Inversion-symmetry protected chiral hinge states in stacks of doped quantum Hall layers

Abstract

We prove the existence of higher-order topological insulators with protected chiral hinge modes in quasi-two-dimensional systems made out of coupled layers stacked in an inversion-symmetric manner. In particular, we show that an external magnetic field drives a stack of alternating pand n-doped buckled honeycomb layers into a higher-order topological phase, characterized by a non-trivial three-dimensional Z2 invariant. We identify silicene multilayers as a potential material platform for the experimental detection of this novel topological insulating phase.

Pfaffian Formalism for Higher-Order Topological Insulators

“…We apply Eq. (13) and (15) and indeed get P 3 = 0, as predicted. However if we replace Θ by T in the implementation of Eq.…”

“…These second-order TIs have a strong connection to TIs, and in particular, if the time-reversal symmetry T is enforced, 2P 3 recovers the Z 2 index of a TI [30]. If the time-reversal symmetry is broken, 2P 3 still defines a Z 2 topological index, as long as a space inversion, rotoinversion or C n T symmetry is preserved [7][8][9][10][11][12][13][14][15], where C n represents n-fold rotation with n = 2, 4, 6, and this Z 2 index, in the absence of time-reversal symmetry, characterizes a second-order TI. For systems invariant under space-inversion or some rotoinversion, this topological index is fully dictated by high-symmetry points and can be conveniently obtained using the framework of topological quantum chemistry [31] or symmetry indicators [32,33].…”

“…(7) and its variations in Eqs. (13) and (15). If the system also preserves a S 4 symmetry, P 3 can be obtained directly from S 4 eigenvalues at high symmetry momenta as in Eq.…”

Bulk-edge and bulk-hinge correspondence in inversion-symmetric insulators

“…To the best of our knowledge, in the previous studies, explanations of bulk-hinge correspondence are roughly classified into two: (i) k · p theory approach [22][23][24][31][32][33]35,37,40,41 , and (ii) Wannier approach 24,25,36,40 . In (i), one starts from the surface Dirac Hamiltonian, which represents anomalous gapless surface states as a low-energy effective Hamiltonian for the surface.…”

Higher-order topological insulators in a crisscross antiferromagnetic model

“…SnTe was the first predicted helical HOTI by firstprinciple calculations in Ref [17], and the crystal bismuth was predicted and experimentally confirmed to possess the helical HOTI phase in Ref [18]. The chiral HOTIs break the TRS and support unidirectionally propagating hinge states [24][25][26]. The Sm-doped Bi 2 Se 3 [27] and EuIn 2 As 2 [28] materials was proposed by first-principle calculations to exhibit the chiral HOTI phase, but the magnetic structure in Sm-doped Bi 2 Se 3 is still under debate.…”