Imaging topologically protected transport with quantum degenerate gases

Abstract

Ultracold and quantum degenerate gases held near conductive surfaces can serve as sensitive, high resolution, and wide-area probes of electronic current flow. Previous work has imaged transport around grain boundaries in a gold wire by using ultracold and Bose-Einstein condensed atoms held microns from the surface with an atom chip trap. We show that atom chip microscopy may be applied to useful purpose in the context of materials exhibiting topologically protected surface transport. Current flow through lithographically tailored surface defects in topological insulators (TI)---both idealized and with the band-structure and conductivity typical of Bi$_{2}$Se$_{3}$---is numerically calculated. We propose that imaging current flow patterns enables the differentiation of an ideal TI from one with a finite bulk--to--surface conductivity ratio, and specifically, that the determination of this ratio may be possible by imaging transport around trenches etched into the TI's surface.Comment: Extensively rewritten, better introduction. 12 pages, 10 figure

Symmetry protected Josephson supercurrents in three-dimensional topological insulators

“…These simulations strongly suggest that the large majority of supercurrent is carried along the surface of the TI, and that this occurs because of crystal symmetries rather than a discrepancy in bulk and surface mobilities. This is in stark contrast to normal state transport simulations for Bi 2 Se 3 , which have shown that when the chemical potential is pushed out of the purely topological regime, current flows primarily through the bulk due to the onset of many additional available states 24 . We find that the supercurrent only degrades if the surface is encumbered with elastic scattering centres, or if bulk disorder is so large that surface-bulk band hybridization occurs.…”

Detecting Chiral Edge States in the Hofstadter Optical Lattice

“…These transport properties are directly related to the existence of chiral edge states: while bulk excitations remain inert, these gapless states carry current along the edge of the system. According to the bulk-edge correspondence [16,17], the Chern numbers characterizing the bulk bands determine the number of edge excitations and their chirality, which protects the edge transport against small perturbations.In view of the experimental progress [8][9][10], an important issue is to identify observables that provide unambiguous signatures of topological phases in a cold-atom framework [18][19][20][21][22][23][24][25][26][27]. This is a crucial topic from an experimental point of view: Measuring the Hall conductivity is more difficult than for solid-state systems due to the absence of particle reservoirs coupled to the system.…”

Sensing Magnetic Fields with a Giant Quantum Wave

“…Both transport and static magnetization at the ≳100-K ferromagnetic metallic and antiferromagnetic insulating transition in colossal magnetoresistive systems may be imaged. Investigations of topologically protected transport should be possible [19,20], as should investigation of the . Suspended between the atom chip and the BEC is the silicon sample substrate (blue) onto which the gold calibration pattern is fabricated.…”