Electric field driven quantum phase transition between band insulator and topological insulator

Abstract

We demonstrate theoretically that electric field can drive a quantum phase transition between band insulator to topological insulator in CdTe/HgCdTe/CdTe quantum wells. The numerical results suggest that the electric field could be used as a switch to turn on or off the topological insulator phase, and temperature can affect significantly the phase diagram for different gate voltage and compositions. Our theoretical results provide us an efficient way to manipulate the quantum phase of HgTe quantum wells. PACS numbers: 73.43.Nq, 72.25.Rb, 73.61.Ga, Topological insulator (TI) is a very recent discovery and has attracted a rapid growing interests due to its novel transport peoperty 1,2,3,4 . Topological insulators possess a gap in the bulk but a gapless edge states at its boundary, therefore display remarkable transport property due to the presence of the topological edge states, e.g., quantum spin Hall effect (QSHE). The QSHE is protected by the time-reversal symmetry and robust against the local perturbation, e.g., impurity scattering. Searching for new TI becomes a central issue in this rapid growing field. Recently, the HgTe QWs have been demonstrated to be a 2D TI to exhibit the QSHE 3 and BiSb alloys have been proven to be a 3D TI with a conducting surface 5 . A few other materials, such as InAs/GaSb QWs, BiSe, BiTe and SbTe alloys 6 , are also predicted to be TIs and demonstrated experimentally. Besides finding new TI materials, searching the ways to drive a band insulator (BI) into a topological insulator is also important. It has been demonstrated to be possibly realized by tuning the thickness of HgTe QW. However, tuning the thickness of QW is not a convenient way to drive the phase transition. Therefore other efficient ways such as external fields and temperature is highly desirable to drive a BI into a TI. These ways would be very important for both potential device applications and basic physics.In this Letter, we demonstrate theoretically that a BI can be driven into a TI by tuning external electric field in CdTe/Hg 1−x Cd x Te/CdTe QWs based on the self-consistent calculation of the eight-band Kane model and the Poisson equation. We demonstrate electric field can change the interband coupling significantly and consequently leads to strong variations of the band structures, i.e., therefore leads to the quantum phase transition from a BI to a TI. We also show phase diagrams at plenty of parameters and consider the temperature effect on the phase transition. One can see that the critical gate voltage of external phase transition can be reduced at high temperature, small Cd composition and thick thickness of well. Our results could be useful in finding the optimized parameters to realize the phase transition in experiment.We consider a CdTe/Hg 1−x Cd x Te/CdTe QW grown along the [001] direction [see Fig. 1 (a) inside the QW will redistribute due to the effect of the electric field. The charge redistribution induces an internal electric field, which affects the charge density distribution, therefore we n...

Topological quantum phase transitions driven by external electric fields in Sb 2 Te 3 thin films

“…In the case of 2D TIs (i.e., quantum spin Hall systems), still another factor affecting the band topology is an electrostatic scalar potential or an external electric field as an effective continuous model predicts that potential difference between upper and lower surfaces can transform topologically nontrivial thin films of Bi 2 Se 3 into topologically trivial ones (17,18). Actually, a model calculation shows that external electric fields can drive the quantum phase transition between TIs and NIs in HgTe quantum wells (19). It has been predicted that thin films of tetradymite semiconductors recently found to be 3D strong topological insulators can be 2D TIs or NIs depending on the thickness (20).…”

Pressure- and temperature-driven phase transitions in HgTe quantum wells

“…14 It has been recently demonstrated that a transition between BI and TI phases can be driven either by electric field 15,16 , applied along the growth direction, or by temperature 17,18 . However, the mentioned works were focused on the evolution of the band structure due to transition between BI and TI phases only, while temperature and electric field effects in the SM phase were ignored.…”

Зонный спектр в гетероструктурах HgTe/CdHgTe p-типа и его перестройка с изменением температуры

“…Последнее открывает допол-нительные возможности для создания перспективных " топологических" приборов, работающих с использова-нием краевых каналов проводимости [19]. К настоящему времени теоретически рассматривались возможности осуществления фазового перехода в КЯ HgTe/CdHgTe между состояниями тривиального и топологического изоляторов с помощью внешнего электрического по-ля [20,21], температуры [10,21,22] и давления [22]. Экс-периментально качественное изменение зонного спектра и наличие такого перехода при изменении темпера-туры впервые было продемонстрировано с помощью транспортных [10] и магнитооптических измерений [23].…”