Piezoelectricity signals topological phase transition
Phase transition is signaled by the discontinuous change of physical response function, while if the phase transition is topological, such change reflects the jump of topological invariant, with the celebrated example of the jump of the Hall conductance across the plateau transition
in the integer quantum Hall system. The physical responses in the current studies are all induced by the electromagnetic field. A natural question then arises: can we probe topological phase transition with other types of perturbation?
In this work, we demonstrate that the piezoelectric response can change discontinuously across a topological quantum phase transition in two dimensional (2D) time-reversal invariant systems with spin-orbit coupling, thus serving as a direct probe of the transition. This work further demonstrates the existence of piezoelectricity jump across the topological phase transition in all the 2D crystals that allow for non-zero piezoelectricity and proposes HgTe/CdTe quantum well and BaMnSb2 as two potential experimental platforms.
Reference
- Piezoelectricity and Topological Quantum Phase Transitions in Two-Dimensional Spin-
Orbit Coupled Crystals with Time-Reversal Symmetry, Jiabin Yu, Chao-Xing Liu, Nature Communications 11, 2290 (2020).
Crystalline symmetry protects Majoranas
One of the cornerstones for topological quantum computations is Majorana quasi-particle, which has been intensively searched in fractional quantum Hall systems and topological superconductors. Conventional semiconductor-based Majorana setups have been following Kitaev’s protocol, where the necessity of proximity induced long-range superconductivity is taken for granted. We proposed interacting Dirac semimetal (DSM) nanowire as a test bed to challenge this common belief. By inserting magnetic flux, a DSM nanowire is driven into 1D crystalline-symmetry-protected semi-metallic phase. Interaction enables the emergence of boundary Majorana zero modes, which is robust as a result of crystalline symmetry protection. Various experimental consequences of Majorana signals are discussed.
Reference
- Zhang, R.-X., & Liu, C. Crystalline Symmetry-Protected Majorana Mode in Number-Conserving Dirac Semimetal Nanowires. Phys. Rev. Lett., 120(15), 156802 (2018).
Boson analog of Topological insulators
Topological insulators of fermions have been well studied and understood in non-interacting electron systems. However, non-interacting bosons will form Bose-Einstein condensate at a low temperature, preventing forming a topologically non-trivial ground state. Thus, unlike fermion systems, interaction plays a key role in realizing boson analog of topological insulator phases in real systems. In this work, we propose to realize boson analog of topological insulator phases, dubbed as “bosonic symmetry protected topological state”, in a bilayer graphene under a strong tilted external magnetic field. Although starting from an electronic system, we demonstrate that all the fermion degrees can be gapped out by standard Coulomb interaction and only bosonic modes, which carry either charge-2e or spin-1, remains at the boundary. Furthermore, spin and momentum are also locked for such boson modes, thus forming “bosonic helical liquids”. We further study the transport of a quantum point contact for such bosonic helical liquids and compare them to fermionic helical liquids. With the realistic interaction parameters, we find a novel charge insulator/spin conductor phase for bosonic helical liquids and charge insulator/spin insulator or charge conductor/spin conductor phase for fermionic helical liquids. Thus, a quantum point contact experiment will provide a “smoking-gun” transport signature for boson analog of topological insulators unambiguously. Similar physics can also emerge in topological mirror Kondo insulators, such as SmB6.
References
- Bilayer Graphene as a platform for Bosonic Symmetry Protected Topological States, Zhen Bi, Ruixing Zhang, Yi-Zhuang You, Andrea Young, Leon Balents, Chao-Xing Liu, Cenke Xu, Phys. Rev. Lett. 118, 126801 (2017)
- Interacting topological phases in thin films of topological mirror Kondo insulators, Rui-Xing Zhang, Cenke Xu, Chao-Xing Liu, Phys. Rev. B 94, 235128 (2016).
- Fingerprints of bosonic symmetry protected topological state in a quantum point contact, Rui-xing Zhang, Chao-xing Liu, Phys. Rev. Lett. 118, 216803 (2017).
Unconventional Pairing Mixing in Half-Heusler Superconductors
In the BCS theory, the Cooper pairs normally have s-wave spin-singlet (S=0) symmetry. In the so-called non-centrosymmetric superconductors, p-wave spin-triplet component (S=1) can be mixed into s-wave spin-singlet component by spin-orbit coupling in absence of inversion symmetry. In this work, we propose a new type of mixed-pairing state, namely the mixture of s-wave spin-singlet and d-wave spin-quintet (S=2) channels, even in the presence of inversion symmetry when electrons effectively carry spin-3/2. We demonstrate the occurrence of singlet-quintet mixing in half-Heusler compounds. As a physical consequence of such pairing mixing, topological nodal-line superconductivity is found in such system and gives rise to at surface Majorana bands. This work provides a possible explanation of unconventional superconducting behaviors observed in superconducting half-Heusler compounds and suggests that these superconducting materials provide a new platform for exploring unconventional and topological superconductivity.
References
- Singlet-Quintet Mixing in Spin-Orbit Coupled Superconductors with j=3/2 Fermions, Jiabin Yu, Chao-Xing Liu, Phys. Rev. B 98, 104514 (2018).
- Unconventional superconductivity and Surface pairing symmetry in Half-Heusler Compounds, Qing-Ze Wang, Jiabin Yu, Chao-Xing Liu, Phys. Rev. B 97, 224507 (2018)
- Surface Majorana flat bands in j = 3/2 superconductors with singlet-quintet mixing,
Jiabin Yu, Chao-Xing Liu, Chin. Phys. B, 2020, 29(1):017402.