Finite-frequency admittance and noise of a helical edge coupled to a magnet

The exchange coupling of the helical edge state of a quantum spin-Hall insulator with an easy-plane magnet has no effect on its dc electrical conductance if the magnet's anisotropy axis is aligned with the spin-quantization axis of the helical edge state [Meng , ]. We here calculate the ac conductance <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>G</a:mi> <a:mi>V</a:mi> </a:msub> <a:mrow> <a:mo>(</a:mo> <a:mi>ω</a:mi> <a:mo>)</a:mo> </a:mrow> </a:mrow> </a:math> and the noise power <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:msub> <b:mi>S</b:mi> <b:mi>V</b:mi> </b:msub> <b:mrow> <b:mo>(</b:mo> <b:mi>ω</b:mi> <b:mo>)</b:mo> </b:mrow> </b:mrow> </b:math> in the presence of a dc bias <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>V</c:mi> </c:math> . While both take the universal values <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:msub> <d:mi>G</d:mi> <d:mi>V</d:mi> </d:msub> <d:mrow> <d:mo>(</d:mo> <d:mrow> <d:mi>ω</d:mi> <d:mo>=</d:mo> <d:mn>0</d:mn> </d:mrow> <d:mo>)</d:mo> </d:mrow> <d:mo>=</d:mo> <d:msup> <d:mi>e</d:mi> <d:mn>2</d:mn> </d:msup> <d:mo>/</d:mo> <d:mi>h</d:mi> </d:mrow> </d:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:msub> <e:mi>S</e:mi> <e:mi>V</e:mi> </e:msub> <e:mrow> <e:mo>(</e:mo> <e:mi>ω</e:mi> <e:mo>=</e:mo> <e:mn>0</e:mn> <e:mo>)</e:mo> </e:mrow> <e:mo>=</e:mo> <e:mn>4</e:mn> <e:msup> <e:mi>e</e:mi> <e:mn>2</e:mn> </e:msup> <e:msub> <e:mi>k</e:mi> <e:mi mathvariant="normal">B</e:mi> </e:msub> <e:mi>T</e:mi> <e:mo>/</e:mo> <e:mi>h</e:mi> </e:mrow> </e:math> in the zero-frequency limit, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:msub> <g:mi>G</g:mi> <g:mi>V</g:mi> </g:msub> <g:mrow> <g:mo>(</g:mo> <g:mi>ω</g:mi> <g:mo>)</g:mo> </g:mrow> </g:mrow> </g:math> and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:msub> <h:mi>S</h:mi> <h:mi>V</h:mi> </h:msub> <h:mrow> <h:mo>(</h:mo> <h:mi>ω</h:mi> <h:mo>)</h:mo> </h:mrow> </h:mrow> </h:math> are quickly suppressed for finite <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mi>ω</i:mi> </i:math> , so that low-frequency transport is effectively noiseless.