Boundary conductance in macroscopic bismuth crystals

Abstract

The interface between a solid and vacuum can become electronically distinct from the bulk. This feature, encountered in the case of quantum Hall effect, has a manifestation in insulators with topologically protected metallic surface states. Non-trivial Berry curvature of the Bloch waves or periodically driven perturbation are known to generate it. Here, by studying the angle-dependent magnetoresistance in prismatic bismuth crystals of different shapes, we detect a robust surface contribution to electric conductivity when the magnetic field is aligned parallel to a two-dimensional boundary between the three-dimensional crystal and vacuum. The effect is absent in antimony, which has an identical crystal symmetry, a similar Fermi surface structure and equally ballistic carriers, but an inverted band symmetry and a topological invariant of opposite sign. Our observation confirms that the boundary interrupting the cyclotron orbits remains metallic in bismuth, which is in agreement with what was predicted by Azbel decades ago. However, the absence of the effect in antimony indicates an intimate link between band symmetry and this boundary conductance.

Magneto-Seebeck effect in bismuth

“…At lower temperatures, one problem of our theory could be that we consider only electronphonon scattering, but not electron-electron scattering. Furthermore, there is a recent report on a difference between bulk and surface conductance at low temperatures in bismuth [18], which is out of the scope of the theory developed here. Lastly, phonon drag is important to the thermoelectricity of bismuth at very low temperatures [12,24,25], but not taken into account here.…”

“…the electron density n equals the hole density p. At low temperatures, they amount only to n = p = 3.0 • 10 −17 cm −3 [16], being equivalent to one carrier of each sign per 10 5 atoms as well as a very small Fermi energy. The very large magnetoresistance reflects the extremely high mobility of the charge carriers, which are ballistic at low temperatures [17,18]. The Fermi surface consists of one hole pocket with parabolic dispersion and three cigar-shaped electron pockets containing Dirac fermions with an extremely anisotropic band structure, the lowest effective mass being equivalent to approximately 10 −3 bare electron masses [19].…”

Dispenser Printed Bismuth‐Based Magnetic Field Sensors with Non‐Saturating Large Magnetoresistance for Touchless Interactive Surfaces

“…[ 21–24 ] LMR is a non‐saturating quantum magnetoresistive effect present in bulk Bi, as well as Bi thin films and nanostructures allowing to achieve >300% resistance change at 5 T at room temperature. [ 19,25–27 ] In terms of the range of detection, the non‐saturating behavior of LMR materials contrasts with the previous sensors based on GMR and AMR effect, where the sensing capabilities are restricted to the low field region where the resistance level saturates and does not change for higher magnetic fields (≈500 mT, and ≈20 mT, for GMR and AMR respectively). Until now, the LMR effect has not been studied in printed materials.…”

Topological Zero-Dimensional Defect and Flux States in Three-Dimensional Insulators

“…For the topological crystalline insulating phases [14,15,[18][19][20][23][24][25][26][27][28][29] that have become known as higher-order TIs (HOTIs) [30-36, 39, 40, 91-106], these efforts have had only recent, incipient success, motivating the present study. Furthermore, though HOTI material candidates are readily accessible, experimental studies of candidate HOTIs have yielded results that have attracted an array of -at times contradictory -explanations [77,98,[107][108][109][110][111][112][113][114][115][116][117][118][119][120][121][122]. In this work, we have performed extensive theoretical and numerical calculations demonstrating that dislocations with integer Burgers vectors [123] in 3D insulators can bind 0D higher-order end (HEND) states with anomalous charge and spin as a consequence of the bulk topology (see Appendices B 1 a, B 1 b, B 2 a, B 2 c, C, and D).…”