Phase crystals

Abstract

Superconducting order owes its properties to broken symmetry of the U (1) phase. In the presence of competing orders, or in pairbreaking environments, usual superconductivity may give way to modified condensates. Here we describe one such alternative, where the low-temperature ground state is more ordered due to formation of a periodic modulation of the phase. This state is manifested by spatially-periodic superflow patterns and circulating currents which break time-reversal symmetry. We demonstrate using microscopic theory how it can be realized near edges of superconductors that host flat bands of zero-energy Andreev bound states. More generally, we trace the origin of phase crystallization to non-local properties of the gradient energy, which implies existence of similar pattern-forming instabilities in many other systems. arXiv:1906.04793v1 [cond-mat.supr-con]

Disorder-robust phase crystal in high-temperature superconductors from topology and strong correlations

“…In both cases θ acquires distinct and modulating non-zero values near the pair breaking [110] edge, thus breaking both time reversal symmetry and translational symmetry along the [110] edge. These modulations define a phase crystal state, 24 previously found in the absence of strong correlations in both quasi-classical theory 22,43 and BdG. 25 Clearly, the phase crystal also thrives in the presence of the strong correlations found in the cuprates, and remarkably here also features multiple new distinct properties.…”

“…This is in agreement with the healing length of the pairing amplitude around single impurities in the cuprates, which instead depends on the proximity to the Mott insulating normal state. 44 In contrast, λ ⊥ in BdG 25 (and also quasiclassical results 24 ) is always related to the superconducting coherence length and has no relation to the charge density fluctuations, as also seen in Fig. 1(d).…”

“…The strikingly short λ ⊥ with strong correlations has important consequences for the phase crystal as its modulations along the edge is set by an intricate energy balance: A spatially varying θ in the bulk costs kinetic energy, whereas such variations in θ along the edge instead lower the free energy through a Doppler shift of the zero-energy states. 23,24 Hence, the very short λ ⊥ in GIMT automatically gives a very short modulation wavelength of the phase crystal along the edge, as is evident in Fig. 1(a).…”

“…[16][17][18][19][20][21] The likely most promising intrinsic scenario involves an exotic state called "phase crystal", which spontaneously breaks both time reversal and translational symmetries along the [110] edge. [22][23][24][25] In this state, the phase of the d-wave superconducting order parameter is modulated along the edge, creating superflow patterns which lower the free energy by Doppler shifting some, but not all, states away from zero energy. This state was originally found in quasiclassical calculations, 22 but subsequently also in a weak-coupling tight-binding model.…”

Self-consistent theory of current injection into $d$ and $d + is$ superconductors

“…One possible explanation for the absence of the split of the ZBCP that has been proposed recently is the formation of an inhomogeneous state at the edge with spontaneous circulating currents below a relatively large transition temperature T * ≈ 0.18T c0 [28,29]. This time-reversal symmetry broken state is referred to as phase crystal [30] and is robust also in presence of strong correlations and Anderson disorder [31]. If this state is formed it also suppresses the nucleation of the subdominant component if the criticial temperature for the formation of subdominant order, T s , is too low.…”