purposes, we use z = it with t real, which then gives the Loschmidt amplitude, that is, the overlap of the time-evolved state with the initial state G(t) = Z(it). It characterizes time evolution and the stationary state after a long waiting time [8], and also yields the characteristic function of work [9], which is accessible experimentally [10]. As the time evolution operator is highly nonlocal, it allows Z(z) to be susceptible to the topological properties of the underlying system. Similarly to the equilibrium situation, the dynamical free energy is defined as the logarithm per unit volume f (t) = −1/N d ln G(t). In the thermodynamic li...

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confidence: 81%

Topological classification of dynamical phase transitions

2015

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“…Taking the first correction due to finiteness of Λ, we have We adopt the minimal tight binding model framework for topological order, in which a single Bi 2 (Se/Te) 3 formula unit within one quintuple layer of the crystal is reduced to two p z orbitals displaced along the surface normal axis [2,42]. These two-orbital unit cells are arranged in an AA stacked hexagonal lattice, with an in-plane lattice constant of a=4.2 nm and a z-axis lattice constant of c, the precise value of which is not physically relevant.…”

Section: A2 the Bound State Energy: Poles Of The T-matrixmentioning

confidence: 99%

Connection topology of step edge state bands at the surface of a three dimensional topological insulator

Jiang

Chiu

et al. 2018

New J. Phys.

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Topological insulators (TIs) in the Bi 2 Se 3 family manifest helical Dirac surface states that span the topologically ordered bulk band gap. Recent scanning tunneling microscopy measurements have discovered additional states in the bulk band gap of Bi 2 Se 3 and Bi 2 Te 3 , localized at one-dimensional step edges. Here numerical simulations of a TI surface are used to explore the phenomenology of edge state formation at the single-quintuple layer step defects found ubiquitously on these materials. The modeled one-dimensional edge states are found to exhibit a stable topological connection to the twodimensional surface state Dirac point.

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“…A 3-dimensional TI with time reversal symmetry [2,[6][7][8][9][10][11][12] exhibits gapless surface states. While the transport properties of a TI are theoretically predicted to be influenced by the topology of its electronic structure [13], much of its experimental confirmation comes from studies of the surface electronic structure [2], specifically on its odd number of Dirac cones.…”

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confidence: 99%

Sharp Raman Anomalies and Broken Adiabaticity at a Pressure Induced Transition from Band to Topological Insulator inSb2Se3

et al. 2013

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The non-trivial electronic topology of a topological insulator is so far known to display signatures in a robust metallic state at the surface. Here, we establish vibrational anomalies in Raman spectra of the bulk that signify changes in electronic topology: an E 2 g phonon softens unusually and its linewidth exhibits an asymmetric peak at the pressure induced electronic topological transition (ETT)in Sb 2 Se 3 crystal. Our first-principles calculations confirm the electronic transition from band to topological insulating state with reversal of parity of electronic bands passing through a metallic state at the ETT, but do not capture the phonon anomalies which involve breakdown of adiabatic approximation due to strongly coupled dynamics of phonons and electrons. Treating this within a four-band model of topological insulators, we elucidate how non-adiabatic renormalization of phonons constitutes readily measurable bulk signatures of an ETT, which will facilitate efforts to develop topological insulators by modifying a band insulator.

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Tight-binding model for topological insulators: Analysis of helical surface modes over the whole Brillouin zone

Cited by 29 publications

References 32 publications

Topological classification of dynamical phase transitions

Topological classification of dynamical phase transitions

Connection topology of step edge state bands at the surface of a three dimensional topological insulator

Sharp Raman Anomalies and Broken Adiabaticity at a Pressure Induced Transition from Band to Topological Insulator inSb2Se3

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