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We study the thermodynamic properties of the two-component $2+1$-dimensional massive Dirac fermions in an external magnetic field. The broken time-reversal symmetry results in the presence of a linear in the magnetic field part of the thermodynamic potential, while in the famous problem of Landau diamagnetism the leading field dependent term is quadratic in the field. Accordingly, the leading term of the explicitly calculated magnetization is anomalous, viz. it is independent of the strength of the magnetic field. The Stv{r}eda formula is employed to describe how the anomalous magnetization is related to the anomalous Hall effect.
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
We provide numerical evidence that the Onsager symmetry remains valid for systems subject to a spatially dependent magnetic field, in spite of the broken time-reversal symmetry. In addition, for the simplest case in which the field strength varies on
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
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 demo
In this work, we perform a statistical study on Dirac Billiards in the extreme quantum limit (a single open channel on the leads). Our numerical analysis uses a large ensemble of random matrices and demonstrates the preponderant role of dephasing mec