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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We present a model of the molecular transistor, operation of which is based on the interplay between two physical mechanisms, peculiar to open quantum systems that act in concert: -symmetry breaking corresponding to coalescence of resonances at the exceptional point of the molecule, connected to the leads, and Fano-Feshbach antiresonance. This switching mechanism can be realised in particular in a special class of molecules with degenerate energy levels, e.g. diradicals, which possess mirror symmetry. At zero gate voltage infinitesimally small interaction of the molecule with the leads breaks the -symmetry of the system that, however, can be restored by application of the gate voltage preserving the mirror symmetry. -symmetry broken state at zero gate voltage with minimal transmission corresponds to the “off” state while the -symmetric state at non-zero gate voltage with maximum transmission – to the “on” state. At zero gate voltage energy of the antiresonance coincides with exceptional point. We construct a model of an all-electrical molecular switch based on such transistors acting as a conventional CMOS inverter and show that essentially lower power consumption and switching energy can be achieved, compared to the CMOS analogues.

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...