| 1. |
- Budich, Jan Carl
(författare)
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Charge conservation protected topological phases
- 2013
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 87:16, s. 161103-
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Tidskriftsartikel (refereegranskat)abstract
- We discuss the relation between particle number conservation and topological phases. In four spatial dimensions, we find that systems belonging to different topological phases in the presence of a U(1) charge conservation can be connected adiabatically, i.e., without closing the gap, upon intermediately breaking this local symmetry by a superconducting term. The time reversal preserving topological insulator states in two and three dimensions which can be obtained from the four-dimensional parent state by dimensional reduction inherit this protection by charge conservation. Hence, all topological insulators can be adiabatically connected to a trivial insulating state without breaking time reversal symmetry, provided an intermediate superconducting term is allowed during the adiabatic deformation. Conversely, in one spatial dimension, non-symmetry-protected topological phases occur only in systems that break U(1) charge conservation. These results can intuitively be understood by considering a natural embedding of the classifying spaces of charge conserving Hamiltonians into the corresponding Bogoliubov-de Gennes classes.
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| 2. |
- Budich, Jan Carl, et al.
(författare)
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Coupled atomic wires in a synthetic magnetic field
- 2017
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Ingår i: Physical Review A. - 2469-9926. ; 95:4
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Tidskriftsartikel (refereegranskat)abstract
- We propose and study systems of coupled atomic wires in a perpendicular synthetic magnetic field as a platform to realize exotic phases of quantum matter. This includes (fractional) quantum Hall states in arrays of many wires inspired by the pioneering work [C. L. Kane et al., Phys. Rev. Lett. 88, 036401 (2002)], as well as Meissner phases and vortex phases in double wires. With one continuous and one discrete spatial dimension, the proposed setup naturally complements recently realized discrete counterparts, i.e., the Harper-Hofstadter model and the two-leg flux ladder, respectively. We present both an in-depth theoretical study and a detailed experimental proposal to make the unique properties of the semicontinuous Harper-Hofstadter model accessible with cold-atom experiments. For the minimal setup of a double wire, we explore how a subwavelength spacing of the wires can be implemented. This construction increases the relevant energy scales by at least an order of magnitude compared to ordinary optical lattices, thus rendering subtle many-body phenomena such as Lifshitz transitions in Fermi gases observable in an experimentally realistic parameter regime. For arrays of many wires, we discuss the emergence of Chern bands with readily tunable flatness of the dispersion and show how fractional quantum Hall states can be stabilized in such systems. Using for the creation of optical potentials Laguerre-Gauss beams that carry orbital angular momentum, we detail how the coupled atomic wire setups can be realized in nonplanar geometries such as cylinders, disks, and tori.
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| 3. |
- Budich, Jan Carl, et al.
(författare)
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Equivalent topological invariants for one-dimensional Majorana wires in symmetry class D
- 2013
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 88:7, s. 075419-
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Tidskriftsartikel (refereegranskat)abstract
- Topological superconductors in one spatial dimension exhibiting a single Majorana bound state at each end are distinguished from trivial gapped systems by aZ(2) topological invariant. Originally, this invariant was calculated by Kitaev in terms of the Pfaffian of the Majorana representation of the Hamiltonian: The sign of this Pfaffian divides the set of all gapped quadratic forms of Majorana fermions into two inequivalent classes. In the more familiar Bogoliubov de Gennes mean-field description of superconductivity, an emergent particle-hole symmetry gives rise to a quantized Zak-Berry phase, the value of which is also a topological invariant. In this work, we explicitly show the equivalence of these two formulations by relating both of them to the phase winding of the transformation matrix that brings the Majorana representation matrix of the Hamiltonian into its Jordan normal form.
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| 4. |
- Budich, Jan Carl, et al.
(författare)
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Fluctuation-driven topological Hund insulators
- 2013
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Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 87:23
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Tidskriftsartikel (refereegranskat)abstract
- We investigate the role of electron-electron interaction in a two-band Hubbard model based on the Bernevig-Hughes-Zhang Hamiltonian exhibiting the quantum spin Hall (QSH) effect. By means of dynamical mean-field theory, we find that a system with topologically trivial noninteracting parameters can be driven into a QSH phase at finite interaction strength by virtue of local dynamical fluctuations. For very strong interaction, the system reenters a trivial insulating phase by going through a Mott transition. We obtain the phase diagram of our model by direct calculation of the bulk topological invariant of the interacting system in terms of its single-particle Green's function.
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| 5. |
- Budich, Jan Carl, et al.
(författare)
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Fractional topological phase in one-dimensional flat bands with nontrivial topology
- 2013
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 88:3, s. 035139-
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Tidskriftsartikel (refereegranskat)abstract
- We consider a topologically nontrivial flat-band structure in one spatial dimension in the presence of nearest-and next-nearest-neighbor Hubbard interaction. The noninteracting band structure is characterized by a symmetry-protected topologically quantized Berry phase. At certain fractional fillings, a gapped phase with a filling-dependent ground-state degeneracy and fractionally charged quasiparticles emerges. At filling 1/3, the ground states carry a fractional Berry phase in the momentum basis. These features at first glance suggest a certain analogy to the fractional quantum Hall scenario in two dimensions. We solve the interacting model analytically in the physically relevant limit of a large band gap in the underlying band structure, the analog of a lowest Landau level projection. Our solution affords a simple physical understanding of the properties of the gapped interacting phase. We pinpoint crucial differences to the fractional quantum Hall case by studying the Berry phase and the entanglement entropy associated with the degenerate ground states. In particular, we conclude that the fractional topological phase in one-dimensional flat bands is not a one-dimensional analog of the two-dimensional fractional quantum Hall states, but rather a charge density wave with a nontrivial Berry phase. Finally, the symmetry-protected nature of the Berry phase of the interacting phase is demonstrated by explicitly constructing a gapped interpolation to a state with a trivial Berry phase.
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| 6. |
- Budich, Jan Carl, et al.
(författare)
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From the adiabatic theorem of quantum mechanics to topological states of matter
- 2013
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Ingår i: Physica Status Solidi. Rapid Research Letters. - : Wiley. - 1862-6254 .- 1862-6270. ; 7:1-2, s. 109-129
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Forskningsöversikt (refereegranskat)abstract
- Owing to the enormous interest the rapidly growing field of topological states of matter (TSM) has attracted in recent years, the main focus of this review is on the theoretical foundations of TSM. Starting from the adiabatic theorem of quantum mechanics which we present from a geometrical perspective, the concept of TSM is introduced to distinguish gapped many body ground states that have representatives within the class of non-interacting systems and mean field superconductors, respectively, regarding their global geometrical features. These classifying features are topological invariants defined in terms of the adiabatic curvature of these bulk insulating systems. We review the general classification of TSM in all symmetry classes in the framework of K-Theory. Furthermore, we outline how interactions and disorder can be included into the theoretical framework of TSM by reformulating the relevant topological invariants in terms of the single particle Green's function and by introducing twisted boundary conditions, respectively. We finally integrate the field of TSM into a broader context by distinguishing TSM from the concept of topological order which has been introduced to study fractional quantum Hall systems.
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| 7. |
- Budich, Jan Carl, et al.
(författare)
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Helical Floquet Channels in 1D Lattices
- 2017
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Ingår i: Physical Review Letters. - 0031-9007. ; 118:10
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Tidskriftsartikel (refereegranskat)abstract
- We show how dispersionless channels exhibiting perfect spin-momentum locking can arise in a 1D lattice model. While such spectra are forbidden by fermion doubling in static 1D systems, here we demonstrate their appearance in the stroboscopic dynamics of a periodically driven system. Remarkably, this phenomenon does not rely on any adiabatic assumptions, in contrast to the well known Thouless pump and related models of adiabatic spin pumps. The proposed setup is shown to be experimentally feasible with state-of-the-art techniques used to control ultracold alkaline earth atoms in optical lattices.
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| 8. |
- Budich, Jan Carl, et al.
(författare)
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Non-Hermitian Topological Sensors
- 2020
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Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 125:18
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Tidskriftsartikel (refereegranskat)abstract
- We introduce and study a novel class of sensors whose sensitivity grows exponentially with the size of the device. Remarkably, this drastic enhancement does not rely on any fine-tuning, but is found to be a stable phenomenon immune to local perturbations. Specifically, the physical mechanism behind this striking phenomenon is intimately connected to the anomalous sensitivity to boundary conditions observed in non-Hermitian topological systems. We outline concrete platforms for the practical implementation of these non-Hermitian topological sensors ranging from classical metamaterials to synthetic quantum materials.
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| 9. |
- Budich, Jan Carl, et al.
(författare)
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Symmetry-protected nodal phases in non-Hermitian systems
- 2019
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Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 99:4
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Tidskriftsartikel (refereegranskat)abstract
- Non-Hermitian (NH) Hamiltonians have become an important asset for the effective description of various physical systems that are subject to dissipation. Motivated by recent experimental progress on realizing the NH counterparts of gapless phases such as Weyl semimetals, here we investigate how NH symmetries affect the occurrence of exceptional points (EPs), that generalize the notion of nodal points in the spectrum beyond the Hermitian realm. Remarkably, we find that the dimension of the manifold of EPs is generically increased by one as compared to the case without symmetry. This leads to nodal surfaces formed by EPs that are stable as long as a protecting symmetry is preserved, and that are connected by open Fermi volumes. We illustrate our findings with analytically solvable two-band lattice models in one and two spatial dimensions, and show how they are readily generalized to generic NH crystalline systems.
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| 10. |
- Budich, Jan Carl, et al.
(författare)
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Time Reversal Symmetric Topological Exciton Condensate in Bilayer HgTe Quantum Wells
- 2014
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Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 112:14, s. 146405-
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Tidskriftsartikel (refereegranskat)abstract
- We investigate a bilayer system of critical HgTe quantum wells, each featuring a spin-degenerate pair of massless Dirac fermions. In the presence of an electrostatic interlayer Coulomb coupling, we determine the exciton condensate order parameter of the system self-consistently. Calculating the bulk topological Z(2) invariant of the resulting mean-field Hamiltonian, we discover a novel time reversal symmetric topological exciton condensate state, coined the helical topological exciton condensate. We argue that this phase can exist for experimentally relevant parameters. Interestingly, due to its multiband nature, the present bilayer model exhibits a nontrivial interplay between spontaneous symmetry breaking and topology: Depending on which symmetry the condensate order parameter spontaneously picks in combined orbital and spin space, stable minima in the free energy corresponding to both trivial and nontrivial gapped states can be found.
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