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

TL;DR

This paper introduces a four-dimensional topological semimetal model with tensor monopoles, revealing novel phase transitions, surface states, and a unique 4D parity magnetic effect driven by topological anomalies.

Contribution

It presents a new 4D semimetal model with tensor monopoles, demonstrating monopole-to-monopole phase transitions and a novel 4D parity magnetic effect from parity anomalies.

Findings

Identification of monopole-to-monopole phase transitions

Discovery of a 4D parity magnetic effect

Potential for simulating higher-dimensional semimetals in synthetic matter

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 4D magnetic effect revealed by our model could be measured by simulating higher-dimensional semimetals in synthetic matter.