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Dirty higher-order Dirac semimetal: Quantum criticality and bulk-boundary correspondence

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Szabó,  András L.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Szabó, A. L., & Roy, B. (2020). Dirty higher-order Dirac semimetal: Quantum criticality and bulk-boundary correspondence. Physical Review Research, 2(4): 043197. doi:10.1103/PhysRevResearch.2.043197.


Cite as: https://hdl.handle.net/21.11116/0000-0009-406A-8
Abstract
We analyze the stability of time-reversal (T) and lattice fourfold (C4) symmetry breaking three-dimensional higher-order topological (HOT) Dirac semimetals (DSMs) and the associated one-dimensional hinge modes in the presence of random pointlike charge impurities. Complementary real space numerical and momentum space renormalization group (RG) analyses suggest that a HOTDSM, while being a stable phase of matter for sufficiently weak disorder, undergoes a continuous quantum phase transition into a trivial metal at finite disorder. However, the corresponding critical exponents (numerically obtained from the scaling of the density of states) are extremely close to the ones found in a dirty, but first-order DSM that on the other hand preserves T and C-4 symmetries, and support two Fermi arc surface states. This observation suggests an emergent superuniversality (insensitive to symmetries) in the entire family of dirty DSMs, as also predicted by a leading-order RG analysis. As a direct consequence of the bulk-boundary correspondence, the hinge modes in a system with open boundaries gradually fade away with increasing randomness, and completely dissolve in the trivial metallic phase at strong disorder.