Incipient loop-current order in the underdoped cuprate superconductors

Abstract

There are growing experimental evidence which indicate discrete symmetry breaking like parity, time-reversal and C4 lattice rotation in the pseudo-gap state of the under-doped copper-oxide based (cuprate) superconductors. The discrete symmetry breaking manifests a true phase transition to an ordered state. A detailed thermodynamic understanding of these orders can answer various puzzles related to the nature of the transition at the pseudogap temperature T * . In this work, we investigate thermodynamic signature of parity and time-reversal symmetry breaking within a theory of two kinds of instabilities in particle-particle (p-p) and particle-hole (p-h) channels in the pseudo-gap state. The p-p and p-h instabilities correspond to superconductivity (SC) and bond-excitonic (BDW) orders respectively. The BDW can generate both modulating charge and current densities. This scenario leads to an intricate competition between the ubiquitous charge density wave and SC, which is prominent in various cuprates in the under-doped regime. We show that a mean-field ground state of coexisting BDW and SC can spontaneously break the parity and time-reversal symmetry below superconducting critical temperature, provided the BDW itself breaks the time-reversal and parity. We describe that an auxiliary order parameter, referred as magneto-electric loop current (MELC) order, can be constructed from a composite of BDW and SC fields. We demonstrate that the MELC order spontaneously breaks parity and time-reversal symmetry and emerges due to a preemptive phase transition at a higher temperature before the primary orders set in.

Loop currents in quantum matter

“…Our recent results in spin-ladders [37] shows that local discrete symmetries are also broken in 1D spin liquid systems, as it has been theoretically predicted. In other models, based on a PDW state [39,40] or a fractionalized PDW instability [41], the PG is described as a highly fluctuating state, where a preemptive phase breaking both T-and P-symmetries (a LC-like phase) is expected at higher temperature. More generally, discrete symmetry breaking usually happens at higher temperature than continuous symmetry breaking.…”

“…For instance in Ref. [41], one starts with two primary states reported at lower temperature deep in the PG state (namely, the incipient CDW and superconductivity, both carrying a d -wave symmetry). The PG state is proposed to be a composite multi-component order parameter, where the system fluctuates between the two primary states which are intertwined.…”

“…terms of a so-called "ancillary state" inseparable from the PG state [38][39][40][41]. The ancillary state is a secondary instability associated to a mother instability which itself effectively opens the PG.…”

“…The ancillary state is a secondary instability associated to a mother instability which itself effectively opens the PG. For instance, it can correspond to pair-density-wave (PDW) states [39][40][41]. Within these approaches, it was first pointed out by Agterberg et al [39] that the LC phase necessarily happens owing to the symmetry and is therefore essential to capture the specific nature of the PG.…”

Loop currents in two-leg ladder cuprates

“…n recent years, the study of doped Mott insulators, such as superconducting (SC) cuprates [1][2][3][4][5] or iridates 6 , raised the question of the existence of other kinds of magnetism. Beyond conventional spin magnetism, a new form of magnetism may originate from magneto-electric loop currents (LCs) [7][8][9][10][11][12][13] or Dirac multipoles [14][15][16][17] . While most of these states are usually discussed for hole-doped quasi-2D transition metal oxides such as cuprates and iridates, the existence of LCs was also addressed in quasi-1D spin ladder cuprates [18][19][20] .…”