Related papers: Topological Dimensions from Disorder and Quantum M…
We consider a 2D electron system on a square lattice with hopping beyond nearest neighbors. The existence of the quantum critical point associated with an electronic topological transition in the noninteracting system results in density…
Tuning dimensionality in van der Waals materials with finite interlayer coupling has introduced various electronic phase transitions by conventional mechanical exfoliation. Particularly when the electronic order is tied to the modulation of…
We investigate numerically and theoretically the effect of spatial disorder on two-dimensional split-step discrete-time quantum walks with two internal "coin" states. Spatial disorder can lead to Anderson localization, inhibiting the spread…
A major research area in discrete geometry is to consider the best way to partition the $d$-dimensional Euclidean space $\mathbb{R}^d$ under various quality criteria. In this paper we introduce a new type of space partitioning that is…
The recent theoretical prediction by Maimbourg and Kurchan [arXiv:1603.05023] that for regular pair-potential systems the virial potential-energy correlation coefficient increases towards unity as the dimension $d$ goes to infinity is…
The interplay between disorder and quantum interference leads to a wide variety of physical phenomena including celebrated Anderson localization -- the complete absence of diffusive transport due to quantum interference between different…
We study the relationship between the quantities that encode the insulating properties of matter: the ground-state quantum metric, the average localization length, and the electric susceptibility. By examining the one-dimensional Anderson…
Complex dielectric media often appear opaque because light traveling through them is scattered multiple times. Although the light scattering is a random process, different paths through the medium can be correlated encoding information…
In this paper, we explore quantum criticality in the disordered Aubry-Andr\'{e} (AA) model. For the pure AA model, it is well-known that it hosts a critical point separating an extended phase and a localized insulator phase by tuning the…
Topological insulators in three dimensions are characterized by a Z2-valued topological invariant, which consists of a strong index and three weak indices. In the presence of disorder, only the strong index survives. This paper studies the…
Static disorder in a noninteracting gas of electrons confined to two dimensions can drive a continuous quantum (Anderson) transition between a metallic and an insulating state when time-reversal symmetry is preserved but spin-rotation…
Topologically protected surface states of three-dimensional topological insulators provide a model framework for studying massless Dirac electrons in two dimensions. Usually a step on the surface of a topological insulator is treated as a…
Fractal-like structures of varying complexity are common in nature, and measure-based dimensions (Minkowski, Hausdorff) supply their basic geometric characterization. However, at the level of fundamental dynamics, which is quantum,…
We consider chiral electrons moving along the 1D helical edge of a 2D topological insulator and interacting with a disordered chain of Kondo impurities. Assuming the electron-spin couplings of random anisotropies, we map this system to the…
The $E_8 \otimes E_8$ octonionic theory of unification suggests that our universe is six-dimensional and that the two extra dimensions are time-like. These time-like extra dimensions, in principle, offer an explanation of the quantum…
Two-dimensional random metal networks possess unique electrical and optical properties, such as almost total optical transparency and low sheet resistance, which are closely related to their disordered structure. Here we present a detailed…
We have found the first instance of a third-order topological Anderson insulator (TOTAI). This disorder-induced topological phase is gapped and characterized by a quantized octupole moment and topologically protected corner states, as…
The massless Dirac electrons found at topological insulator surfaces are thought to be influenced very little by weak, non-magnetic disorder. However, a resonance effect of strongly perturbing non-magnetic impurities has been theoretically…
One-dimensional topological Anderson insulators provide a paradigm for disorder-induced topological phases in which the underlying system turns from a trivial to a topological phase. It is widely recognized that the latter vanishes at large…
As part of condensed-matter physics, the field of Anderson localization concerns the study of conductance of electrons in a random medium. We summarize and explain the results obtained in "A new numerical approach to Anderson…