Condensed Matter Physics Seminar
“Higher order topological states: General principle of construction and their realizations”
VLADIMIR JURIČIĆ
NORDITA Nordic Institute for Theoretical Physics
Abstract: Topological gapless edge or surface states are protected by the bulk topological invariant and arise as a consequence of the so-called bulk-boundary correspondence, which is a hallmark feature of a topological state. Recently, the notion of topological states of matter has been extended to the so-called higher order topological (HOT) states featuring gapless surface states at boundaries of co-dimension higher than one, such as hinges and corners.
In this talk, I will particularly discuss a general principle of construction for these states within the Dirac Hamiltonian framework [1]. As I will show, if a D-dimensional first-order or regular topological phase involves m Hermitian matrices that anticommute with additional p−1 mutually anticommuting matrices, it is conceivable to realize an nth-order HOT phase, where n=1,...,p, with appropriate combinations of discrete symmetry-breaking Wilsonian masses. This principle will be illustrated on prototypical three-dimensional gapless systems, such as a nodal-loop semimetal possessing SU(2) spin-rotational symmetry, and Dirac semimetals, transforming under (pseudo)spin- 1/2 or 1 representations. The former system permits an unprecedented realization of a fourth-order phase, without any surface zero modes. The crystalline symmetries play an important for HOT states, but, as I will show, they can also be realized in amorphous solids [2]. Particularly, as long as structural disorder is confined by the outer crystalline boundary, the system continues to host corner states, realizing an amorphous HOT insulator. However, as structural disorder percolates to the edges, corner states start to dissolve into amorphous bulk, and ultimately the system becomes a trivial insulator. Finally, I will discuss a realization of an out-of-equilibrium second order topological insulator, which is obtained from a quantum spin Hall insulator by using a rather generic kicking protocol involving a mass that breaks time-reversal and fourfold rotational symmetries [3].
1. D. Calugaru, V. Juričić, and B. Roy, Phys. Rev. B 99, 041301(R) (2019).
2. A. Agarwala, V. Juričić, and B. Roy, B., arXiv:1902.00507.
3. T. Nag, V. Juričić, and B. Roy, arXiv:1904.07247.
Thursday, October 17, 2019
2:00 PM
Gant South Building, Room GS-213K
For more information, contact: Anna Huang at anna.huang@uconn.edu