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Register a new userElastic backscattering of quantum spin Hall edge modes from Coulomb interactions with non-magnetic impurities
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We demonstrate that electrostatic interactions between helical electrons at the edge of a quantum spin Hall insulator and a dynamical impurity can induce quasi-elastic backscattering. Modelling the impurity as a two-level system, we show that transitions between counterpropagating Kramers-degenerate electronic states can occur without breaking time-reversal symmetry, provided that the impurity also undergoes a transition. The associated electrical resistance has a weak temperature dependence down to a non-universal temperature scale. Our results extend the range of known backscattering mechanisms in helical edge modes to include scenarios where electron tunnelling out of the system is absent.
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The outstanding transport properties expected at the edge of two-dimensional time-reversal invariant topological insulators have proven to be challenging to realize experimentally, and have so far only been demonstrated in very short devices. In search for an explanation to this puzzling observation, we here report a full first-principles calculation of topologically protected transport at the edge of novel quantum spin Hall insulators - specifically, Bismuth and Antimony halides - based on the non-equilibrium Greens functions formalism. Our calculations unravel two different scattering mechanisms that may affect two-dimensional topological insulators, namely time-reversal symmetry breaking at vacancy defects and inter-edge scattering mediated by multiple co-operating impurities, possibly non-magnetic. We discuss their drastic consequences for typical non-local transport measurements as well as strategies to mitigate their negative impact. Finally, we provide an instructive comparison of the transport properties of topologically protected edge states to those of the trivial edge states in MoS$_2$ ribbons. Although we focus on a few specific cases (in terms of materials and defect types) our results should be representative for the general case and thus have significance beyond the systems studied here.
We investigate nonperturbatively the effect of a magnetic dopant impurity on the edge transport of a quantum spin Hall (QSH) insulator. We show that for a strongly coupled magnetic dopant located near the edge of a system, a pair of transmission anti-resonances appear. When the chemical potential is on resonance, interaction effects broaden the anti-resonance width with decreasing temperature, thus suppressing transport for both repulsive and moderately attractive interactions. Consequences for the recently observed QSH insulating phase of the $1$-T$^{prime}$ of WTe$_2$ are briefly discussed.
Fractional conductance is measured by partitioning $ u = 1$ edge state using gate-tunable fractional quantum Hall (FQH) liquids of filling 1/3 or 2/3 for current injection and detection. We observe two sets of FQH plateaus 1/9, 2/9, 4/9 and 1/6, 1/3, 2/3 at low and high magnetic field ends of the $ u = 1$ plateau respectively. The findings are explained by magnetic field dependent equilibration of three FQH edge modes with conductance $e^2/3h$ arising from edge reconstruction. The results reveal remarkable enhancement of the equilibration lengths of the FQH edge modes with increasing field.
Conductance of the edge modes as well as conductance across the co-propagating edge modes around the u = 4/3, 5/3 and 2 quantum Hall states are measured by individually exciting the modes. Temperature dependent equilibration rates of the outer unity conductance edge mode are presented for different filling fractions. We find that the equilibration rate of the outer unity conductance mode at u = 2 is higher and more temperature sensitive compared to the mode at fractional filling 5/3 and 4/3. At lowest temperature, equilibration length of the outer unity conductance mode tends to saturate with lowering filling fraction u by increasing magnetic field B. We speculate this saturating nature of equilibration length is arising from an interplay of Coulomb correlation and spin orthogonality.
We consider an impurity with a spin degree of freedom coupled to a finite reservoir of non-interacting electrons, a system which may be realized by either a true impurity in a metallic nano-particle or a small quantum dot coupled to a large one. We show how the physics of such a spin impurity is revealed in the many-body spectrum of the entire finite-size system; in particular, the evolution of the spectrum with the strength of the impurity-reservoir coupling reflects the fundamental many-body correlations present. Explicit calculation in the strong and weak coupling limits shows that the spectrum and its evolution are sensitive to the nature of the impurity and the parity of electrons in the reservoir. The effect of the finite size spectrum on two experimental observables is considered. First, we propose an experimental setup in which the spectrum may be conveniently measured using tunneling spectroscopy. A rate equation calculation of the differential conductance suggests how the many-body spectral features may be observed. Second, the finite-temperature magnetic susceptibility is presented, both the impurity susceptibility and the local susceptibility. Extensive quantum Monte-Carlo calculations show that the local susceptibility deviates from its bulk scaling form. Nevertheless, for special assumptions about the reservoir -- the clean Kondo box model -- we demonstrate that finite-size scaling is recovered. Explicit numerical evaluations of these scaling functions are given, both for even and odd parity and for the canonical and grand-canonical ensembles.
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