Moving frame theory of zero-bias photocurrent on the surface of topological insulators

The recent observation of zero-biased photocurrent on the surface of topological insulators allows to spin-orbit-coupled two-dimensional Dirac cones as ideal platforms for the manipulation of the tilt of Dirac cone. We show that the in-plane effective magnetic field <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mover accent="true"><a:mi>B</a:mi><a:mo>̃</a:mo></a:mover></a:math> implements a moving frame transformation on the topological insulators' helical surface states. As a result, photo-excited electrons on the surface undergo a Galilean boost proportional to the effective in-plane magnetic field <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mover accent="true"><c:mi>B</c:mi><c:mo>̃</c:mo></c:mover></c:math>. The boost velocity is transversely proportional to <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mover accent="true"><e:mi>B</e:mi><e:mo>̃</e:mo></e:mover></e:math>. This explains why the experimentally observed photocurrent depends linearly on <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mover accent="true"><g:mi>B</g:mi><g:mo>̃</g:mo></g:mover></g:math>. Our theory, while consistent with the observation that at leading order the effect does not depend on the polarization of the incident radiation, at next leading order in <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mover accent="true"><i:mi>B</i:mi><i:mo>̃</i:mo></i:mover></i:math> predicts a polarization dependence in both parallel and transverse directions to the polarization. We also predict two induced Fermi-surface effects that can serve as further confirmation of our moving frame theory. Based on the estimated value <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:mi>ζ</k:mi><k:mo>≈</k:mo><k:mn>0.34</k:mn></k:mrow></k:math> of the tilt parameter for a magnetic field of <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mrow><l:mover accent="true"><l:mi>B</l:mi><l:mo>̃</l:mo></l:mover><l:mo>∼</l:mo><l:mn>3</l:mn><l:mi mathvariant="normal">T</l:mi></l:mrow></l:math>, our geometric picture qualifies the surface Dirac cone of magnetic topological insulators as an accessible platform for the synthesis and experimental investigation of strong analog gravitational phenomena.