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When magnetic field $B$ is applied to a metal, nearly all observable quantities exhibit oscillations periodic in $1/B$. Such quantum oscillations reflect the fundamental reorganization of electron states into Landau levels as a canonical response of the metal to the applied magnetic field. We predict here that, remarkably, in the recently discovered Dirac and Weyl semimetals quantum oscillations can occur in the complete absence of magnetic field. These zero-field quantum oscillations are driven by elastic strain which, in the space of the low-energy Dirac fermions, acts as a chiral gauge potential. We propose an experimental setup in which the strain in a thin film (or nanowire) can generate pseudomagnetic field $b$ as large as 15T and demonstrate the resulting de Haas-van Alphen and Shubnikov-de Haas oscillations periodic in $1/b$.
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Weyl semimetals in a magnetic field give rise to interesting non-local electronic orbits: the ballistic transport through the bulk enabled by the chiral Landau levels is combined with a momentum-space sliding along the surface Fermi-arc driven by the Lorentz force. Bulk chiral Landau levels can also be induced by axial fields whose sign depends on the chirality of the Weyl point. However, the microscopic perturbations that give rise to them can be described in terms of gauge fields only in the low-energy sectors around the Weyl points. In addition, since pseudo-fields are intrinsic, there is no apparent reason for a Lorentz force that causes sliding along the Fermi-arcs. Therefore, the existence of non-local orbits driven exclusively by pseudo-fields is not obvious. Here, we show that for systems with at least four Weyl points in the bulk spectrum, non-local orbits can be induced by axial fields alone. We discuss the underlying mechanisms by a combination of analytical semi-classical theory, the microscopic numerical study of wave-packet dynamics, and a surface Greens function analysis.
Resonant transmission through electronic quantum states that exist at the zero points of a magnetic field gradient inside a ballistic quantum wire is reported. Since the semiclassical motion along such a line of zero magnetic field takes place in form of unidirectional snake trajectories, these states have no classical equivalence. The existence of such quantum states has been predicted more than a decade ago by theoretical considerations of Reijniers and coworkers [1]. We further show how their properties depend on the amplitude of the magnetic field profile as well as on the Fermi energy.
Shubnikov de Haas resistance oscillations of highly mobile two dimensional helical electrons propagating on a conducting surface of strained HgTe 3D topological insulator are studied in magnetic fields B tilted by angle $theta$ from the normal to the conducting layer. Strong decrease of oscillation amplitude A is observed with the tilt: $A sim exp(-xi/cos(theta))$, where $xi$ is a constant. Evolution of the oscillations with temperature T shows that the parameter $xi$ contains two terms: $xi=xi_1+xi_2 T$. The temperature independent term, $xi_1$, describes reduction of electron mean free path in magnetic field B pointing toward suppression of the topological protection of the electron states against impurity scattering. The temperature dependent term, $xi_2 T$, indicates increase of the reciprocal velocity of 2D helical electrons suggesting modification of the electron spectrum in magnetic fields.
The magnetotransport of highly mobile 2D electrons in wide GaAs single quantum wells with three populated subbands placed in titled magnetic fields is studied. The bottoms of the lower two subbands have nearly the same energy while the bottom of the third subband has a much higher energy ($E_1approx E_2<<E_3$). At zero in-plane magnetic fields magneto-intersubband oscillations (MISO) between the $i^{th}$ and $j^{th}$ subbands are observed and obey the relation $Delta_{ij}=E_j-E_i=kcdothbaromega_c$, where $omega_c$ is the cyclotron frequency and $k$ is an integer. An application of in-plane magnetic field produces dramatic changes in MISO and the corresponding electron spectrum. Three regimes are identified. At $hbaromega_c ll Delta_{12}$ the in-plane magnetic field increases considerably the gap $Delta_{12}$, which is consistent with the semi-classical regime of electron propagation. In contrast at strong magnetic fields $hbaromega_c gg Delta_{12}$ relatively weak oscillating variations of the electron spectrum with the in-plane magnetic field are observed. At $hbaromega_c approx Delta_{12}$ the electron spectrum undergoes a transition between these two regimes through magnetic breakdown. In this transition regime MISO with odd quantum number $k$ terminate, while MISO corresponding to even $k$ evolve $continuously$ into the high field regime corresponding to $hbaromega_c gg Delta_{12}$
A new type of angular oscillations of the high-frequency conductivity for conductors with a band-contact line has been predicted. The effect is caused by groups of charge carriers near the self-intersection points of the Fermi surface, where the electron energy spectrum is near-linear and can be described by anisotropic Dirac cone model. The amplitude of the resonance peaks satisfies the simple sum rule. The ease in changing the degree of anisotropy of the Dirac cone due to the angle of inclination of the magnetic field makes the considered type of oscillations attractive for experimental observation of relativistic effects
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