Bulk-interface correspondence from quantum distance in flat band systems

Abstract

The key notion of topological analysis is the bulk-boundary correspondence, which provides us with direct access to the topological structure of a Bloch wave function via the existence of boundary or interface modes. While only the topology of the wave function has been considered relevant to boundary modes, we first demonstrate that another geometric quantity, the so-called quantum distance, can host a new kind of bulk-interface correspondence. We consider a generic class of two-dimensional flat band systems, where the flat band has a parabolic band-crossing with another dispersive band. While such flat bands are known to be topologically trivial, we show that the nonzero maximum quantum distance between the eigenstates of the flat band around the touching point guarantees the existence of boundary modes at the interface between two domains with different chemical potentials. Moreover, the maximum quantum distance can predict even the explicit form of the dispersion relation and decay length of the interface modes

Flat Bands in Network Superstructures of Atomic Chains

“…When the Coulomb interaction between electrons is introduced, the flat bands host unconventional superconductivity [4][5][6][7][8][9][10][11][12], ferromagnetism [13][14][15][16][17][18][19], Wigner crystal [20][21][22][23], and fractional Chern insulator [3,[24][25][26][27][28][29][30][31][32][33]. The quantum distance, one of the geometric quantities of the Bloch wavefunction, plays an important role in the anomalous Landau levels [34,35], a new kind of bulk-interface correspondence [36], and appearance of the topological non-contractible loop states in flat band systems [37]. Moreover, it was revealed that the quantum metric [38] is the key quantity in the physics of the superfluidity [39,40] and orbital magnetic susceptibility [41,42].…”