The study of surface states in a semi-infinite crystal

Scientific Reports
Huiping WangRuibao Tao

Abstract

An infinite three dimensional (3D) crystal can be constructed by an infinite number of parallel 2D (hkl) crystal planes (CPs) coupled to each other. Based on lattice model Hamiltonian with the hopping between the nearest neighbor (1NN) CPs and all possible neighbor hoppings within each CP, we analytically prove that a (hkl) cut crystal will not accommodate any surface states if the original infinite crystal has the reflection symmetry which results in the forward transfer matrix F to be equal to the backward one B, named as F-B dynamical symmetry. We also study the effect of the longer range couplings among the nNN (n > 1) CPs and surface relaxation on our conclusion and find that the small perturbation from both factors has no effect on our conclusion based on the perturbation theory. Thus our model may have the potential for studying surface states in some cut crystals with low-index surfaces. Our result may be helpful to visually predict which cutting direction in some non-topological crystals is unfavorable to generate surface states.

References

Oct 15, 1994·Physical Review. B, Condensed Matter·B FangK M Ho
Sep 15, 1989·Physical Review. B, Condensed Matter·W C Fan, A Ignatiev
Jul 7, 1986·Physical Review Letters·J E Northrup
Oct 16, 1995·Physical Review Letters·J A StroscioM Weinert
Oct 26, 2005·Physical Review Letters·C L Kane, E J Mele
Dec 31, 2005·Physical Review Letters·C L Kane, E J Mele
Dec 16, 2006·Science·B Andrei BernevigShou-Cheng Zhang
Mar 16, 2007·Physical Review Letters·Liang FuE J Mele
Jul 23, 2008·Physical Review Letters·Chaoxing LiuShou-Cheng Zhang
Jan 27, 2009·Nature Materials·J SeidelR Ramesh
Apr 28, 2009·Physical Review Letters·Jian LiShun-Qing Shen
Jun 13, 2009·Physical Review Letters·Xiao-Liang QiShou-Cheng Zhang
Mar 1, 2012·Nature Materials·D MeierM Fiebig
Mar 10, 2012·Physical Review Letters·Shusa DengGerardo Ortiz

❮ Previous
Next ❯

Related Concepts

Related Feeds

Birth Defects

Birth defects encompass structural and functional alterations that occur during embryonic or fetal development and are present since birth. The cause may be genetic, environmental or unknown and can result in physical and/or mental impairment. Here is the latest research on birth defects.