Z3-vestigial nematic order due to superconducting fluctuations in the doped topological insulators NbxBi2Se3 and CuxBi2Se3

Abstract

Abstract A state of matter with a multi-component order parameter can give rise to vestigial order. In the vestigial phase, the primary order is only partially melted, leaving a remaining symmetry breaking behind, an effect driven by strong classical or quantum fluctuations. Vestigial states due to primary spin and charge-density-wave order have been discussed in iron-based and cuprate materials. Here we present the observation of a partially melted superconductivity in which pairing fluctuations condense at a separate phase transition and form a nematic state with broken Z 3 , i.e., three-state Potts-model symmetry. Thermal expansion, specific heat and magnetization measurements of the doped topological insulators Nb x Bi 2 Se 3 and Cu x Bi 2 Se 3 reveal that this symmetry breaking occurs at $${{T}}_{\mathrm{nem}} \simeq 3.8\,K$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>nem</mml:mi></mml:mrow></mml:msub><mml:mo>≃</mml:mo><mml:mn>3.8</mml:mn><mml:mspace/><mml:mi>K</mml:mi></mml:math> above $${T}_{{\mathrm{c}}} \simeq 3.25\,K$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo>≃</mml:mo><mml:mn>3.25</mml:mn><mml:mspace/><mml:mi>K</mml:mi></mml:math> , along with an onset of superconducting fluctuations. Thus, before Cooper pairs establish long-range coherence at T c , they fluctuate in a way that breaks the rotational invariance at T nem and induces a crystalline distortion.