Soliton phase near antiferromagnetic quantum critical point in Q1D conductors

Abstract

In frameworks of a nesting model for Q1D organic conductor at the antiferromagnetic (SDW) quantum critical point the first-order transition separates metallic state from the soliton phase having the periodic domain structure. The low temperature phase diagram also displays the 2nd-order transition line between the soliton and the uniformly gapped SDW phases. The results agree with the phase diagram of (TMTSF)2PF6 near critical pressure [T. Vuletic et al., Eur. Phys. J. B 25, 319 (2002)]. Detection of the 2nd-order transition line is discussed. We comment on superconductivity at low temperature.PACS numbers: 71.30.+h, 74.70.Kn, 75.30.Fv We address the issue of quantum critical point (QCP) for the itinerant antiferromagnetism (AFM) (also known as spin-density wave state (SDW)) in Q1D compounds. As it was pointed out in [2], the standard renormalization group (RG) analysis is not applicable for superconductivity QCP and theoretical models for AFM with nesting features because no expansion in a form of a Landau functional is possible near QCP at T = 0 in these cases. QCP with increase in pressure have been observed for SDW in the Bechgaard salts (TMTSF) 2 X (with X=PF 6 [3], AsF 6 [4]) and recently investigated in many details in [1]. According to [1], the phase diagram of (TMTSF) 2 PF 6 near its critical pressure, p c ∼ 9.4kbar, indeed, has a rather complicated character. However, the experimental fact that the transition from metallic to SDW state is of the first order suggests that quantum fluctuations do not play decisive role near p c , and the overall phase diagram near p c for (TMTSF) 2 PF 6 can be understood already on a mean field level.The most unexpected finding in [1] is the discovery of a pressure interval below p c , where SDW and metal phases (SDW and superconductivity (SC) at lower T ) coexist as parallel domains running perpendicular to the chain direction. Such coexistence is difficult to understand for the 1st order transition that takes place at constant pressure [1]. In what follows we propose that such domains can be interpreted as formation of a new phase of the soliton walls suggested first theoretically for the Q1D electron spectrum in [5,6,7]. Domains inside the SDW interval were also observed in [8]. We shall see that it is rather natural to expect SC in these domains at lower temperature. In this presentation we restrict ourselves mainly by the effects related to the physics of SDW. Superconductivity appears at lower temperature than the onset of the SDW/metal phase transition, and we only comment on it at the end.For the SDW description we adopt the standard Q1D model of two open Fermi surface (FS) sheets with the energy spectrum of free electrons in the form:with dispersion in the direction perpendicular to theThe conditionis assumed to conserve the number of electrons. The angular brackets mean averaging over p ⊥ : where u(Q) has a maximum at some Q 0 . Interaction (5) is renormalized after summing up the ladder diagrams:

Superconductivity on the density-wave background with soliton-wall structure

“…In the pressure interval P c1 < P < P c the new state develops, where the DW coexists with superconductivity at rather low temperature T < T SC c , while at higher temperature T SC < T < T DW the DW state coexists with the metallic phase. This coexistence takes place via the formation of small ungapped pockets [16] or via the soliton phase [12,13,14]. We take the DW transition temperature to be much greater than the SC transition temperature, T ≈ 0.1K.…”

“…[13] Compared to the uniformly gapped DW state, the soliton phase gains the kinetic energy of quasiparticles in the half-filled soliton phase due to the term ε + (k y ) in (4), which compensates the energy loss of the non-uniform DW structure. The soliton wall concentration n s depends on external pressure P via the dependence on electron dispersion.…”

“…[13]). The result substantially depends on the harmonic content of electron dispersion t ⊥ (k ⊥ ) [13]. For typical dispersion, at P → P c1 the soliton band width E − /∆ 0 → 0, which corresponds to a phase transition from the uniform DW to the soliton phase.…”

“…Such a strong spatial modulation of the DW order parameter costs energy W of the order of the DW energy gap ∆ 0 , which is much larger than the energy gain due to the surviving of SC state. In this case, the soliton wall scenario [9,10,11,12,13,14] is more favorable, where the energy loss W due to nonuniform DW order parameter is compensated by the large kinetic energy of soliton-band quasiparticles. [11,13] SC appearing in the soliton wall phase of spin-density wave (SDW) has the triplet SC pairing [14] in agreement with experiments in (TMTSF) 2 PF 6 .…”

“…In this case, the soliton wall scenario [9,10,11,12,13,14] is more favorable, where the energy loss W due to nonuniform DW order parameter is compensated by the large kinetic energy of soliton-band quasiparticles. [11,13] SC appearing in the soliton wall phase of spin-density wave (SDW) has the triplet SC pairing [14] in agreement with experiments in (TMTSF) 2 PF 6 . [15] Another microscopic structure was proposed [14] and investigated [16] recently, where the small ungapped Fermi-surface pockets in the DW state appear due to the imperfect nesting of Fermi surface (FS) and lead to the SC instability.…”