The quantum phase transition between the three dimensional Dirac semimetal and diffusive metal can be induced by increasing disorder. Taking system of a disordered ${\mathbb{Z}}_{2}$ topological insulator as an important example, we compute single particle density states kernel polynomial method. We focus on regions: at boundary two topologically distinct phases, tricritical point phases metal, lying strong obeys novel parameter scaling, collapsing onto branches universal scaling function,...

A modified periodic boundary condition adequate for non-hermitian topological systems is proposed. Under this a number characterizing the system defined in same way as corresponding hermitian and hence, at cost of introducing an additional parameter that characterizes skin effect, idea bulk-edge correspondence limit can be applied almost it is. We develop framework through analysis SSH model with chiral symmetry, prove generalized space. finite region space nontrivial pair winding numbers...

A global phase diagram of disordered weak and strong topological insulators is established numerically. As expected, the location boundaries renormalized by disorder, a feature recognized in study so-called Anderson insulator. Here, we report unexpected quantization, i.e., robustness against disorder conductance peaks on these boundaries. Another highlight work emergence two subregions insulator under disorder. According to size dependence conductance, surface states are either robust or...

Non-Hermiticity and dephasing, collaborating in an unusual wave-packet dynamics, realize unconventional entanglement evolution a disordered, interacting, asymmetric (nonreciprocal) quantum medium. Taking the Hatano-Nelson model as concrete example, we first consider how wave packet spreads non-Hermitian disordered system for demonstrating that it is very different from Hermitian case. Interestingly, cascadelike spreading case suppressed clean limit at weak disorder, while revives vicinity of...

The electronic spectrum on the spherical surface of a topological insulator reflects an active property helical state that stems from constraint its spin curved surface. induced connection can be interpreted as effective vector potential associated with fictitious magnetic monopole at center sphere. strength is found to $g=\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}$, being smallest finite (absolute) value compatible Dirac quantization condition. We have established explicit correspondence...

The entanglement dynamics in a non-Hermitian quantum system is studied numerically and analyzed from the viewpoint of quasiparticle picture. As concrete model, we consider one-dimensional tight-binding model with asymmetric hopping (Hatano-Nelson model) under onsite disorder nearest-neighbor interaction. opposed to an assertion previous studies, this very different one its Hermitian counterpart, especially delocalized regime weak disorder; there entropy ${S}_{\mathrm{ent}}(t)$ shows...

Effects of disorder on two-dimensional Z2 topological insulator are studied numerically by the transfer matrix method. Based scaling analysis, phase diagram is derived for a model HgTe quantum well as function strength and magnitude energy gap. In presence sz non-conserving spin-orbit coupling, finite metallic region found that partitions two topologically distinct insulating phases. As increases, narrow-gap trivial undergoes series transitions; first to metal, second insulator, third...

A workable model for describing dislocation lines introduced into a three-dimensional topological insulator is proposed. We show how fragile surface Dirac cones of weak evolve protected gapless helical modes confined to the vicinity line. It demonstrated that (either strong or weak) acquire finite-size energy gap when deformed cylinder penetrating otherwise surfaceless system. that, with nontrivial Burgers vector introduced, plays role stabilizing one-dimensional states.

The nontrivialness of a topological insulator (TI) is characterized either by bulk invariant or the existence protected metallic surface state. Yet, in realistic samples finite size, this does not necessarily guarantee gaplessness Depending on geometry and indices, finite-size energy gap different nature can appear, and, correspondingly, exhibit various scaling behaviors gap. spin-to-surface locking provides one such gap-opening mechanism, resulting power-law Weak strong TIs show degrees...

Three-dimensional topological insulators are characterized by the presence of protected gapless spin helical surface states. In realistic samples these states extended from one to another, covering entire sample. Generally, on a curved insulator an electron in state acquires Berry phase as expression constraint that effective must follow tangential real space geometry. Such adds up pi when encircles, e.g., once around cylinder. Realistic compounds also often layered, i.e., anisotropic. We...

A weak topological insulator (WTI) bears, generally, an even number of Dirac cones on its surface; they are susceptible doubling, while the surface a certain orientation it shows no cone. On this "dark" WTI, we predict existence single pair isolated 1D perfectly conducting channels that forms either closed loop or segment line. The former is associated typically with atomic-layer-thick island formed dark surface, latter shown to be consequence crystal (screw) dislocations terminating surface.

Localization properties of the doped ${Z}_{2}$ topological insulator are studied by weak localization theory. The disordered Kane-Mele model for graphene is taken as a prototype and analyzed with attention to effects mass term, intervalley scattering, Rashba spin-orbit interaction. known tendency antilocalize in absence scattering between $K$ ${K}^{\ensuremath{'}}$ points naturally placed massless limit model. latter shown have unitary behavior even magnetic field due term. When introduced,...

The spectrum and wave function of helical edge modes in ${Z}_{2}$ topological insulator are derived on a square lattice using Bernevig-Hughes-Zhang (BHZ) model. BHZ model is characterized by ``mass'' term $M(\mathbit{k})=\ensuremath{\Delta}\ensuremath{-}B{\mathbit{k}}^{2}$. A realizes when the parameters $\ensuremath{\Delta}$ $B$ fall regime, either $0<\ensuremath{\Delta}/B<4$ or $4<\ensuremath{\Delta}/B<8$. At $\ensuremath{\Delta}/B=4$, which separates cases positive negative (quantized)...

Employing scaling analysis of the localization length, we deduce critical exponent metal--topological insulator transitions induced by disorder. The obtained $\ensuremath{\nu}\ensuremath{\sim}2.7$ shows no conspicuous deviation from value established for metal--ordinary in systems symplectic class. We investigate topological phase diagram upon carrier doping to reveal nature so-called Anderson (TAI) region. metal--TAI transition is also first estimated, shown be undistinguishable above...

Spectrum and wave function of gapless edge modes are derived analytically for a tight-binding model topological insulators on square lattice. Particular attention is paid to dependence geometries such as the straight (1,0) zigzag (1,1) edges in thermodynamic limit. The key technique identify operators that combine annihilate state effective one-dimensional (1D) with momentum along edge. In edge, mode present either around center 1D Brillouin zone or its boundary, depending location bulk...

Bulk-boundary correspondence is the cornerstone of topological physics. In some non-Hermitian system this fundamental relation broken in sense that number calculated for Bloch energy band under periodic boundary condition fails to reproduce properties open boundary. To restore bulk-boundary such systems a framework beyond theory needed. We develop based on modified allows proper description bulk insulator manner consistent with its properties. Taking version Su-Schrieffer-Heeger model as an...

We discuss the quantum Hall effect of bilayer graphene with finite gate voltage where Fermi energy exceeds interlayer hopping energy. calculated magnetic susceptibility, diagonal and off-diagonal conductivities in finite-magnetic-field formalism, observed crossover integer from two independent monolayer type system to strongly coupled systems by changing ratio voltage. also case multilayer Bernal stacking

A graphene $pn$ junction is studied theoretically in the presence of both intrinsic and Rashba spin-orbit couplings. We show that a crossover from perfect reflection to transmission achieved at normal incidence by tuning perpendicular electric field. By further studying angular dependent transmission, we demonstrate can be clearly distinguished trivial band gap effects. also investigate how effects modify conductance Fano factor associated with potential step $nn$ $np$ cases.

Unusual electronic property of a Weyl semi-metallic nanowire is revealed. Its band dispersion exhibits multiple subbands partially flat dispersion, originating from the Fermi arc states. Remarkably, lowest energy bear finite size gap, implying that electrons in surface states are susceptible spin Berry phase. This shown to be consequence spin-to-surface locking We verify this behavior and existence phase low-energy effective theory on cylindrical by deriving latter bulk Hamiltonian. point...

We report on short ballistic (SB) Josephson coupling in junctions embedded a planar heterostructure of graphene. Ballistic is confirmed by the Fabry-Perot-type interference junction critical current ${I}_{c}$. The product ${I}_{c}$ and normal-state resistance ${R}_{N}$, normalized zero-temperature gap energy ${\mathrm{\ensuremath{\Delta}}}_{0}$ superconducting electrodes, turns out to be exceptionally large close 2, an indication strong SB limit. However, shows temperature dependence that...

Existence of a protected surface state described by massless Dirac equation is defining property the topological insulator. Though this statement can be explicitly verified on an idealized flat surface, it remains to addressed what extent could general. On curved modified spin connection terms. Here, in light differential geometry, we give general framework for constructing starting from Hamiltonian bulk insulators. The obtained unified description clarifies physical meaning connection.

We discuss the conductance of quantum wires in terms Tomonaga-Luttinger liquid (TLL) theory. use explicitly charge fractionalization scheme which results from chiral symmetry model. suggest that standard two-terminal (2T) measurement depend on coupling TLL with reservoirs and can be interpreted as different boundary conditions at interfaces. propose a three-terminal (3T) geometry third contact is connected weakly to bulk subjected large bias current. develop renormalization-group (RG)...

We show how the two-dimensional (2D) topological insulator evolves, by stacking, into a strong or weak with different indices, proposing new conjecture that goes beyond an intuitive picture of crossover from quantum spin Hall to insulator. Studying conductance under boundary conditions, we demonstrate existence two conduction regimes in which happens through either surface edge channels. are complementary and exclusive. Conductance maps presence absence disorder introduced, together 2D...