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Title: The Quantum Spin Hall Effect: Theory and Experiment

Abstract

The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in the bulk, but have topologically protected edge states due to the time reversal symmetry. In two dimensions the helical edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. Here we review a recent theory which predicts that the QSH state can be realized in HgTe/CdTe semiconductor quantum wells. By varying the thickness of the quantum well, the band structure changes from a normal to an 'inverted' type at a critical thickness d{sub c}. We present an analytical solution of the helical edge states and explicitly demonstrate their topological stability. We also review the recent experimental observation of the QSH state in HgTe/(Hg,Cd)Te quantum wells. We review both the fabrication of the sample and the experimental setup. For thin quantum wells with well width d{sub QW} < 6.3 nm, the insulating regime shows the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells (d{sub QW} > 6.3 nm), the nominally insulatingmore » regime shows a plateau of residual conductance close to 2e{sup 2}/h. The residual conductance is independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance is destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d{sub c} = 6.3 nm, is also independently determined from the occurrence of a magnetic field induced insulator to metal transition.« less

Authors:
; ; ; ; ; ;
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
973788
Report Number(s):
SLAC-PUB-13924
TRN: US201007%%391
DOE Contract Number:  
AC02-76SF00515
Resource Type:
Journal Article
Journal Name:
J.Phys.Soc.Jap.77:031007,2008
Additional Journal Information:
Journal Name: J.Phys.Soc.Jap.77:031007,2008
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; DIMENSIONS; FABRICATION; HALL EFFECT; MAGNETIC FIELDS; PHYSICS; QUANTUM WELLS; SPIN; STABILITY; SYMMETRY; THICKNESS; Other,MATSCI

Citation Formats

Konig, Markus, Buhmann, Hartmut, Molenkamp, Laurens W, /Wurzburg U., Hughes, Taylor L, /Stanford U., Phys. Dept., Liu, Chao-Xing, /Tsinghua U., Beijing /Stanford U., Phys. Dept., Qi, Xiao-Liang, Zhang, Shou-Cheng, and /Stanford U., Phys. Dept. The Quantum Spin Hall Effect: Theory and Experiment. United States: N. p., 2010. Web.
Konig, Markus, Buhmann, Hartmut, Molenkamp, Laurens W, /Wurzburg U., Hughes, Taylor L, /Stanford U., Phys. Dept., Liu, Chao-Xing, /Tsinghua U., Beijing /Stanford U., Phys. Dept., Qi, Xiao-Liang, Zhang, Shou-Cheng, & /Stanford U., Phys. Dept. The Quantum Spin Hall Effect: Theory and Experiment. United States.
Konig, Markus, Buhmann, Hartmut, Molenkamp, Laurens W, /Wurzburg U., Hughes, Taylor L, /Stanford U., Phys. Dept., Liu, Chao-Xing, /Tsinghua U., Beijing /Stanford U., Phys. Dept., Qi, Xiao-Liang, Zhang, Shou-Cheng, and /Stanford U., Phys. Dept. 2010. "The Quantum Spin Hall Effect: Theory and Experiment". United States. https://www.osti.gov/servlets/purl/973788.
@article{osti_973788,
title = {The Quantum Spin Hall Effect: Theory and Experiment},
author = {Konig, Markus and Buhmann, Hartmut and Molenkamp, Laurens W and /Wurzburg U. and Hughes, Taylor L and /Stanford U., Phys. Dept. and Liu, Chao-Xing and /Tsinghua U., Beijing /Stanford U., Phys. Dept. and Qi, Xiao-Liang and Zhang, Shou-Cheng and /Stanford U., Phys. Dept.},
abstractNote = {The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in the bulk, but have topologically protected edge states due to the time reversal symmetry. In two dimensions the helical edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. Here we review a recent theory which predicts that the QSH state can be realized in HgTe/CdTe semiconductor quantum wells. By varying the thickness of the quantum well, the band structure changes from a normal to an 'inverted' type at a critical thickness d{sub c}. We present an analytical solution of the helical edge states and explicitly demonstrate their topological stability. We also review the recent experimental observation of the QSH state in HgTe/(Hg,Cd)Te quantum wells. We review both the fabrication of the sample and the experimental setup. For thin quantum wells with well width d{sub QW} < 6.3 nm, the insulating regime shows the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells (d{sub QW} > 6.3 nm), the nominally insulating regime shows a plateau of residual conductance close to 2e{sup 2}/h. The residual conductance is independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance is destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d{sub c} = 6.3 nm, is also independently determined from the occurrence of a magnetic field induced insulator to metal transition.},
doi = {},
url = {https://www.osti.gov/biblio/973788}, journal = {J.Phys.Soc.Jap.77:031007,2008},
number = ,
volume = ,
place = {United States},
year = {Fri Mar 19 00:00:00 EDT 2010},
month = {Fri Mar 19 00:00:00 EDT 2010}
}