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arXiv:1703.01621 · Physical review. B./Physical review. B

Dynamical generation of superconducting order of different symmetries in hexagonal lattices

Hossein Dehghani, Aditi Mitra

Published Nov 2, 2017• 12 citations
arXivHTMLPDF

Abstract

The growth of superconducting order after an interaction quench in a hexagonal lattice is studied. The cases of both time-reversal (TR) preserving graphene, as well as the TR broken Haldane model, are explored. Spin singlet superconducting order is studied where the $s,\phantom{\rule{0.16em}{0ex}}d+id$, and $d\ensuremath{-}id$ wave orders are the irreducible representations of the hexagonal lattice. For small quenches, the $d$-wave order parameter grows the fastest, a result also expected when the system is in thermal equilibrium. For the TR symmetry preserving case, the growth rate of the two $d$-wave orders is identical, while the TR-broken case prefers one of the chiral $d$-wave orders over the other, leading to a TR broken topological superconductor. As the interaction quench becomes larger, a smooth crossover is found where eventually the growth rate of the $s$ wave becomes the largest. Thus for large interaction quenches, the $s$ wave is preferred over the $d$ wave for both TR preserving and TR broken systems. This result is explained in terms of the high energy quasiparticles responsible for the dynamics as the interaction quench amplitude grows. The results are relevant for time-resolved measurements that can probe the symmetry of the superconducting fluctuations in a transient regime.

DOI
10.1103/physrevb.96.195110

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The growth of superconducting order after an interaction quench in a hexagonal lattice is studied. The cases of both time-reversal (TR) preserving graphene, as well as the TR broken Haldane model, are explored. Spin singlet superconducting order is studied where the s,d+ids,\phantom{\rule{0.16em}{0ex}}d+ids,d+id, and d\ensuremath−idd\ensuremath{-}idd\ensuremath−id wave orders are the irreducible representations of the hexagonal lattice. For small quenches, the ddd-wave order parameter grows the fastest, a result also expected when the system is in thermal equilibrium. For the TR symmetry preserving case, the growth rate of the two ddd-wave orders is identical, while the TR-broken case prefers one of the chiral ddd-wave orders over the other, leading to a TR broken topological superconductor. As the interaction quench becomes larger, a smooth crossover is found where eventually the growth rate of the sss wave becomes the largest. Thus for large interaction quenches, the sss wave is preferred over the ddd wave for both TR preserving and TR broken systems. This result is explained in terms of the high energy quasiparticles responsible for the dynamics as the interaction quench amplitude grows. The results are relevant for time-resolved measurements that can probe the symmetry of the superconducting fluctuations in a transient regime.
We study the quench dynamics of a topological ppp-wave superfluid with two competing order parameters, ${\mathrm{\ensuremath{\Delta}}}_{\ifmmode\pm\else\textpm\fi{}}(t)$. When the system is prepared in the p+ipp+ipp+ip ground state and the interaction strength is quenched, only ${\mathrm{\ensuremath{\Delta}}}_{+}(t)$ is nonzero. However, we show that fluctuations in the initial conditions result in the growth of ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{-}}(t)$ and chaotic oscillations of both order parameters. We term this behavior phase III'. In addition, there are two other types of late-time dynamics---phase I where both order parameters decay to zero and phase II where ${\mathrm{\ensuremath{\Delta}}}_{+}(t)$ asymptotes to a nonzero constant while ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{-}}(t)$ oscillates near zero. Although the model is nonintegrable, we are able to map out the exact phase boundaries in parameter space. Interestingly, we find phase III' is unstable with respect to breaking the time-reversal symmetry of the interaction. When one of the order parameters is favored in the Hamiltonian, the other one rapidly vanishes and the previously chaotic phase III' is replaced by the Floquet topological phase III that is seen in the integrable chiral ppp-wave model.
We investigate the properties of the nearest-neighbor singlet pairing and the emergence of ddd-wave superconductivity in the doped honeycomb lattice considering the limit of large interactions and the $t\ensuremath{-}{J}_{1}\ensuremath{-}{J}_{2}$ model. First, by applying a renormalized mean-field procedure as well as slave-boson theories which account for the proximity to the Mott-insulating state, we confirm the emergence of ddd-wave superconductivity, in agreement with earlier works. We show that a small but finite J2{J}_{2}J2​ spin coupling between next-nearest neighbors stabilizes ddd-wave symmetry compared to the extendedsss-wave scenario. At small hole doping, to minimize the energy and to gap the whole Fermi surface or all the Dirac points, the superconducting ground state is characterized by a d+idd+idd+id singlet pairing assigned to one valley and a $d\ensuremath{-}id$ singlet pairing to the other, which then preserves time-reversal symmetry. The slightly doped situation is distinct from the heavily doped case (around 3/8 and 5/8 filling) supporting a pure chiral d+idd+idd+id symmetry and breaking time-reversal symmetry. Then, we apply the functional renormalization group and study in more detail the competition between antiferromagnetism and superconductivity in the vicinity of half filling. We discuss possible applications to strongly correlated compounds with copper hexagonal planes such as In3{}_{3}3​Cu2{}_{2}2​VO9{}_{9}9​. Our findings are also relevant to the understanding of exotic superfluidity with cold atoms.
Dynamical quantum phase transitions (DQPTs) are topologically characterized in quantum quench dynamics in topological systems. In this paper, we study Loschmidt amplitudes and DQPTs in quantum quenches in mirror-symmetric topological phases. Based on the topological classification of mirror-symmetric insulators, we show that mirror symmetry creates symmetry-protected DQPTs. If mirror symmetry is present, topologically robust DQPTs can occur in quantum quenches, even in high-dimensional time-reversal invariant systems. Then, we also show that symmetry-protected DQPTs occur in quenches in two-dimensional chiral-symmetric systems with mirror symmetry. Mirror-symmetry-protected DQPTs can be easily captured by a reduced rate function. Moreover, we introduce dynamical topological order parameters for mirror-symmetry-protected DQPTs. Finally, we demonstrate DQPTs using lattice models for a time-reversal invariant topological crystalline insulator and a higher-order topological insulator.
Motivated by recent ultrafast pump-probe experiments on high-temperature superconductors, we discuss the transient dynamics of a d-wave BCS model after a quantum quench of the interaction parameter. We find that the existence of gap nodes, with the associated nodal quasiparticles, introduces a decay channel which makes the dynamics much faster than in the conventional s-wave model. For every value of the quench parameter, the superconducting gap rapidly converges to a stationary value smaller than the one at equilibrium. Using a sudden approximation for the gap dynamics, we find an analytical expression for the reduction of spectral weight close to the nodes, which is in qualitative agreement with recent experiments.
Two-dimensional time-reversal-invariant topological superconductors host helical Majorana fermions at their boundary. We study the fate of these edge states under the combined influence of strong interactions and disorder, using the effective one-dimensional (1D) lattice model for the edge introduced by Jones and Metlitski [Phys. Rev. B 104, 245130 (2021)]. We specifically develop a strong-disorder renormalization-group analysis of the lattice model and identify a regime in which time-reversal is broken spontaneously, creating random magnetic domains; Majorana fermions localize to domain walls and form an infinite-randomness fixed point, identical to that appearing in the random transverse-field Ising model. While this infinite-randomness fixed point describes a fine-tuned critical point in a purely 1D system, in our edge context there is no obvious time-reversal-preserving perturbation that destabilizes the fixed point. Our analysis thus suggests that the infinite-randomness fixed point emerges as a stable phase on the edge of two-dimensional topological superconductors when strong disorder and interactions are present.
Neutral-atom quantum simulators provide a powerful platform for realizing strongly correlated phases, enabling access to dynamical signatures of quasiparticles and symmetry breaking processes. Motivated by recent observations of quantum phases in flux-frustrated ladders with non-vanishing ground state currents, we investigate interacting bosons on the dimerized BBH lattice in two dimensions-originally introduced in the context of higher-order topology. After mapping out the phase diagram, which includes vortex superfluid (V-SF), vortex Mott insulator (V-MI), and featureless Mott insulator (MI) phases, we focus on the integer filling case. There, the MI/V-SF transition simultaneously breaks the Z2T\mathbb Z_2^{T}Z2T​ and U(1) symmetries, where Z2T\mathbb Z_2^{T}Z2T​ corresponds to time-reversal symmetry (TRS). Using a slave-boson description, we resolve the excitation spectrum across the transition and uncover a chiral Higgs mode whose mass softens at criticality, providing a dynamical hallmark of emergent chirality that manifests via the oscillation of the loop currents in quench dynamics. Our results establish an experimentally realistic setting for probing unconventional TRS-broken phases and quasiparticles with intrinsic chirality in strongly interacting quantum matter.