Abstract
Grapheneis a massless Dirac fermion system, featuring Dirac points in momentum space. It was also first identified as a quantum spin Hall (QSH) insulator when considering spin–orbit coupling (SOC), which opens a band gap at the Dirac points. This discovery has initiated new research efforts to study the QSH effect, towards its application for quantum computing and spintronics. Although the QSH effect has been observed in HgTe quantum wells, the SOC strength of graphene is too small (~1 µeV) to induce the topological insulator phase in an experimentally achievable temperature regime. Here, we perform a systematic atomistic simulation to design two-dimensional sp–sp2 hybrid carbon sheets to discover new Dirac systems, hosting the QSH phase. 21 out of 31 newly discovered carbon sheets are identified as Dirac fermion systems without SOC, distinct from graphene in the number, shape, and position of the Dirac cones occurring in the Brillouin zone. Moreover, we find 19 out of the 21 new Dirac fermion systems become QSH insulators with a sizable SOC gap enhanced up to an order of meV, thus allowing for the QSH effect at experimentally accessible temperatures. In addition, based on the 26 Dirac fermion systems, we make a connection between the number of Dirac points without SOC and the resultant QSH phase in the presence of SOC. Our findings present new prospects for the design of topological materials with desired properties.
Highlights
Since the first synthesis of graphene,[1] a two-dimensional (2D) atomic layer of sp2-bonded carbon atoms, it has received tremendous attention due to its unique electronic,[2,3] mechanical, and chemical properties[4,5,6,7] as well as unconventional superconducting behavior.[8]
The massless Dirac fermions hosted in graphene without spin–orbit coupling (SOC) as quasi-particles allow for fascinating physical phenomena, such as the Klein tunneling and half-integer quantum Hall effects.[2,3]
It was expected that graphene could open a sizable SOC gap at the Dirac point, becoming a 2D topological insulator (TI), supporting quantum spin
Summary
Since the first synthesis of graphene,[1] a two-dimensional (2D) atomic layer of sp2-bonded carbon atoms, it has received tremendous attention due to its unique electronic,[2,3] mechanical, and chemical properties[4,5,6,7] as well as unconventional superconducting behavior.[8] The massless Dirac fermions hosted in graphene without spin–orbit coupling (SOC) as quasi-particles allow for fascinating physical phenomena, such as the Klein tunneling and half-integer quantum Hall effects.[2,3] When including SOC, a Dirac fermion system can exhibit even more exciting phenomena related electronic band topology. These experiments have made it more feasible to synthesize sp–sp[2] hybrid carbon sheets as alternating 2D Dirac fermion systems, which can overcome the limitations of graphene
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