Fluctuations and the Higgs Mechanism in Underdoped Cuprates

Abstract

The physics of the pseudo-gap phase of high temperature cuprate superconductors has been an enduring mystery in the past thirty years. The ubiquitous presence of the pseudo-gap phase in under-doped cuprates suggests that its understanding holds a key in unraveling the origin of high temperature superconductivity. In this paper, we review various theoretical approaches to this problem, with a special emphasis on the concept of emergent symmetries in the under-doped region of those compounds. We differentiate the theories by considering a few fundamental questions related to the rich phenomenology of these materials. Lastly we discuss a recent idea of two kinds of entangled preformed pairs which open a gap at the pseudo-gap onset temperature T * through a specific Higgs mechanism. We give a review of the experimental consequences of this line of thoughts.The Pseudo-Gap (PG) state of the cuprates was discovered in 1989 [1], three years after the discovery of high temperature superconductivity in those compounds. It was first observed in nuclear magnetic resonance (NMR) experiments, in an intermediate doping regime 0.06 < p < 0.20, as a loss of the density of states at the Fermi level [1-3] at temperatures above the superconducting transition temperature T c . Subsequently, angle resolved photo emission spectroscopy (ARPES) established that a part of the Fermi surface is gapped in the Anti-Nodal Region (ANR) (regions close to (0, ±π) and (±π, 0) points) of the Brillouin zone, leading to the formation of Fermi 'arcs'. Though the PG state shows behaviors of a metal, the appearance of Fermi 'arcs' instead of a full Fermi surface results into the violation of the conventional Luttinger theorem of Fermi liquid theory. Furthermore, surface spectroscopies like ARPES (see e.g. [4][5][6][7][8]) and scanning tunneling spectroscopy [9][10][11] show that the magnitude of the anti-nodal (AN) gap is unchanged when entering the superconducting (SC) phase below T c (see Fig. 1a). The PG state persists up to a temperature T * which decreases linearly with doping. The AN gap is also visible in two-body spectroscopy, for example in the B 1g channel of Raman scattering [12][13][14], which shows that below T c , the pair breaking gap of superconductivity follows the T * line with doping, in good agreement with the AN gap observed in ARPES. In contrast to the SC phase, the PG state is found to be independent of disorder or magnetic field. Despite of numerous invaluable experimental and theoretical investigations over the last three decades, various puzzles of the PG state remains to be solved.In this paper, we review three different theoretical per-spectives to the PG state of cuprate superconductors.We then focus on one specific theoretical approach where fluctuations protected by a specific Higgs mechanism are held responsible for the unusual properties of the pseudogap phase.

Phase-resolved Higgs response in superconducting cuprates

“…Our observation may indicate preformed Cooper pairs in cuprates without global phase coherence, or the intense terahertz field might enforce phase coherence above T c 12 . The pseudogap, and its various ordered phases including the CDW order, may also play a role in THG above T c 31,32 .…”

Anomalous softening of phonon-dispersion in cuprate superconductors

“…The 'pseudo-gap' phase [1][2][3][4][5][6][7][8] of the under-doped high-temperature copper-oxide based superconductors (cuprates) remains incomprehensible even after decades of research, by and large due to a complex interplay of several symmetry broken orders [9,10]. A universally present translational symmetry broken order in the cuprates is a charge-density wave (CDW) order [11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Energy-length scaling of critical phase fluctuations in the cuprate pseudogap phase

“…For example, there exist two anomalous energy scales: one is the antinodal superconducting gap Δ SN AC (defined by the peak signal of the B 1g Raman response below T c [11]) with a monotonic decrease as the CDW gap (see Figure 1C); the other is the CDW onset temperature T CDW with a dome dependence similar to the superconducting T c (see Figure 1A), suggesting a possible intertwined mechanism between superconductivity and CDW. Do they come from composite energy scales, such as the product or quadrature coupling of two-order parameters [31,51]? If so, does the scaling include characteristic lengths of CDW, superconductivity, or even loop current?…”

“…On the other hand, numerical solutions of the Hubbard model obtain a correct T* line, but it is hard to accurately determine the phase boundaries and the competition between density wave and uniform phases at a finite temperature [26]. Besides, intertwined orders involving both particle-particle (i.e., superconductivity) and particle-hole (e.g., DWO) pairing channels provide a comprehensive description of angle-resolved photoemission spectroscopy (ARPES) data [29,30], but the stability of the emergent symmetry and the multiple wave vectors trick remains questionable [22,31].…”