No Arabic abstract
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-reversal symmetry (TRS) broken by their magnetic structure or applied magnetic field is delicate. In this study, we present a method to investigate TRS broken by the magnetic structure by analyzing magnetic quantum oscillations (MQOs). As is known, if a material is nonmagnetic, the MQO phases can only be two distinct values of 0 or $pi$ from the orbits. When the magnetic structure breaks the TRS, the MQO phase deviates from these values, and the deviation is called the anomalous phase. We observed the anomalous phase in Fe-doped NbSb2, where magnetic Fe impurities break the TRS. The phase of a high-doped sample largely deviates from the phases of low-doped and pristine samples, indicating the anomalous phase. In MQOs, different types of magnetic structures afford different field dependence to the phase; this makes it easy to discern different magnetic structures, which respond differently with magnetic fields. This method can complement the Hall measurement and will provide useful information by itself for studying the magnetic structure of materials.
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 tube-threading magnetic flux, which breaks the time-reversal symmetry and lifts the valley degeneracy. This field-induced symmetry breaking thus overcomes the Coulomb-induced intervalley mixing which is predicted to make the lowest exciton state optically inactive (or ``dark).
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 only in one direction, we analytically derive the result. For the generic case, a qualitative explanation is provided.
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.
Time-reversal (T) symmetry breaking is a fundamental physics concept underpinning a broad science and technology area, including topological magnets, axion physics, dissipationless Hall currents, or spintronic memories. A best known conventional model of macroscopic T-symmetry breaking is a ferromagnetic order of itinerant Bloch electrons with an isotropic spin interaction in momentum space. Anisotropic electron interactions, on the other hand, have been a domain of correlated quantum phases, such as the T-invariant nematics or unconventional superconductors. Here we report discovery of a broken-T phase of itinerant Bloch electrons with an unconventional anisotropic spin-momentum interaction, whose staggered nature leads to the formation of two ferromagnetic-like valleys in the momentum space with opposite spin splittings. We describe qualitatively the effect by deriving a non-relativistic single-particle Hamiltonian model. Next, we identify the unconventional staggered spin-momentum interaction by first-principles electronic structure calculations in a four-sublattice antiferromagnet Mn5Si3 with a collinear checkerboard magnetic order. We show that the staggered spin-momentum interaction is set by nonrelativistic spin-symmetries which were previously omitted in relativistic physics classifications of spin interactions and topological quasiparticles. Our measurements of a spontaneous Hall effect in epilayers of antiferromagnetic Mn5Si3 with vanishing magnetization are consistent with our theory predictions. Bloch electrons with the unconventional staggered spin interaction, compatible with abundant low atomic-number materials, strong spin-coherence, and collinear antiferromagnetic order open unparalleled possibilities for realizing T-symmetry broken spin and topological quantum phases.