June 18, 2013

In solids, the kinetic energy of an

electron generally increases as the square of its momentum. By contrast, in a

Topological Insulator such as Bi_{2}Te_{2}Se, electrons on the surface are

predicted to be Dirac Fermions for which the energy increases linearly with

momentum. In a magnetic field *B*, the

allowed states of an electron are quantized into Landau Levels (LLs). The

sequential emptying of occupied LLs in an increasing field leads to quantum

oscillations in the conductance G_{xx} (Fig. 1A). A key signature of Dirac

Fermions is the existence of an extra half-period in the oscillations called “π-Berry

Phase shift”. (Technically, this arises from the ½ Landau Level that exists at

zero energy.) The quantum oscillations provide an elegant way to “count”

directly the available levels. By plotting the fields *B*_{n} of the minima in G_{xx} against the integer *n* (*n*

counts the number of levels still to be emptied), one may determine the

ultimate value of n by extrapolation to infinite field (1/Bà 0).

Measurements to 45 Teslas on a

crystal of Bi_{2}Te_{2}Se by Xiong *et
al.
*[1] reveal that there is ½ level left (Fig. 1B), consistent with Dirac

Fermions. The uncertainties in this experiment are unusually low because of the

large number of oscillations observed and the low index of the last datum (

The results provide firm evidence that the oscillations in Bi

indeed arise from Dirac Fermions.