Quantum transport through pairs of edge states of opposite chirality at electric and magnetic boundaries

Abstract

We theoretically investigate electrical transport in a quantum Hall system hosting bulk and edge current carrying states. Spatially varying magnetic and electric confinement creates pairs of current carrying lines that drift in the same or opposite directions depending on whether confinement is applied by a magnetic split gate or a magnetic strip gate. We study the electronic structure through calculations of the local density of states and conductivity of the channel as a function of the chirality and wave-function overlap of these states. We demonstrate a shift of the conductivity peaks to high or low magnetic field depending on chirality of pairs of edge states and the effect of chirality on backscattering amplitude associated with collisional processes.

Non-uniform magnetic fields for single-electron control

“…In particular, different settings of the non-linear magnetic field can be used to guide electron trajectories to a desired region of space. Furthermore, it is shown that certain evolution patterns such as snake trajectories and edge states, 2,26,27 which are expected from classical considerations, are maintained by quantum evolution. They can be used to guide and manipulate an electron state by restraining it in a desired region, splitting the density distribution, or affecting its spreading.…”

“…The field of electron quantum optics studies and applies electromagnetic (EM) field-controlled phenomena for manipulating electron states in solid-state quantum systems. [1][2][3][4][5] Ideally, transport theories should describe both processes governing electron trajectories and wave phenomena such as interference and diffraction in multiple dimensions. Theories based on EM potentials rely on formal mathematical apparatus related to the choice of scalar and vector potentials, which, however, obscures the physical aspects and thus the heuristic understanding of electron evolution.…”

Generation, manipulation and detection of snake state trajectories of a neutral atom in a ring-cavity

“…The snake trajectories of electrons had been widely studied in various condensed matter systems consisting of two-dimensional electron gas [27,30,32,37], graphene p − n junctions [25,26], etc. It may be noted that the dimensions of the magnetic field for an electron, [M A −1 T −2 ], includes the dimensions of charge, ([q] = [AT ]).…”

“…The first experimental confirmation of such states was carried in a 2DEG realised in GaAs-AlGaAs heterostructure by K. von Klitzing's group [29]. These developments were subsequently followed by a substantial number of theoretical and experimental studies [30][31][32][33][34][35][36][37].…”

Instability induced by exchange forces in a 2D electron gas in a magnetic field with uniform gradient

“…Using qualitative reasoning Müller also pointed out that the classical electron trajectory is snakelike and weaves around the B z = 0 line. Other authors (including the present author) [4][5][6][7][8] followed up with various other calculations but none included the exchange force. As it turns out, the omission is crucial; exchange effects are so large that calculations not including them might need to be reassessed or redone.…”