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arXiv:2004.06925 · Physical review. B./Physical review. B

Electronic multipoles and multiplet pairs induced by Pomeranchuk and Cooper instabilities of Bogoliubov Fermi surfaces

Shun-Ta Tamura, Shoma Iimura, Shintaro Hoshino

Published Jul 6, 2020• 21 citations
arXivHTMLPDF

Abstract

It was recently pointed out that Fermi surfaces can survive even in superconductors. Here, the authors study the instability of such systems toward electronic ordering. The ordered states are classified into diagonal and off-diagonal ones, which, respectively, indicate the Pomeranchuk instability and Cooper pairing not of original electrons but of Bogoliubov particles (bogolons). The corresponding order parameters are expanded by multipole moments and multiplet pair amplitudes of original electrons. These results provide insights into superconductors with multiple phase transitions.

DOI
10.1103/physrevb.102.024505

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It was recently pointed out that Fermi surfaces can survive even in superconductors. Here, the authors study the instability of such systems toward electronic ordering. The ordered states are classified into diagonal and off-diagonal ones, which, respectively, indicate the Pomeranchuk instability and Cooper pairing not of original electrons but of Bogoliubov particles (bogolons). The corresponding order parameters are expanded by multipole moments and multiplet pair amplitudes of original electrons. These results provide insights into superconductors with multiple phase transitions.
We theoretically investigate the evolution and instability of the Bogoliubov Fermi surface (BFS) in the spherical j=3/2j=3/2j=3/2 model under a Zeeman field. The applied field induces a pronounced expansion in the BFS with jz=±3/2j_z = \pm 3/2jz​=±3/2 component. Such behavior can be detected by spectroscopic techniques such as angle-resolved photoemission spectroscopy (ARPES). Interestingly, the Pauli susceptibility exhibits behavior that appears discontinuous just below the transition temperature at zero field, even though it is a second-order transition. This is due to spontaneous magnetization. Furthermore, the analysis of the bogolon correlations in the superconducting phase suggests the possibility of the chiral ppp- or fff-wave bogolon pairing instabilities rather than the Pomeranchuk instability. These chiral states coexist with the chiral ddd-wave superconducting state, spontaneously break inversion symmetry, and lead to the disappearance of the torus-shaped BFS structure.
Abstract The nesting of the Fermi surfaces of an electron and a hole pocket separated by a vector Q commensurate with the lattice in conjunction with the interaction between the quasiparticles can give rise to a rich phase diagram. Of particular importance is itinerant antiferromagnetic order in the context of pnictides and heavy fermion compounds. By mismatching the nesting the order can gradually be suppressed and as the Néel temperature tends to zero a quantum critical point is obtained. A superconducting dome above the quantum critical point can be induced by the transfer of pairs of electrons between the pockets. The conditions under which such a dome arises are studied. In addition numerous other phases may arise, e.g. charge density waves, non‐Fermi liquid behavior, non‐s‐wave superconductivity, Pomeranchuk instabilities of the Fermi surface, nematic order, and phases with persistent orbital currents.
We study the competition between a Pomeranchuk instability in spin-channel with angular momentum l = 1 and an attractive BCS interaction, favoring Cooper pair formation. We compute the phase diagram at mean-field level, finding a transition between two superconductor phases: a homogeneous and a modulated superconductor, with similar characteristics of the FFLO state. Differently from FFLO, time-reversal symmetry is preserved due to the spontaneous generation of a spin-orbit coupling. An experimental signature for this phase transition could be the simultaneous observation of anisotropic superconductivity and an anomalous Hall effect. A Fermi liquid is, except in one dimension, a very stable state of matter 1 . At least two type of instabilities, related with attractive interactions, are known: Pomeranchuk 2 and superconductor instabilities. Pomeranchuk instabilities occur in the presence of two-body interactions containing a strong attractive component in the forward scattering channel with a definite angular momentum. In the context of Landau theory, the instability sets in when one or more dimensionless Landau parameters F s,a l , with angular momentum l in the charge
We analyze a mean-field model of electrons on a square lattice with two types of interaction: forward scattering favoring a ddd-wave Pomeranchuk instability and a BCS pairing interaction driving ddd-wave superconductivity. By tuning the interaction parameters a rich variety of phase diagrams is obtained. If the BCS interaction is not too strong, Fermi surface symmetry breaking is stabilized around van Hove filling, and coexists with superconductivity at low temperatures. For pure forward scattering Fermi surface symmetry breaking occurs typically via a first order transition at low temperatures. The presence of superconductivity reduces the first order character of this transition and, if strong enough, can turn it into a continuous one. This gives rise to a quantum critical point within the superconducting phase. The superconducting gap tends to suppress Fermi surface symmetry breaking. For a relatively strong BCS interaction, Fermi surface symmetry breaking can be limited to intermediate temperatures, or can be suppressed completely by pairing.
Weak attractive interactions in a spin-imbalanced Fermi gas induce a multiparticle instability, binding multiple fermions together. The maximum binding energy per particle is achieved when the ratio of the number of up- and down-spin particles in the instability is equal to the ratio of the up- and down-spin densities of states in momentum at the Fermi surfaces, to utilize the variational freedom of all available momentum states. We derive this result using an analytical approach, and verify it using exact diagonalization. The multiparticle instability extends the Cooper pairing instability of balanced Fermi gases to the imbalanced case, and could form the basis of a many-body state, analogously to the construction of the Bardeen-Cooper-Schrieffer theory of superconductivity out of Cooper pairs.
Interactions in Fermi systems can induce a "Pomeranchuk instability" leading to orientational symmetry breaking, that is, nematic order. In a metallic system close to such an instability the Fermi surface is easily deformed by anisotropic perturbations, and exhibits enhanced collective fluctuations. We discuss electrons on a square lattice near a Pomeranchuk instability with d-wave symmetry. The strong response of such a system to a small orthorhombic perturbation can explain naturally the large in-plane anisotropy of electronic and magnetic properties observed in detwinned YBCO crystals. Fluctuations in a quantum critical regime near the instability provide a mechanism for non-Fermi liquid behavior. They lead to a singular forward scattering interaction, which destroys fermionic quasi-particles on the whole Fermi surface except at "cold spots" on the Brillouin zone diagonal. The decay rate for DC transport is linear in temperature except at the cold spots, where conventional Fermi liquid behavior survives. In clean systems this gives rise to a T 3/2 temperature dependence of the DC resistivity, as observed in some overdoped cuprates. In the presence of disorder, the resistivity is linear in T at low temperatures.