arXiv subjects

Yi-Dong Wu

Publications and source records attributed to Yi-Dong Wu.

9 recordsLinked to original sources

arXiv2023

Topology of Wilson-loop spectrum and periodic evolution of surface-state Fermi arc

Wilson-loop has been widely used to characterize the topological property of topological insulators, high order topological insulators and topological semimetals. Both bulk topological invariants and nontrivial boundary properties can be deduced from the topology of Wilson-loop spectrum. However, no attempt has been made to observe it. In this letter we demonstrate the topology of Wilson-loop spectrum can be observed by using the existing technology for observing surface-state Fermi arc. We predict that the surface-state Fermi arc sweeps the whole surface Brillouin zone in a continuous periodic process and thus generates a surface that is topologically equivalent to the Wilson-loop spectrum. So by observing the evolution of surface-state Fermi arc in the periodic process we can get the topology of Wilson-loop spectrum.

cond-mat.str-el↗

arXiv2019

Corner states are not topologically protected

Recently there is a surge of interests in the so-called topologically protected corner states in 2D and 3D systems. Such systems are considered as high order topological insulators. Wannier centers are used as topological invariants to characterize bulk systems. The existence of corner states is considered as a reflection of the topological non-triviality of bulk energy bands. We demonstrate that the Wannier centers are not topological invariants by showing they depend on the choices of unit cells. The same bulk system can be considered as both topological and trivial with two equally possible types of unit cells. We show the existence of corner states only reflects different choices of boundaries of the same bulk system. The corner states disappears in the so-called topological state if we choose a different boundary with the same symmetry as the original one. On the other hand, equally robust corner states can be realized in the so-called trivial state.

cond-mat.str-el↗

arXiv2019

Topological properties in one-dimensional periodic systems

Recently there is trend to study topological properties in one-dimensional(1D) periodic systems. Concepts such as Zak phase are considered as topological invariants that characterize the bulk bands. The bulk 1D systems are classified to topologically nontrivial and trivial phases according to the value of the so-called topological invariant. The existence of edge states or interface states is viewed as a hallmark of the topological nontriviality of the 1D systems. In this work we demonstrate the so-called topological properties in 1D systems are not topological by showing they are description-dependent: the same system can be both topological and trivial depending on how we describe the system. We demonstrate that Zak phase and other related concepts are not topological invariants by showing they depend on the choice of gauge, especially on the choice of unit cell. We show, for the same bulk system, edge states or interface states can be both present and absent depending the choices of boundaries. So the existence of localized states in 1D system is only a boundary property.

cond-mat.str-el↗

arXiv2016

Simulating topological phases and topological phase transitions with classical strings

The discovery of the topological insulators has fueled a surge of interests in the topological phases in periodic systems. Topological insulators have bulk energy gap and topologically protected gapless edge states. The edge states in electronic systems have been detected by observing the transport properties the Hgte quantum wells. The electromagnetic analogues of such electronic edge states have been predicted and observed in photonic crystals, coupled resonators and linear circuits. However, the edge state spectrums of the two dimensional insulators and their electromagnetic analogues haven't been directly measured and thus the gaplessness of the edge states hasn't been experimentally confirmed. Here I show the classical strings are more convenient choice to study the topological phases than the electromagnetic waves. I found that classical strings with periodic densities can simulate a variety of topological phases in condensed matter physics including two dimensional topological insulators, three dimensional topological semimetals and weak topological insulators. Because the eigenfrequencies and eigenfunctions of the strings can be easily measured, not only the gapless edge state spectrum but also the bulk topological invariant can now be directly observed. Further more I show the topological phase transitions can be simulated by the strings. My results show the richness of topological phases of mechanical waves. I anticipate my work to be a starting point to study the topological properties of mechanical waves. Even richer topological phases other than those have been found in electronics systems can be explored when we use more general mechanical waves e.g. waves in membranes with periodic densities. These phases may provide guides to hunt novel topological properties in other branches of science.

cond-mat.mes-hall↗

arXiv2013

Comment on "Time reversal polarization and a Z2 adiabatic spin pump"

In Ref 1[Phy. Rev. B 74, 195312(2006)] Fu and Kane propose a spin pump for onedimensional (1D) insulating Hamiltonians. They claim that this spin pump is a Z2 pump because For an isolated system, a single closed cycle of the pump changes the expectation value of the spin at each end even when spin-orbit interactions violate the conservation of spin. A second cycle, however, returns the system to its original state. A Z2 topological invariant is proposed to characterize the Z2 pump. In this comment we show their discussion on the spin pump is inaccurate. Their reason why the isolated system return to its original state after second cycle is unjustified and several claims contradict to this return of the system are made in Ref 1. Detailed calculations and concrete examples show the degeneracy of the first excited state at t = 0, T; is not split by the electron-electron interaction in the way described in Ref 1 and there is level crossing at t = T. In fact, despite of a detailed search, not a single system behave as described in Fig. 1(d) in Ref 1 has been found. Thus we conclude the isolated system won't return to its original state after two cycles and the spin pump is not a Z2 pump in general.

cond-mat.mes-hall↗

arXiv2013

On the single-electron theory of quantum spin Hall effect in two dimensional topological insulators

Recently we wrote a paper on the theory of the quantum spin Hall effect(QSHE) in two dimensional(2D) topological insulators(TIs)1 which have been considered as do not add much new insight to the exhaustively studied topic of TI within a single-electron picture by the referees. In this paper we review the papers on the mechanism of the QSHE which have significant influence on understanding of the subject. By illustrating the failures of the previous works we show our paper do contribute a different point of view to this topic, which we believe is not only a new but also the correct way to approach the problem at the single-electron level.

cond-mat.mes-hall↗

arXiv2012

Chern pump: a bridge between integer quantum Hall effect and quantum spin Hall effect

We propose a electron-pumping mechanism called Chern pump to explain the integer quantum Hall effect(IQHE) in the Chern insulator. By using the parallel transport gauge in the hybrid Wannier representation we establish the bulk and edge states correspondence in the Chern insulator. The same correspondence can also be established in two dimensional(2D) topological insulator(TI). So we can consider 2D TI as two time reversal(TR) related CIs put together. The quantum spin Hall effect(QSHE) can be viewed as two TR related Chern pumps pumping electrons to opposite directions. Compared with the Z2 spin pump, the two Chern pumps explanation of QSHE is inherently 2D and predict that the QSHE can be detected in isolated device, thus make the QSHE directly measurable.

cond-mat.mes-hall↗

arXiv2012

Band Topology or Geometry?

The study of topology of energy bands in solid has always been interesting and fruitful. Historically, Thouless et al proposed the TKNN number or Chern number of the energy bands to explain the quantization of Hall conductance in the integer quantum Hall effect. Recently, Z2 topological insulators have been intensively studied and similarly topological crystalline insulators are proposed.These materials exhibit nontrivial charge or spin transport properties that is due to the existence of metallic edge states. The edge states are protect by the topology of the energy bands of the bulk material and the band topology are described by some invariants similar to the TKNN number. However, these invariants are crude and strongly dependent on the symmetry. Here we give an unified picture of the relationship of the edge states and the geometry of the energy bands. We show the band geometry determines not only the topological but also the geometrical properties of the edge states and the picture is applicable when the symmetries are broken.

cond-mat.mtrl-sci↗

arXiv2011

A Coherent Physics Picture of Topological Insulators at Single-Particle Level

The study of topological property of band insulators is an interesting branch of condensed matter physics. Two types of topologically nontrivial insulators have been extensively studied. The first type is characterized by a nonzero TKNN invariant or Chern number[1] which is directly related to the quantization of Hall conductance in the integer quantum Hall effect. Haledane propose a model with this type of band structure even in the absence of a macroscopic magnetic field[2]. We refer to such materials "Chern insulator". The second type called "Z2 topological insulators" is proposed recently[3, 4]. Quantum spin Hall effect has been predicted and observed in such systems.[5, 6]. Despite the recent intensively study there are still some fundamental problems that aren't quite clear about Z2 insulators even at the single-particle level. For example, it's claimed that Z2 insulators will return to its origin state after two cycles, thus coupling to the reservoirs is important for the Z2 insulators to continuously pump spin[7]. Theoretical and experimental results show quantum spin Hall effect is an edge state transport property of the materials and coupling to the reservoir seems not play an important role. So the Z2 picture is not satisfactory in explaining these phenomena. We study the relationship of the ground states of Z2 insulators and that of Chern insulator. Combined with the results of recent researches on polarization of Chern insulators[8] and topology of edge states[9] we propose a coherent physics picture of topological insulators.

cond-mat.mtrl-sci↗