Four-dimensional semimetals with tensor monopoles: From surface states to topological responses

Abstract

Quantum anomalies offer a useful guide for the exploration of transport phenomena in topological semimetals. In this work, we introduce a model describing a semimetal in four spatial dimensions, whose nodal points act like tensor monopoles in momentum space. This system is shown to exhibit monopole-to-monopole phase transitions, as signaled by a change in the value of the topological Dixmier-Douady invariant as well as by the associated surface states on its boundary. We use this model to reveal an intriguing "4D parity magnetic effect," which stems from a parity-type anomaly. In this effect, topological currents are induced upon time modulating the separation between the fictitious monopoles in the presence of a magnetic perturbation. Besides its theoretical implications in both condensed matter and quantum field theory, the peculiar four-dimensional (4D) magnetic effect revealed by our model could be measured by simulating higher-dimensional semimetals in synthetic matter.

Non-Abelian tensor Berry connections in multi-band topological systems

“…which provides the topological charge of the 4D real Dirac cone. Also in this case, the chiral symmetry protects the stability of this topological number similarly to the case of 4D tensor monopoles 22,23,25 . In fact, this four-dimensional phase can be seen as a stack of the IT -and S-symmetric 3D gapped phases.…”

“…Importantly, a generalization of Abelian Berry connections have been recently proposed 22,23 , where the new connections behave like Abelian antisymmetric tensor (Kalb-Ramond 24 ) gauge fields in momentum/parameter space. These tensor Berry connections have been employed to characterise the topology of 3D chiral topological insulators 23 and 4D topological semimetals 22,25,26 where the Dixmier-Douady (DD) invariant replaces the Chern number. The theoretical developments recently let to the experimental measurement of the DD invariant in 4D synthetic systems 27,28 .…”

Fractional Quantum Hall Effect for Extended Objects: from Skyrmionic Membranes to Dyonic Strings

“…We now insert the static gauge potential in Eq. (15) in the above equation such that the only non-zero component is given by…”

“…Higher-dimensional topological matter represents a very active field of research due to the possibility to engineer synthetic dimensions in suitable artificial setups [1][2][3][4][5][6]. In fact, topological invariants in four and higher dimensions and novel quantum effects such as the higher-dimensional Thouless pumping and anomalous quantum transports can be experimentally detected and measured in synthetic matter [7][8][9][10][11][12][13][14][15][16][17][18][19]. At microscopic level, these phases deal with point-like quasiparticles.…”

Topological Electromagnetic Effects and Higher Second Chern Numbers in Four-Dimensional Gapped Phases

“…For instance, the (2 + 1)-D Chern-Simons theory describes the quantum anomalous Hall effect in 2D Chern insulators [9], the (3 + 1)D axion field theory describes the magnetoelectric effect in 3D Z 2 TIs [10], and the (3 + 1)D mixed axion theory [11] describes the EM response in certain 3D topological crystalline insulators [12]. Similarly, TSMs also exhibit topological transport phenomena described by the mixed Chern-Simons/axion theory [13][14][15][16][17] and can be understood via quantum anomalies [18], such as parity anomaly in 2D and 4D TSMs [19,20], chiral anomaly in 3D Weyl semimetals [21,22], and Z 2 and chiral anomalies in 3D Dirac semimetals [23].…”