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arXiv:2410.11326 · Journal of the Physical Society of Japan

Evolution and Instability of Bogoliubov Fermi Surfaces under Zeeman Field

T. Mori, Hiroshi Watanabe, Hiroaki Ikeda

Published Jan 29, 2025• 0 citations
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Abstract

We theoretically investigate the evolution and instability of the Bogoliubov Fermi surface (BFS) in the spherical $j=3/2$ model under a Zeeman field. The applied field induces a pronounced expansion in the BFS with $j_z = \pm 3/2$ 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 $p$- or $f$-wave bogolon pairing instabilities rather than the Pomeranchuk instability. These chiral states coexist with the chiral $d$-wave superconducting state, spontaneously break inversion symmetry, and lead to the disappearance of the torus-shaped BFS structure.

DOI
10.7566/jpsj.94.023704

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Journal of Experimental and Theoretical Physics Letters•Dec 1, 2017•2 citations
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.
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 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.
We study the Fermi-surface instabilities of the Pomeranchuk type [Sov. Phys. JETP 8, 361 (1959)] in the spin-triplet channel with high orbital partial waves [Fla(l>0)][{F}_{l}^{a}(l>0)][Fla​(l>0)]. The ordered phases are classified into two classes, dubbed the $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ phases by analogy to the superfluid 3He^{3}\mathrm{He}3He A and B phases. The Fermi surfaces in the $\ensuremath{\alpha}$ phases exhibit spontaneous anisotropic distortions, while those in the $\ensuremath{\beta}$ phases remain circular or spherical with topologically nontrivial spin configurations in momentum space. In the $\ensuremath{\alpha}$ phase, the Goldstone modes in the density channel exhibit anisotropic overdamping. The Goldstone modes in the spin channel have a nearly isotropic underdamped dispersion relation at small propagating wave vectors. Due to the coupling to the Goldstone modes, the spin-wave spectrum develops resonance peaks in both the $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ phases, which can be detected in inelastic neutron-scattering experiments. In the ppp-wave channel $\ensuremath{\beta}$ phase, a chiral ground-state inhomogeneity is spontaneously generated due to a Lifshitz-like instability in the originally nonchiral systems. Possible experiments to detect these phases are discussed.
The deformation of the Fermi surface induced by Coulomb interactions is investigated in the $t\ensuremath{-}{t}^{\ensuremath{'}}$-Hubbard model. The interplay of the local U and extended V interactions is analyzed. It is found that the interactions V enhance small anisotropies producing deformations of the Fermi surface that break the point group symmetry of the square lattice at the Van Hove filling. This Pomeranchuk instability competes with magnetic instabilities and is suppressed at a critical value U(V).U(V).U(V). The interaction V effectively renormalizes the ${t}^{\ensuremath{'}}$ parameter to smaller values, which favors nesting. It also induces changes in the topology of the Fermi surface, which can go from holelike to electronlike. This may explain the results of recent angle-resolved photoemission spectroscopy experiments.
Interplay of Pomeranchuk instability (spontaneous symmetry breaking of the Fermi surface) and ddd-wave superconductivity is studied for the repulsive Hubbard model on the square lattice with the dynamical mean-field theory combined with the fluctuation exchange approximation (FLEX+DMFT). We show that the fourfold symmetric Fermi surface becomes unstable against a spontaneous distortion into twofold near the van Hove filling, where the symmetry of superconductivity coexisting with the Pomeranchuk-distorted Fermi surface is modified from the ddd-wave pairing to the (d+s)(d+s)(d+s) wave. By systematically shifting the position of van Hove filling with varied second- and third-neighbor hoppings, we find that the transition temperature TcPI{T}_{\mathrm{c}}^{\mathrm{PI}}TcPI​ for the Pomeranchuk instability is more sensitively affected by the position of van Hove filling than the superconducting TcSC{T}_{\mathrm{c}}^{\mathrm{SC}}TcSC​. This implies that the filling region for strong Pomeranchuk instability and that for the TcSC{T}_{\mathrm{c}}^{\mathrm{SC}}TcSC​ dome can be separated, and that Pomeranchuk instability can appear even if the peak of TcPI{T}_{\mathrm{c}}^{\mathrm{PI}}TcPI​ is lower than the peak of TcSC{T}_{\mathrm{c}}^{\mathrm{SC}}TcSC​. An interesting finding is that the Fermi surface distortion can enhance the superconducting TcSC{T}_{\mathrm{c}}^{\mathrm{SC}}TcSC​ in the overdoped regime, which is explained with a perturbational picture for small distortions.
The relation between the broken rotational symmetry of a system and the topology of its Fermi surface is studied for the two-dimensional system with the quasiparticle interaction f ( p , p' ) having a sharp peak at | p − p' | = q 0 . It is shown that, in the case of attraction and q 0 = 2 p F the first instability manifesting itself with the growth of the interaction strength is the Pomeranchuk instability. This instability appearing in the L = 2 channel gives rise to a second order phase transition to a nematic phase. The Monte Carlo calculations demonstrate that this transition is followed by a sequence of the first and second order phase transitions corresponding to the changes in the symmetry and topology of the Fermi surface. In the case of repulsion and small values of q 0 , the first transition is a topological transition to a state with the spontaneously broken rotational symmetry, namely, corresponding to the nucleation of L ≃ π( p F / q 0 − 1) small hole pockets at the distance p F − q 0 from the center and the deformation of the outer Fermi surface with the characteristic multipole number equal to L . At q 0 → 0, when the model under study transforms to the two-dimensional Nozières model, the multipole number characterizing the spontaneous deformation is L → ∞, whereas the infinitely folded Fermi curve acquires the Hausdorff dimension D = 2 which corresponds to the state with the fermion condensate.