Jackiw-Rebbi zero modes in non-uniform topological insulator nanowire

Jana, Sayan; Saha, Arijit; Das, Sourin

doi:10.1103/physrevb.100.085428

Cited by 7 publications

(3 citation statements)

References 50 publications

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“…Such configuration could be feasible in the laboratory through modern strain techniques in Dirac materials, such as scanning tuneling spectroscopy [47,48]. It is worth noticing that the considered electromagnetic profiles are setting up two uncoupled Jackiw-Rebbi (J-R) models for the dynamics along in each direction [49][50][51]. This observation can be seen precisely in figure 1.…”

Section: Discussionmentioning

confidence: 93%

Dirac materials in parallel non-uniform electromagnetic fields generated by SUSY: a chiral Planar Hall Effect

Pérez-Pedraza,

García-Muñoz,

Raya

2024

Phys. Scr.

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Within a Supersymmetric Quantum Mechanics (SUSY-QM) framework, the (3+1) Dirac equation describing a Dirac material in the presence of external parallel electric and magnetic fields is solved. Considering static but non-uniform electric and magnetic profiles with translational symmetry along the y-direction, the Dirac equation is transformed into two decoupled pairs of Schrödinger equations, one for each chirality of the fermion fields. Taking trigonometric and hyperbolic profiles for the vector and scalar potentials, respectively, we arrive at SUSY partner Pöschl-Teller-like quantum potentials. Restricting to the conditions of the potentials that support an analytic zero-mode solution, we obtain a nontrivial current density perpendicular to the electric and magnetic fields, thus, defining a plane where these three vectors become coplanar, indicating the possibility of realizing the Planar Hall Effect. Furthermore, this non-vanishing current density is the sum of current densities for the left- and right-chiralities, suggesting that the net current is a consequence of chiral symmetry. Possible application in current steering of solitonic nature through a Type-I Weyl semimetal is discussed.

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Section: Discussionmentioning

confidence: 93%

Dirac materials in parallel non-uniform electromagnetic fields generated by SUSY: a chiral Planar Hall Effect

Pérez-Pedraza,

García-Muñoz,

Raya

2024

Phys. Scr.

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“…localized at 𝜏 0 , where the sign change of cos 𝜙 𝜏 ensures that the solution remains normalizable on both sides of the transition. Such an ansatz fails for 𝜂 ≠ 1 because the decay of the bound state needs to be different in regions with a different gap [68,69]. We therefore try a judicious rewriting of the Hamiltonian (A2) that immediately suggests a better ansatz, namely…”

Section: Appendix A: Jackiw-rebbi Derivation Of Edge Mode Spectrummentioning

confidence: 99%

Quantum tunneling in the presence of a topology-changing fermionic bath

Roberts¹,

Behrends²,

Béri³

2021

Preprint

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Coupling a quantum particle to a fermionic bath suppresses the particle's amplitude to tunnel, even at zero temperature. While this effect can generally be neglected for gapped baths-a key feature for superconducting qubits-, it is possible for the bath to be gapped near the potential minima between which the particle tunnels, but different minima to correspond to different bath topologies. This enforces the bath to undergo gap closing along the tunneling path. In this work, we investigate quantum tunneling in the presence of such a topology-changing fermionic bath. We develop a field theory for this problem, linking the instantons describing tunneling in a bath of 𝑑 space dimensions to topological boundary modes of systems in 𝑑 +1 dimensions, thus stepping a level higher in a dimensional hierarchy. We study in detail a 𝑑 = 1 example, inspired by planar Josephson junctions where the particle coordinate is the superconducting phase whose value sets the electronic topology. We find that the topology change suppresses tunneling by a factor scaling exponentially with the system size. This translates to a correspondingly enhanced suppression of the energy splitting for the lowest-lying states, despite these being linear combinations of states near potential minima where the bath is gapped. Our results help to estimate the influence of charging energy on topological phases arising due to the Josephson effect and, conversely, to assess the potential utility of such topological systems as superconducting qubits. For moderate-sized baths, the incomplete suppression of tunneling opens the prospects of quantum-mechanical superpositions of many-body states of different topology, including superpositions of states with and without Majorana fermions.

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“…Importantly, while the possible presence of edge states influences the total boundary charge only by an integer number, the fractional part of the boundary charge contains contributions from all extended states and is directly related to bulk properties via the Zak-Berry phase. [16][17][18][19][20][21][22] Fractional boundary charges (FBCs) of this type have been studied in a large variety of systems, including different types of one-dimensional (1D) models, [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] topological crystalline insulators, [42][43][44][45][46] higher-order topological insulators, [47][48][49][50][51][52][53][54] and the integer quantum Hall effect (IQHE). 33 The FBCs in these examples were found to display various interesting features such as quantization in the presence of symmetries, 37 universal dependencies on certain system parameters, 22,30,…”

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confidence: 99%

Fractional boundary charges with quantized slopes in interacting one- and two-dimensional systems

Laubscher,

Weber,

Kennes

et al. 2021

Preprint

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We study fractional boundary charges (FBCs) for two classes of strongly interacting systems. First, we study strongly interacting nanowires subjected to a periodic potential with a period that is a rational fraction of the Fermi wavelength. For sufficiently strong interactions, the periodic potential leads to the opening of a charge density wave gap at the Fermi level. The FBC then depends linearly on the phase offset of the potential with a quantized slope determined by the period. Furthermore, different possible values for the FBC at a fixed phase offset label different degenerate ground states of the system that cannot be connected adiabatically. Next, we turn to the fractional quantum Hall effect (FQHE) at odd filling factors ν = 1/(2l + 1), where l is an integer. For a Corbino disk threaded by an external flux, we find that the FBC depends linearly on the flux with a quantized slope that is determined by the filling factor. Again, the FBC has 2l + 1 different branches that cannot be connected adiabatically, reflecting the (2l + 1)-fold degeneracy of the ground state. These results allow for several promising and strikingly simple ways to probe strongly interacting phases via boundary charge measurements.

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Jackiw-Rebbi zero modes in non-uniform topological insulator nanowire

Cited by 7 publications

References 50 publications

Dirac materials in parallel non-uniform electromagnetic fields generated by SUSY: a chiral Planar Hall Effect

Dirac materials in parallel non-uniform electromagnetic fields generated by SUSY: a chiral Planar Hall Effect

Quantum tunneling in the presence of a topology-changing fermionic bath

Fractional boundary charges with quantized slopes in interacting one- and two-dimensional systems

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