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Register a new userDynamics of emergent Cooper pairing at finite temperatures
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We study the time evolution of a system of fermions with pairing interactions at a finite temperature. The dynamics is triggered by an abrupt increase of the BCS coupling constant. We show that if initially the fermions are in a normal phase, the amplitude of the BCS order parameter averaged over the Boltzman distribution of initial states exhibits damped oscillations with a relatively short decay time. The latter is determined by the temperature, the single-particle level spacing, and the ground state value of the BCS gap for the new coupling. In contrast, the decay is essentially absent when the system was in a superfluid phase before the coupling increase.
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We show that Cooper pairing can occur intrinsically away from the Fermi surface in $j=3/2$ superconductors with strong spin-orbit coupling and equally curved bands in the normal state. In contrast to conventional pairing between spin-$1/2$ electrons, we derive that pairing can happen between inter-band electrons having different total angular momenta, i.e., $j=1/2$ with $j=3/2$ electrons. Such superconducting correlations manifest themselves by a pair of indirect gap-like structures at finite excitation energies. An observable signature of this exotic pairing is the emergence of a pair of symmetric superconducting coherence peaks in the density of states at finite energies. We argue that finite-energy pairing is a generic feature of high-spin superconductors, both in presence and absence of inversion symmetry.
Since the proposal of monopole Cooper pairing in Ref. [1], considerable research efforts have been dedicated to the study of Copper pair order parameters constrained (or obstructed) by the nontrivial normal-state band topology at Fermi surfaces. In the current work, we propose a new type of topologically obstructed Cooper pairing, which we call Euler obstructed Cooper pairing. The Euler obstructed Cooper pairing widely exists between two Fermi surfaces with nontrivial band topology characterized by nonzero Euler numbers; such Fermi surfaces can exist in the $PT$-protected spinless-Dirac/nodal-line semimetals with negligible spin-orbit coupling, where $PT$ is the space-time inversion symmetry. An Euler obstructed pairing channel must have pairing nodes on the pairing-relevant Fermi surfaces, and the total winding number of the pairing nodes is determined by the sum or difference of the Euler numbers on the Fermi surfaces. In particular, we find that when the normal state is nonmagnetic and the pairing is weak, a sufficiently-dominant Euler obstructed pairing channel with zero total momentum leads to nodal superconductivity. If the Fermi surface splitting is small, the resultant nodal superconductor hosts hinge Majorana zero modes, featuring the first class of higher-order nodal superconductivity originating from the topologically obstructed Cooper pairing. The possible dominance of the Euler obstructed pairing channel near the superconducting transition and the robustness of the hinge Majorana zero modes against disorder are explicitly demonstrated using effective or tight-binding models.
When both two-electron textit{and} two-hole Cooper-pairing are treated on an equal footing in the ladder approximation to the Bethe-Salpeter (BS) equation, the zero-total-momentum Cooper-pair energy is found to have two textit{real} solutions $mathcal{E}_{0}^{BS}=pm 2hbar omega_{{D}%}/sqrt{{e}^{2/lambda }+{1}}$ which coincide with the zero-temperature BCS energy gap $Delta =hbar omega_{D}/sinh (1/lambda) $ in the weak coupling limit. Here, $hbar omega_{D}$ is the Debye energy and $lambda geq 0$ the BCS model interaction coupling parameter. The interpretation of the BCS energy gap as the binding energy of a Cooper-pair is often claimed in the literature but, to our knowledge, never substantiated even in weak-coupling as we find here. In addition, we confirm the two purely-textit{imaginary} solutions assumed since at least the late 1950s as the textit{only} solutions, namely, $mathcal{E}_{0}^{BS}=pm i2hbar omega_{{D}}/sqrt{{e}^{2/lambda}{-1}}.$
We numerically prove photoinduced $eta$-pairing in a half-filled fermionic Hubbard chain at both zero and finite temperature. The result, obtained by combining the matrix-product-state based infinite time-evolving block decimation technique and the purification method, applies to the thermodynamic limit. Exciting the Mott insulator by a laser electric field docked on via the Peierls phase, we track the time-evolution of the correlated many-body system and determine the optimal parameter set for which the nonlocal part of the $eta$-pair correlation function becomes dominant during the laser pump at zero and low temperatures. These correlations vanish at higher temperatures and long times after pulse irradiation. In the high laser frequency strong Coulomb coupling regime we observe a remnant enhancement of the Brillouin-zone boundary pair-correlation function also at high temperatures, if the Hubbard interaction is about a multiple of the laser frequency, which can be attributed to an enhanced double occupancy in the virtual Floquet state.
The idea that preformed Cooper pairs could exist in a superconductor above its zero-resistance state has been explored for unconventional, interface, and disordered superconductors, yet direct experimental evidence is lacking. Here, we use scanning tunneling noise spectroscopy to unambiguously show that preformed Cooper pairs exist up to temperatures much higher than the zero-resistance critical temperature $T_{C}$ in the disordered superconductor titanium nitride, by observing a clear enhancement in the shot noise that is equivalent to a change of the effective charge from 1 to 2 electron charges. We further show that spectroscopic gap fills up rather than closes when increasing temperature. Our results thus demonstrate the existence of a novel state above $T_{C}$ that, much like an ordinary metal, has no (pseudo)gap, but carries charge via paired electrons.
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