Theories for the 3D Quantum Hall effects

The discovery of the quantum Hall effect has led to three Nobel prizes and the booming field of topological phases of quantum matter. The quantum Hall effect is usually observed in 2D. It has been a long-standing challenge to realize a quantum Hall effect in 3D.
We predict a new mechanism of 3D quantum Hall effect in topological semimetals [1-2]. Topological semimetals, which host topologically-protected surface states, known as the Fermi arcs. The Fermi arcs at two opposite surfaces can form a 2D electron gas that supports a 3D quantum Hall effect. Possible signatures are observed in the topological Dirac semimetal Cd3As2 [e.g., Faxian Xiu et al., Nature 565, 331 (2019)]. This 3D quantum Hall give an example of (d-2)-dimensional boundary states in higher-order topological phases of matter [3].
On the other hand, the charge-density-wave mechanism of the 3D quantum Hall effect has been observed recently in ZrTe5 [Liyuan Zhang et al., Nature 569, 537 (2019)]. We develop a theory for the CDW mechanism of the 3D quantum Hall effect [4] and coexisting meta-insulator transition [5]. The theories can capture the main features in the experiment. More importantly, it poses a rare case, in which one magnetic field can induce an order-parameter phase transition in one dimension but a topological phase transition in other two dimensions.

References:
[1] C. M. Wang et al., PRL 119, 136806 (2017).
[2] Hai-Zhou Lu, National Science Review 6, 208 (2019).
[3] Rui Chen et al., PRL 127, 066801 (2021).
[4] Fang Qin et al., PRL 125, 206601 (2020).
[5] Peng-Lu Zhao et al., PRL 127, 046602 (2021).

**Theories for the 3D Quantum Hall effects**

The discovery of the quantum Hall effect has led to three Nobel prizes and the booming field of topological phases of quantum matter. The quantum Hall effect is usually observed in 2D. It has been a long-standing challenge to realize a quantum Hall effect in 3D.
We predict a new mechanism of 3D quantum Hall effect in topological semimetals [1-2]. Topological semimetals, which host topologically-protected surface states, known as the Fermi arcs. The Fermi arcs at two opposite surfaces can form a 2D electron gas that supports a 3D quantum Hall effect. Possible signatures are observed in the topological Dirac semimetal Cd3As2 [e.g., Faxian Xiu et al., Nature 565, 331 (2019)]. This 3D quantum Hall give an example of (d-2)-dimensional boundary states in higher-order topological phases of matter [3].
On the other hand, the charge-density-wave mechanism of the 3D quantum Hall effect has been observed recently in ZrTe5 [Liyuan Zhang et al., Nature 569, 537 (2019)]. We develop a theory for the CDW mechanism of the 3D quantum Hall effect [4] and coexisting meta-insulator transition [5]. The theories can capture the main features in the experiment. More importantly, it poses a rare case, in which one magnetic field can induce an order-parameter phase transition in one dimension but a topological phase transition in other two dimensions.

References:
[1] C. M. Wang et al., PRL 119, 136806 (2017).
[2] Hai-Zhou Lu, National Science Review 6, 208 (2019).
[3] Rui Chen et al., PRL 127, 066801 (2021).
[4] Fang Qin et al., PRL 125, 206601 (2020).
[5] Peng-Lu Zhao et al., PRL 127, 046602 (2021).

Hai-Zhou Lu

The discovery of topologically non-trivial materials has shaped much of recent research in condensed matter physics.

In particular, the interplay of topology with magnetism and superconductivity has enabled advances that have both fundamental and practical implications. The conference will bring together leading researchers working on these topics and will be broadcast online to allow world-wide participation.