PHYSICAL REVIEW B 90, 195311 (2014) First-principles study of HgTe/CdTe heterostructures under perturbations preserving time-reversal symmetry Jonas Anversa and Paulo Piquini * Departamento de Fisica, Universidade Federal de Santa Maria, 97105-900, Santa Maria, RS, Brazil Adalberto Fazzio Instituto de Fisica, Universidade de S˜ ao Paulo, CP 66318, 05315-970, S˜ ao Paulo, SP, Brazil Tome M. Schmidt Instituto de Fisica, Universidade Federal de Uberlˆ andia, CP 593, 38400-902, Uberl ˆ andia, MG, Brazil (Received 26 April 2014; revised manuscript received 5 October 2014; published 21 November 2014) The observation of the quantum spin Hall effect without the need of an external magnetic field in HgTe/CdTe heterostructures triggered the study of materials exhibiting persistent spin-polarized electronic currents at their interfaces. These Dirac-like spin states are predicted to be topologically protected against perturbations preserving time-reversal symmetry. However, nonmagnetic (time-reversal preserving) perturbations will certainly affect these interface states. In this work, the density functional theory is used to characterize the topologically protected states of the (001) HgTe/CdTe heterostructure as well as to understand the influence of external adiabatic parameters as pressure and electric fields on these states. The intrasite Hubbard U term is seen to be important to correctly describe the HgTe bulk band structure. It is shown that, differently from the three-dimensional topological insulators, the HgTe/CdTe interface states present fully in-plane Rashba-like spin texture. Further, biaxial external pressures and electric fields perpendicular to the interfaces are seen to change the energetics and dispersion of the protected states, modifying the energy ordering of the crossing of the polarized interface states inside the band structure, and altering their Fermi velocities while not changing the topological quantum phase. These adiabatic variables can then be used to tune the topologically protected states with respect to the Fermi level. DOI: 10.1103/PhysRevB.90.195311 PACS number(s): 73.20.−r, 73.21.Fg I. INTRODUCTION The topological insulators (TIs) constitute a material phase with potential application in spintronics and quantum information [1], serving also as a platform to investigate fundamental physics concepts [2]. This new field in solid-state physics is based on the fact that the spin-orbit interaction can turn a material with a fully insulating gap in the bulk into one presenting gapless surface/interface states, which are protected against perturbations preserving time reversal symmetry (TRS). This phenomenon, called quantum spin Hall effect (QSHE), was proposed by Kane et al. [3]. Bernevig et al. [4] showed that a HgTe/CdTe quantum well structure would be a material system where the QSHE could be observed. This was successfully verified by the Molenkamps group [5], through electronic transport measurements, showing for the first time the distinctive signature of the interface spin-polarized states on this class of topological insulator (TI) materials. After this decisive experimental verification, several theo- retical and experimental studies have been performed aiming to find new TI materials, and to understand the underlying phys- ical principles governing the QSHE [6,7]. In a recent work, K¨ ufner and Bechstedt [8] used ab initio density functional theory to study the edge states of HgTe quantum wells and qualitatively verified the previous result of a four-band k · p approach [4]. On the other hand, Luo and Zunger [9], using an * paulo.piquini@ufsm.br atomistic pseudopotential method, showed that the topological states of the HgTe/CdTe heterostructure are two-dimensional (2D) interface states, instead of 1D edge states as proposed by Bernevig et al. [4]. Fu and Kane [10] introduced a method to evaluate the Z 2 invariants, and used a four-band tight-binding model to obtain these invariants in 2D and 3D TIs. Most of the transport properties of the HgTe/CdTe quantum well have been intensively studied [11,12]. The effects of transverse electric fields on HgTe/CdTe heterostructures have been studied by Liu et al. [13]. Chen et al. [14] studied the influence of a magnetic field on electronic transport in HgTe/CdTe quantum wells and showed that the quantum spin Hall effect can survive under magnetic fields up to 10 T. Wang et al. [15] obtained that the transport through the QSH state is robust, with the conductivity having a constant value of 2e 2 /h independently of the number, shape, strength, or length of the scattering potential. Sengupta et al. [16] used the k · p method to study the critical well thickness dependence on external stress, temperature, and electric fields. However, the effective application of future devices based on TI materials requires an accurate characterization of the gapless topological states as well as an understanding of how these states behave under usual external perturbations. Hence, an accurate description of the band structure of TIs through density functional theory calculations under different external conditions is crucial. In this work we show that a correct description of the levels close to the top of the valence band of the HgTe band structure requires the inclusion of the intrasite Hubbard U Coulomb repulsion term in the density functional formalism. The evolution of the band structure of 1098-0121/2014/90(19)/195311(9) 195311-1 ©2014 American Physical Society