## Superconducting quantum dots

**Systems of interest:**single-level quantum dots with local Coulomb interaction connected to metallic and superconducting (BCS) leads that can be described by the superconducting impurity Anderson model

**Methods:**second order perturbation theory in Coulomb interaction stregth, numerical renormalization group (NRG), CT-HYB quantum Monte Carlo

**Goal:**consistent description of the behavior of the subgap Andreev bound states (Yu-Shiba-Rusinov states) and the Josephson current in the vicinity of the single-doublet (zero-pi) quantum phase transition### Related publications

P. Zalom, V. Pokorný, and T. Novotný, Phys. Rev. B**103**, 035419 (2021).

V. Pokorný, M. Žonda, G. Loukeris, and T. Novotný, JPS Conf. Proc.**30**, 011002 (2020).

A. Kadlecová, M. Žonda, V. Pokorný, and T. Novotný,

Phys. Rev. Applied**11**, 044094 (2019).

V. Pokorný, M. Žonda, Physica B**536**, 488 (2018).

T. Domański, M. Žonda, V. Pokorný, G. Górski, V. Janiš, and T. Novotný,

Phys. Rev. B**95**, 045104 (2017).

V. Janiš, V. Pokorný, and M. Žonda, Eur. Phys. J. B**89**, 197 (2016).

M. Žonda, V. Pokorný, V. Janiš, and T. Novotný, Phys. Rev. B**93**, 024523 (2016).

M. Žonda, V. Pokorný, V. Janiš, and T. Novotný, Sci. Rep.**5**, 8821 (2015).

### Presentations

18. 6. 2019, IoP CAS, Prague, Czech Republic

3. 4. 2019, DPG Spring Meeting, Regensburg, Germany

12. 3. 2018, DPG Spring Meeting, Berlin, Germany

1. 1. 2018, Universität Regensburg, Germany

29. 11. 2016, IoP CAS, Prague, Czech Republic

24. 3. 2015, IoP CAS, Prague, Czech Republic

17. 10. 2014, IIASS, Vietri sul Mare (Salerno), Italy### Software

SQUAD -**SU**perconducting**QUA**ntum**D**ot - set of python scripts to calculate properties of these systems using the diagrammatic second order perturbation method

SQUAD-CTHYB - a TRIQS-based code to calculate properties of these systems using the CT-HYB quantum Monte-Carlo method## Molecular electronics

**Systems of interest:**spinful molecules attached to metallic or insulating substrates or leads

**Methods:**density functional theory (DFT), non-equilibrium Green functions (NEGF)

**Goal:**search for molecular systems suitable as building elements of molecular spintronic devices### Related publications

H. Li et al, Angew. Chem. Int. Ed.**56**14145 (2017).### Presentations

17. 2. 2020, Albert-Ludwigs-Universität Freiburg, Germany

2. 7. 2019, Prague, Czech Republic

20. 7. 2018, Universität Regensburg, Germany

### Reseach group homepage

Computational theory of condensed matter group## Thermodynamically consistent description of quantum criticality

We are developing methods based on diagrammatic perturbation techniques to study quantum criticality in interacting electron systems described by lattice models (e.g. Anderson or Hubbard model). Methods are based on the parquet construction of two-particle functions and provide a consistent description that is free of unphysical symmetry breaking and does not violate conservation laws.

### Related publications

V. Janiš, A. Klíč, J. Yan, and V. Pokorný, Phys. Rev. B**102**, 205120 (2020).

V. Janiš, P. Zalom, V. Pokorný, and A. Klíč, Phys. Rev. B**100**, 195114 (2019).

V. Janiš, V. Pokorný, and A. Kauch, Phys. Rev. B**95**, 165113 (2017).

V. Janiš, A. Kauch, and V. Pokorný, Phys. Rev. B**95**, 045108 (2017).

### Presentations

Poster from the 2017 summer school in Tallahassee (pdf)### Software

SPEpy -**S**implified**P**arquet**E**quations in**py**thon - set of python scripts to calculate properties of the single-impurity Anderson model using the simplified parquet equation solver## Correlated materials with strong spin-orbit interactions

We use the combination of ab-initio (LDA) methods and dynamical mean-field theory (DMFT) to study materials with strong effect of spin-orbit coupling on their electronic and magnetic properties. The focus lies on transition-metal oxides with heavy ions such as iridium and osmium. We use the continuous-time quantum Monte-Carlo method in the strong-coupling limit (CT-HYB) to solve the underlying impurity problem.

### Related publications

K. Pajskr, P. Novák, V. Pokorný, J. Kolorenč, R. Arita, and J. Kuneš, Phys. Rev. B**93**, 035129 (2016).## Correlated electrons in disordered alloys (PhD thesis)

We developed methods to calculate charge transport in disordered systems of elastically scattered electrons. These diagrammatic methods are based on an asymptotic limit to high spatial dimensions and utilize advanced diagram summation techniques on the two-particle level. They allow us to calculate electrical conductivity and diffusion coefficient for arbitrary disorder strength. The numerical calculations are performed on the disordered Anderson model and the Falicov-Kimball model.

### Related publications

V. Janiš and V. Pokorný, Phys. Rev. B**90**, 045143 (2014).

V. Pokorný and V. Janiš, J. Phys.: Cond. Mat.**25**, 175502 (2013).

V. Janiš and V. Pokorný, Ann. Phys. (Berlin)**523**, 715 (2011).

V. Janiš and V. Pokorný, Phys. Rev. B**81**, 165103 (2010).

PhD thesis (English, pdf, defended in 2013 at Charles University in Prague).### Presentations

24. 4. 2012, IoP CAS, Prague, Czech Republic

14. 10. 2011, IIASS, Vietri sul Mare (Salerno), Italy

## Critical properties of the mixed-spin Heisenberg model (Master thesis)

We studied the critical properties of the anisotropic mixed spin-1 and spin-1/2 quantum Heisenberg model using a simple two-site mean-field approximation. We treat in detail the system on the simple cubic lattice considering both exchange anisotropy and uniaxial singe-ion anisotropy. The critical behavior is analysed and the complete phase diagrams were calculated, where aside from the typical ferromagnetic phase a low-temperature quantum ordered phase is described.

### Related publications

A. Bobák, V. Pokorný, and J. Dely, J. Phys.: Conf. Ser.**200**, 022001 (2010).

A. Bobák, V. Pokorný, and J. Dely, Physica A**388**, 2157 (2009).

Master thesis (Slovak, pdf, defended in 2008 at Pavol Jozef Šafárik University in Košice).### Presentations

16. 12. 2008, IoP CAS, Prague, Czech Republic