Signatures of topology in ballistic bulk transport of HgTe quantum wells

Abstract

We calculate bulk transport properties of two-dimensional topological insulators based on HgTe quantum wells in the ballistic regime. Interestingly, we find that the conductance and the shot noise are distinctively different for the so-called normal regime (the topologically trivial case) and the so-called inverted regime (the topologically non-trivial case). Thus, it is possible to verify the topological order of a two-dimensional topological insulator not only via observable edge properties but also via observable bulk properties. This is important because we show that under certain conditions the bulk contribution can dominate the edge contribution which makes it essential to fully understand the former for the interpretation of future experiments in clean samples. The physics of topological insulators, that are bulk insulators with certain topological properties, is one of the most active areas in modern condensed matter research. These insulators can be either characterized by bulk Chern numbers [1] or by a so-called Z 2 topological order, in which a system, that is invariant under timereversal symmetry (TRS), is classified into two classes according to whether there are an even or odd number of Kramers partners of edge states at a given boundary of the system [2]. The latter classification makes it illustrative how to distinguish a topologically trivial from a topologically non-trivial insulator with respect to TRS. If there is an odd number of Kramers partners at a given edge then the system is considered to be topologically non-trivial because no scattering potential that preserves TRS can scatter a left-mover into a right-mover. This scattering process is strictly forbidden by TRS [3]. If instead there is an even number of Kramers partners at a given edge, the system is called topologically trivial because the edge states are not protected anymore against potential scattering by TRS and, hence, a left-mover can rather easily scatter into a right-mover and vice versa.Only one year after the prediction has been made that HgTe quantum wells (QWs) are prime candidates for two-dimensional topological insulators [4], experimental evidence based on edge state transport has been found [5]. In HgTe QWs, the thickness of the well controls the topology, meaning that thinner wells (below a critical thickness) are topologically trivial insulators and thicker wells (above a critical thickness) are topologically nontrivial insulators. The former is called normal regime, the latter inverted regime, and the critical thickness has been coined mass-inversion point with respect to the effective model discussed in more detail below. To the best of our knowledge, all experimental evidence both in twodimensional [5] as well as three-dimensional topological insulators [6] is based on the physics of the edges. In this Letter, we propose a way to experimentally distinguish a trivial from a non-trivial two-dimensional topological insulator using bulk properties only. We calculate the linear conductance as well as the Fano factor ...

Interplay of bulk and edge states in transport of two-dimensional topological insulators

“…We will refer to it as mini-gap from here on. One can notice that outside of the bulk gap (solid lines) the signals of the normal and the inverted regimes behave similar, like it was found for wide structures 12,13 . Within the gap however and for the PBC, a clear conductance peak in the inverted regime around E f = 0 is seen, while in the normal regime the transport is almost completely suppressed.…”

“…it was found for wide structures 12,13 . Within the gap however and for the PBC, a clear conductance peak in the inverted regime around E f = 0 is seen, while in the normal regime the transport is almost completely suppressed.…”

“…(13). Our analysis will focus on the lowest modes in PBC and HBC, which give the largest contribution to the signal.…”

“…To analyze the influence of disorder let us here vary the sample structure and the parameters, similarly as it was performed for PBC in Ref. 13. First we decrease the width of the sample to 150 nm.…”

“…12 that a non-monotonic conductance as a function of geometrical aspect ratio in metal/HgTe/metal junctions with a characteristic maximum describes the topological insulator regime. The conductance maximum occurs when incoming metallic bulk states tunnel through a short and wide two-dimensional topological insulator and is robust against scalar disorder on the order of the energy gap 13 . However, so far this analysis was limited to the periodic boundary conditions (PBC) and neglected the existence of edge states, which can significantly modify the behavior in experimentally relevant setups.…”