Loop Currents and Anomalous Hall Effect from Time-Reversal Symmetry-Breaking Superconductivity on the Honeycomb Lattice

Abstract

We study a tight-binding model on the honeycomb lattice of chiral d-wave superconductivity that breaks time-reversal symmetry. Due to its nontrivial sublattice structure, we show that it is possible to construct a gauge-invariant time-reversal-odd bilinear of the pairing potential. The existence of this bilinear reflects the sublattice polarization of the pairing state. We show that it generates persistent loop current correlations around each lattice site and opens a topological mass gap at the Dirac points, resembling Haldane's model of the anomalous quantum Hall effect. In addition to the usual chiral d-wave edge states, there also exist electron-like edge resonances due to the topological mass gap. We show that the presence of loop-current correlations directly leads to a nonzero intrinsic ac Hall conductivity, which produces the polar Kerr effect without an external magnetic field. Similar results also hold for the nearest-neighbor chiral p-wave pairing. We briefly discuss the relevance of our results to superconductivity in twisted bilayer graphene.

Anapole superconductivity from $${{{{{{{\mathcal{PT}}}}}}}}$$-symmetric mixed-parity interband pairing

“…This suggests that it is not sufficient to consider only the pairing potential Δ(k), since it is not gauge invariant. Instead of Δ(k) alone, we need to consider gauge-invariant bilinear products of Δ(k) and Δ † (k) 36 in order to reveal conditions for realizing the asymmetric BS. Here, we focus on the simplest bilinear products, that is, Δ(k)Δ † (k).…”

“…For instance, multiband superconductors have attracted much attention as a platform realizing odd-frequency pairing 34 . In T -symmetry breaking superconductors, an intrinsic anomalous Hall effect emerges owing to the multiband nature of Cooper pairs 5,[35][36][37][38] . In particular, evenparity T -symmetry breaking superconductors host topologically protected Bogoliubov Fermi surfaces in the presence of interband pairing 39,40 .…”

Anapole superconductivity from $\mathcal{PT}$-symmetric mixed-parity interband pairing

“…This suggests that it is not sufficient to consider only the pairing potential Δ( 𝒌), since it is not gauge invariant. Instead of Δ( 𝒌) alone, we need to consider gauge-invariant bilinear products of Δ( 𝒌) and Δ † ( 𝒌) [31] in order to reveal conditions for realizing the asymmetric BS. Here, we focus on the simplest bilinear products, that is, Δ( 𝒌)Δ † ( 𝒌).…”

“…For instance, multiband superconductors have attracted much attention as a platform realizing odd-frequency pairing [29]. In T -symmetry breaking superconductors, an intrinsic anomalous Hall effect emerges owing to the multiband nature of Cooper pairs [5,[30][31][32][33]. In particular, even-parity T -symmetry breaking superconductors host topologically protected Bogoliubov Fermi surfaces in the presence of interband pairing [34,35].…”

Spin-orbit-coupled superconductivity with spin-singlet non-unitary pairing

“…In condensed matter physics, research on unconventional superconductivity [1,2] remains an crucial topic and continues to uncover new questions and challenges, since the discovery of the heavy-fermion superconductors (SCs) [3] and the d-wave pairing states in hightemperature cuprate SCs [4][5][6][7]. In addition to the anisotropic gap functions (e.g., p, d, f, g-wave...), the sublattice or orbital-dependent pairings [8][9][10] are alternative avenue to realize unconventional SCs. They might be realized in multi-orbital correlated electronic systems, whose candidate materials include iron-based SCs [11][12][13][14][15][16][17][18][19][20][21], Cu-doped Bi 2 Se 3 [22,23], half-Heusler compounds [24][25][26][27][28][29][30][31][32][33], and possibly Sr 2 RuO 4 [34][35][36][37] etc.…”