Vestigial nematic order and superconductivity in the doped topological insulator Cu x Bi2Se3

Abstract

If the topological insulator Bi 2 Se 3 is doped with electrons, superconductivity with T c = 3-4 K emerges for a low density of carriers (n = 10 20 cm −3 ) and with a small ratio of the superconducting coherence length and Fermi wave length: ξ/λ F = 2…4. These values make fluctuations of the superconducting order parameter increasingly important, to the extend that the T c -value is surprisingly large. Strong spin-orbit interaction led to the proposal of an odd-parity pairing state. This begs the question of the nature of the transition in an unconventional superconductor with strong pairing fluctuations. We show that for a multi-component order parameter, these fluctuations give rise to a nematic phase at T nem > T c . Below T c several experiments demonstrated a rotational symmetry breaking where the Cooper pair wave function is locked to the lattice. Our theory shows that this rotational symmetry breaking, as vestige of the superconducting state, already occurs above T c . The nematic phase is characterized by vanishing offdiagonal long range order, yet with anisotropic superconducting fluctuations. It can be identified through direction-dependent para-conductivity, lattice softening, and an enhanced Raman response in the E g symmetry channel. In addition, nematic order partially avoids the usual fluctuation suppression of T c .

Uniaxial-strain control of nematic superconductivity in SrxBi2Se3

“…In Nb x Bi 2 Se 3 , a spontaneous lattice distortion occurring at a temperature slightly above T c has been experimentally reported 41 , apparently consistent with the theoretical proposal of vestigial nematic order induced by superconducting fluctuation 42 . In this experiment, H c2 along x is found to become larger (corresponding to the Δ 4x state) after the lattice spontaneously shrinks along the y (a * ) axis, inferring a negative coupling constant g. This observation, obtained with passive lattice response, is consistent with and complementary to the observation of the present work using active lattice control.…”

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

“…As we will explain below, these observations are perfectly consistent with a vestigial nematic phase of symmetry-breaking pairing fluctuations, recently predicted in Ref. 25 . This observation of a genuine symmetry breaking of pairing fluctuations above T c is qualitatively distinct from the gradual onset of order-parameter fluctuations in the disordered phase 26 or the crossover to Bose-Einstein condensation of pairs 27 .…”

“…5b the diamagnetic susceptibility obtained within the theory of Ref. 25 . The susceptibility is compared with the data of Fig.…”

Structural distortion behind the nematic superconductivity in Sr x Bi2Se3

“…This fact is a strong indication that the same structural distortion governs the nematic magnetoresistance in both SC and normal state. The anisotropic magnetoresistance in the normal state slowly weakens with temperature (figures 2(e), (f)), and preserves its 2-fold symmetry up to 200 K. In other words, the SC in-plane axis can be anticipated from AMR not only close to T c , as recently predicted in [27], but also well above T c , i.e, this effect is of structural nature.…”