Conductivity of a two-dimensional HgTe layer near the critical width: The role of developed edge states network and random mixture of p - and n -domains

Abstract

The conductivity of 2D HgTe quantum well with a width ∼ 6.3nm, close to the transition from ordinary to topological insulating phases, is studied. The Fermi level is supposed to get to the overall energy gap. The consideration is based on the percolation theory. We have found that the width fluctuations convert the system to a random mixture of domains with positive and negative energy gaps with internal edge states formed near zero gap lines. In the case with no potential fluctuations, the conductance of a finite sample is provided by a random network of the edge states. The zero temperature conductivity of an infinite sample is determined by the free motion of electrons along the zero-gap lines and tunneling between them.The conductance of a single p-n junction, which is crossed by the edge state, is found. The result is applied to the situation when potential fluctuations transform the system to a mixture of p-and n-domains. It is stated that the tunneling across p-n junctions forbids the low-temperature conductivity of a random system, but the latter is restored due to the random edge states crossing the junctions.

Transport through the network of topological channels in HgTe based quantum well

“…In order to estimate the width of the channels we per- formed additional measurements of the Hall effect at low magnetic fields. Surprisingly, we find that the Hall effect near the percolation threshold is completely suppressed in a narrow interval of carrier densities in agreement with the percolation model [26,27].…”

“…We suppose that in our sample |ξ − ξ c | << 1 so that a network of OI and TI domains is formed and the ZGLs cover the entire sample. It is worth noting, however, that in a realistic random network of channels a low temperature non-zero 2D conductivity may occur only if electrons can tunnel between the adjacent channels, for which a finite channel width is required [27]. One can estimate that :…”

“…where α = ∂∆(w)/∂w| w=wc , ∆ is the rms energy gap fluctuation value, v is the electron velocity, r is parameter, which is close to 0.45 [27]. The conductivity of the network can be estimated from the equation [27]:…”

“…where D ≃ av(∆a/ v) p is the diffusion coefficient , p is a coefficient close to 0.15. We estimate the corresponding HgTe QW parameters from [27]…”

“…In addition to the gap fluctuations there will also be variations of the electrostatic potential due to random distribution of charged impurities. For the Fermi energy located near the Dirac point the system conductivity is attributed to the percolation along zero energy channels [26,27].…”