Majorana corner modes in a second-order Kitaev spin liquid

Dwivedi, Vatsal; Hickey, Ciarán; Eschmann, Tim; Trebst, Simon

doi:10.1103/physrevb.98.054432

Cited by 51 publications

(38 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In terms of second-order TSCs in 2D, the MZMs will emerge at its corners i.e., Majorana corner states (MCSs), which are localized at the intersection of two gapped topologically distinct edges. The study of MCSs is still at a very exploratory stage, and a few works are recently reported: high-temperature Majorana Kramers pairs with time-reversal symmetry localized at corners [42][43][44], MCSs in a p-wave superconductor with an inplane external magnetic field [45], Majorana bound states (MBSs) in a second-order Kitaev spin liquid [46], as well as 2D and 3D second-order TSCs with (p+ip) and (p+id) superconductors [47].…”

Section: Introductionmentioning

confidence: 99%

Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor

2018

View full text Add to dashboard Cite

Conventional n-dimensional topological superconductors (TSCs) have protected gapless (n − 1)dimensional boundary states. In contrast to this, second-order TSCs are characterized by topologically protected gapless (n − 2)-dimensional states with usual gapped (n − 1)-boundaries.Here, we study a second-order TSC with a two-dimensional (2D) magnetic topological insulator (TI) proximity-coupled to a high-temperature superconductor, where Majorana bound states (MBSs) are localized at the corners of a square sample with gapped edge modes. Due to the mirror symmetry of the hybrid system considered here, there are two MBSs at each corner for both cases: d-wave and s±-wave superconducting pairing. We present the corresponding topological phase diagrams related to the role of the magnetic exchange interaction and the pairing amplitude. A detailed analysis, based on edge theory, reveals the origin of the existence of MBSs at the corners of the 2D sample, which results from the sign change of the Dirac mass emerging at the intersection of any two adjacent edges due to pairing symmetry. Possible experimental realizations are discussed. Our proposal offers a promising platform for realizing MBSs and performing possible non-Abelian braiding in 2D systems. arXiv:1806.07002v2 [cond-mat.mes-hall]

show abstract

Section: Introductionmentioning

confidence: 99%

Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor

2018

View full text Add to dashboard Cite

show abstract

“…Thus, the appearance of the local magnetization is ubiquitous in the Kitaev-type models. Needless to say, in many models, various kinds of topological boundary states such as chiral edge modes [32] and corner modes [40] have been found to appear.…”

Section: B Comparison With Related Workmentioning

confidence: 99%

Majorana edge magnetization in the Kitaev honeycomb model

Mizoguchi

Koma

2019

Phys. Rev. B

View full text Add to dashboard Cite

We propose an approach to detect the peculiarity of Majorana fermions at the edges of Kitaev magnets. As is well known, a pair of Majorana edge modes is realized when a single complex fermion splits into real and imaginary parts which are, respectively, localized at the left and right edges of a sample magnet. Reflecting both of this peculiarity of the Majorana fermions and the ground-state degeneracy caused by the existence of the Majorana edge zero modes, the spins at the edges of the sample magnet are expected to behave as a peculiar "free" spin which exhibits a unidirectional magnetization without any transverse magnetization when applied a sufficiently weak external magnetic field. For the Kitaev honeycomb model, we obtain the expression of the Majorana edge magnetization by relying on standard techniques to diagonalize a free fermion Hamiltonian. The magnetization profile thus obtained indeed shows the expected behavior. We also elucidate the relation between the Majorana edge flat band and the bulk winding number from a weak topological point of view. I. INTRODUCTIONKitaev introduced a seminal quantum spin model [1] which realizes the desired properties of quantum spin liquids [2, 3], whose study was initiated by Anderson. More precisely, Kitaev's model is defined on the honeycomb lattice, and mapped to a free Majorana ferminon model. In consequence, the model is exactly solvable, and shows short-range spin correlations [4]. Although Kitaev's model is fairly artificial, some materials, e.g., A 2 IrO 3 (A = Na, Li) [5, 6] and α-RuCl 3 [7], are expected to exhibit very similar properties to those of the Kitaev honeycomb model [8][9][10][11][12]. In particular, detecting the evidence of the Majorana fermions is one of the central issues in condensed matter physics [13][14][15][16][17][18][19].On the other hand, the Kitaev honeycomb model with open boundaries shows many Majorana zero modes at the edges [20]. In fact, the zero modes form a flat band. This is nothing but a consequence of the weak topological character [21][22][23][24][25][26] of the model. In fact, the celebrated bulk-edge correspondence [27,28] ensures the relation between the number of the Majorana edge zero modes and the winding number for the bulk Hamiltonian when the Fermi energy, which equals zero in the present system, lies in the spectral or mobility gap of the Hamiltonian. Interestingly, similar Majorana edge flat bands were found to appear also in the gapless regime of the Hamiltonian, depending on the geometry of the edges [20].As is well known, a pair of Majorana edge modes appears when a single complex fermion splits into real and imaginary parts which are, respectively, localized at the left and right edges of the system. Therefore, a single Majorana fermion has only a real degree of freedom as

show abstract

“…Higher-order topological phases have been studied in systems protected by order-two symmetries (e.g., reflection and inversion symmetry [22][23][24][26][27][28]), rotational invariance [25,29,30], and combinations of the above [31][32][33]. Gapless hinge and corner excitations may also appear in interacting models [34,35], Floquet phases [36,37] and can coexist with gapless surface states [38]. Higher-order topology does not necessarily rely on an underlying regular lattice, but can be also found in quasicrystals respecting certain spatial symmetries [39,40].…”

Section: Introductionmentioning

confidence: 99%

Second-order bulk-boundary correspondence in rotationally symmetric topological superconductors from stacked Dirac Hamiltonians

2020

View full text Add to dashboard Cite

Two-dimensional second-order topological superconductors host zero-dimensional Majorana bound states at their boundaries. In this work, focusing on rotation-invariant crystalline topological superconductors, we establish a bulk-boundary correspondence linking the presence of such Majorana bound states to bulk topological invariants introduced by Benalcazar et al. We thus establish when a topological crystalline superconductor protected by rotational symmetry displays second-order topological superconductivity. Our approach is based on stacked Dirac Hamiltonians, using which we relate transitions between topological phases to the transformation properties between adjacent gapped boundaries. We find that in addition to the bulk rotational invariants, the presence of Majorana boundary bound states in a given geometry depends on the interplay between weak topological invariants and the location of the rotation center relative to the lattice. We provide numerical examples for our predictions and discuss possible extensions of our approach.

show abstract

Majorana corner modes in a second-order Kitaev spin liquid

Cited by 51 publications

References 55 publications

Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor

Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor

Majorana edge magnetization in the Kitaev honeycomb model

Second-order bulk-boundary correspondence in rotationally symmetric topological superconductors from stacked Dirac Hamiltonians

Contact Info

Product

Resources

About