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The realization of quantum spin Hall (QSH) effect in HgTe quantum wells (QWs) is considered a milestone in the discovery of topological insulators. The QSH edge states are predicted to allow current to flow at the edges of an insulating bulk, as demonstrated in various experiments. A key prediction of QSH theory that remains to be experimentally verified is the breakdown of the edge conduction under broken time reversal symmetry (TRS). Here we first establish a rigorous framework for understanding the magnetic field dependence of electrostatically gated QSH devices. We then report unexpected edge conduction under broken TRS, using a unique cryogenic microwave impedance microscopy (MIM), on a 7.5 nm HgTe QW device with an inverted band structure. At zero magnetic field and low carrier densities, clear edge conduction is observed in the local conductivity profile of this device but not in the 5.5 nm control device whose band structure is trivial. Surprisingly, the edge conduction in the 7.5 nm device persists up to 9 T with little effect from the magnetic field. This indicates physics beyond simple QSH models, possibly associated with material- specific properties, other symmetry protection and/or electron-electron interactions.
Near-infrared magneto-optical spectroscopy of single-walled carbon nanotubes reveals two absorption peaks with an equal strength at high magnetic fields ($>$ 55 T). We show that the peak separation is determined by the Aharonov-Bohm phase due to the
The behavior of conduction electrons on magnetic structures has been intensely investigated. A typical example is the anomalous Hall effect in a ferromagnet. However, distinguishing various anomalous and normal Hall signals induced from the time-reve
We propose a minimal effective two-dimensional Hamiltonian for HgTe/CdHgTe quantum wells (QWs) describing the side maxima of the first valence subband. By using the Hamiltonian, we explore the picture of helical edge states in tensile and compressive
The Zeeman splitting of the conduction band in the HgTe quantum wells both with normal and inverted spectrum has been studied experimentally in a wide electron density range. The simultaneous analysis of the SdH oscillations in low magnetic fields at
The solutions for the helical edge states for an effective continuum model for the quantum spin Hall effect in HgTe/CdTe quantum wells are presented. For a sample of a large size, the solution gives the linear dispersion for the edge states. However,