Collapse of resonances in semiconductor heterostructures as a transition with symmetry breaking in an open quantum system

Горбацевич, А. А.; Zhuravlev, M. N.; Kapaev, V. V.

doi:10.1134/s106377610808013x

Cited by 15 publications

(18 citation statements)

References 18 publications

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“…13,44,45 However, its location, in general, has no direct relation to the coalescence of resonances and, hence, to physical observables. 12,18 Although, as was shown in Refs. 46,47 , physical properties of the system do change at EP of the scattering matrix of a system with balanced gain and loss, where two unimodular eigenvalues of the S-matrix turn into two non-unimodular.…”

Section: Introductionmentioning

confidence: 76%

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Unified theory of resonances and bound states in the continuum in Hermitian tight-binding models

Горбацевич

Shubin

2017

Phys. Rev. B

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We study transport properties of an arbitrary two terminal Hermitian system within a tightbinding approximation and derive the expression for the transparency in the form, which enables one to determine exact energies of perfect (unity) transmittance, zero transmittance (Fano resonance) and bound state in the continuum (BIC). These energies correspond to the real roots of two energy-dependent functions that are obtained from two non-Hermitian Hamiltonians: the Feshbach's effective Hamiltonian and the auxiliary Hamiltonian, which can be easily deduced from the effective one. BICs and scattering states are deeply connected to each other. We show that transformation of a scattering state into a BIC can be formally described as a "phase transition" with divergent generalized response function. Design rules for quantum conductors and waveguides are presented, which determine structures exhibiting coalescence of both resonances and antiresonances resulting in the formation of almost rectangular transparency and reflection windows. The results can find applications in construction of molecular conductors, broad band filters, quantum heat engines and waveguides with controllable BIC formation.

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Section: Introductionmentioning

confidence: 76%

“…Thus, according to Eqs. (12) and (21) the problem of divergence of transmission at BIC's energy, discussed, for example, in Ref. 49 , is resolved easily.…”

Section: Bound States In the Continuummentioning

confidence: 99%

Unified theory of resonances and bound states in the continuum in Hermitian tight-binding models

Горбацевич

Shubin

2017

Phys. Rev. B

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“…Hence one should expect that the S-matrix language would be appropriate to describe the PT -SB phenomena in PT -symmetric systems as well. The evolution of the S-matrix poles in PT -symmetric systems do bear some features peculiar to the EP picture 28,29 but the cross section versus energy dependence doesn't match exactly the evolution of the S-matrix poles 24,28,30 . It was established in Ref.…”

Section: Introductionmentioning

confidence: 96%

“…Just this transformation was described in the dissipationless resonant tunneling heterostructure (RTS) in Ref. 24 , which was called collapse of resonances (CR). CR is accompanied by SB of the electronic density distribution, which is symmetric at the unit transparency resonance and becomes asymmetric after CR.…”

Section: Introductionmentioning

confidence: 99%

PT-symmetry breaking in resonant tunneling heterostructures

Горбацевич

Shubin

2016

Jetp Lett.

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We present fermionic model based on symmetric resonant tunneling heterostructure, which demonstrates spontaneous symmetry breaking in respect to combined operations of space inversion (P) and time reversal (T ). PT -symmetry breaking manifests itself in resonance coalescence (collapse of resonances). We show that resonant energies are determined by eigenvalues of auxiliary pseudoHermitian PT -invariant Hamiltonian.Spontaneous symmetry breaking (SSB) is a central concept in different fields of modern physics, especially in particle physics [1] and condensed matter physics [2][3][4][5][6]. SSB means that the symmetry of the system changes (lowers) at some value of a system parameter, which itself does not change the symmetry directly. Recently a new class of SSB phenomena was introduced in PT -invariant systems [7][8][9]. Such systems are invariant with respect to both space inversion (P) and time reversal (T ) and are described by PT -invariant pseudo-Hermitian Hamiltonian, which can possess real eigenvalues [7]. At some magnitude of Hamiltonian parameter two real eigenvalues coalesce and transform into another two with nonzero imaginary parts of different signs and with equal real parts -PT -symmetry breaking (PT -SB) [7][8][9]. Such points in the parameter space are known as exceptional points (EP) [10][11][12]. The eigenstate of the Hamiltonian at EP is nondegenerate (contrary to crossing point).Hamiltonian eigenvalue with positive imaginary part corresponds to nonunitary evolution of wave function, which is forbidden by norm preserving condition. Hence, it was not clear whether fermionic systems could exist with some relation to pseudo-Hermitian PT -invariant Hamiltonian. Up to now all realistic applications of PT -SB with possible experimental manifestations have been based on the formal equivalence of Schröedinger and wave equations and described electromagnetic phenomena [13][14][15][16][17][18]. T -breaking terms in the wave equation correspond to well established gain/loss processes. Superconducting PT -invariant model was considered in Ref. [19]. Tbreaking terms in this case describe creation/annihilation processes in bosonic Cooper-pair field.In this paper we present fermionic model with (PT -SB) based on symmetric resonant tunneling structure (RTS). RTS is a typical example of an open quantum system. SSB phenomenon in open quantum system has been already described in the early treatments [20] based on Caldeira-Legget model where SSB could be attributed to tunneling suppressed by dissipation. Later in Ref. [21] it was shown that in symmetric RTS without dissipation SSB can occur at the point where two resonances coalesce. This phenomenon was called the collapse of resonances (CR). In this paper we construct auxiliary pseudoHermitian PT -invariant Hamiltonian whose eigenvalues exactly correspond to resonance energies and EP describe CR. In condensed matter physics the description and classification of states with broken symmetry are based on group theory, which limits the possible number of different st...

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“…The mathematical complication is that in the majority of theoretical papers [10][11][12][13][14][15][16][17] simplified models of nano-systems (mainly the plane ones) are used. These models are based at the δ-barrier approximation of RTS rectangular potential barriers.…”

Section: Introductionmentioning

confidence: 99%

Electronic Conductivity in Open Cylindrical Two-Barrier Symmetric Resonance Tunnel Structure

et al. 2010

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The theory of resonance energies and widths of electron quasi-stationary states and electronic conductivity in open cylindrical two-barrier symmetric resonance tunnel structure is developed. The complete Schrodinger equation is solved within the model of effective masses for rectangular potential wells and barriers. Interaction between electrons and electromagnetic field was taken into account using the approximation of the small signal. The calculations of spectral parameters are performed for In 0.53 Ga 0.47 As/In 0.52 Al 0.48 As resonance tunnel structure. The dependences of conductivity on the energy of mono-energy electrons beam falling at the system and electromagnetic field energy absorbed or emitted by the system are obtained and analyzed. The relation between experimentally measured parameters of conductivity and resonance widths of electron quasi-stationary states in open resonance tunnel structure is established.

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Collapse of resonances in semiconductor heterostructures as a transition with symmetry breaking in an open quantum system

Cited by 15 publications

References 18 publications

Unified theory of resonances and bound states in the continuum in Hermitian tight-binding models

Unified theory of resonances and bound states in the continuum in Hermitian tight-binding models

PT-symmetry breaking in resonant tunneling heterostructures

Electronic Conductivity in Open Cylindrical Two-Barrier Symmetric Resonance Tunnel Structure

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