Here are the results from the relevant queries on my database constructed from the downloads available from the FIDE rating download website for players with rapid ratings of 2700 and over. Since you also ask for countries I've included distinct player/country combinations. So, for instance, Caruana appears for both Italy and the US.
The "Period" is the first FIDE rating list in which the player achieved the rating. If the player didn't play rated rapid for a year after that then they obviously retain the rating for the next year so the "Period" is the year and month in which FIDE first recorded that rating for them.
It is interesting how old some of these peak rapid ratings are. It looks like maybe the top players don't play that much rapid, compared to blitz and standard?
PlayerName FedName MaxRating Period
- Carlsen, Magnus Norway 2919 2017/07
- Vachier-Lagrave, Maxime France 2873 2019/11
- Caruana, Fabiano Italy 2858 2014/07
- Nakamura, Hikaru United States 2853 2019/06
- So, Wesley United States 2852 2018/07
- Grischuk, Alexander Russia 2851 2017/07
- Ivanchuk, Vassily Ukraine 2844 2016/01
- Ding, Liren China 2836 2020/01
- Mamedyarov, Shakhriyar Azerbaijan 2833 2017/07
- Aronian, Levon Armenia 2830 2015/03
- Karjakin, Sergey Russia 2830 2012/08
- Caruana, Fabiano United States 2829 2015/03
- Dominguez Perez, Leinier Cuba 2826 2017/12
- Anand, Viswanathan India 2822 2018/04
- Nepomniachtchi, Ian Russia 2821 2015/11
- Korobov, Anton Ukraine 2818 2019/12
- Dominguez Perez, Leinier United States 2816 2018/09
- Artemiev, Vladislav Russia 2812 2018/11
- Fedoseev, Vladimir Russia 2810 2018/01
- Kramnik, Vladimir Russia 2799 2016/03
- Svidler, Peter Russia 2799 2014/08
- Wang, Hao China 2795 2019/04
- Yu, Yangyi China 2795 2017/05
- Morozevich, Alexander Russia 2791 2014/10
- Topalov, Veselin Bulgaria 2790 2013/07
- Radjabov, Teimour Azerbaijan 2788 2012/07
- Kobyliansky, Igor Ukraine 2787 2020/01
- Dreev, Aleksey Russia 2785 2013/01
- Kasparov, Garry Russia 2783 2017/09
- Dubov, Daniil Russia 2779 2019/01
- Giri, Anish Netherlands 2779 2017/10
- Malakhov, Vladimir Russia 2777 2014/01
- Onischuk, Vladimir Ukraine 2775 2019/02
- Duda, Jan-Krzysztof Poland 2774 2020/01
- Andreikin, Dmitry Russia 2773 2013/10
- Leko, Peter Hungary 2773 2014/01
- Le, Quang Liem Vietnam 2771 2014/10
- Inarkiev, Ernesto Russia 2767 2017/11
- Sjugirov, Sanan Russia 2765 2016/01
- Wang, Yue China 2765 2014/01
- Adams, Michael England 2764 2014/01
- Kamsky, Gata United States 2762 2013/03
- Jakovenko, Dmitry Russia 2759 2019/11
- Harikrishna, P. India 2758 2018/12
- Rublevsky, Sergei Russia 2757 2015/10
- Gelfand, Boris Israel 2755 2017/01
- Tomashevsky, Evgeny Russia 2752 2014/07
- Vitiugov, Nikita Russia 2752 2012/11
- Wei, Yi China 2752 2020/01
- Zhigalko, Sergei Belarus 2752 2015/11
- Bu, Xiangzhi China 2751 2018/05
- Navara, David Czech Republic 2751 2017/10
- Fressinet, Laurent France 2750 2013/01
- Kovalenko, Igor Latvia 2750 2016/02
- Ponomariov, Ruslan Ukraine 2748 2013/11
- Rapport, Richard Hungary 2748 2017/10
- Short, Nigel D England 2744 2017/01
- Nguyen, Ngoc Truong Son Vietnam 2743 2015/09
- Wojtaszek, Radoslaw Poland 2743 2013/03
- Shirov, Alexei Latvia 2742 2014/02
- Kryvoruchko, Yuriy Ukraine 2740 2015/11
- Guseinov, Gadir Azerbaijan 2739 2015/11
- Mamedov, Rauf Azerbaijan 2739 2018/10
- Ponkratov, Pavel Russia 2737 2018/01
- Moussard, Jules France 2736 2019/10
- Oparin, Grigoriy Russia 2736 2021/01
- Naiditsch, Arkadij Germany 2735 2013/01
- Riazantsev, Alexander Russia 2735 2017/01
- Bacrot, Etienne France 2733 2015/05
- Anton Guijarro, David Spain 2732 2017/09
- Bologan, Viktor Moldova 2732 2012/07
- Zubov, Alexander Ukraine 2731 2019/04
- Xiong, Jeffrey United States 2730 2019/11
- Cheparinov, Ivan Bulgaria 2727 2014/03
- Chigaev, Maksim Russia 2727 2018/07
- Jobava, Baadur Georgia 2727 2014/07
- Savchenko, Boris Russia 2727 2018/01
- Matlakov, Maxim Russia 2726 2019/11
- Movsesian, Sergei Armenia 2725 2016/01
- Eljanov, Pavel Ukraine 2724 2013/10
- Brunello, Sabino Italy 2722 2019/11
- Pantsulaia, Levan Georgia 2722 2018/01
- Petrosian, Tigran L. Armenia 2721 2019/01
- Rakhmanov, Aleksandr Russia 2721 2018/05
- Salem, A.R. Saleh United Arab Emirates 2720 2019/01
- Bogdanovich, Stanislav Ukraine 2719 2016/07
- Safarli, Eltaj Azerbaijan 2718 2019/09
- Vallejo Pons, Francisco Spain 2718 2013/07
- Vidit, Santosh Gujrathi India 2718 2017/01
- Amonatov, Farrukh Tajikistan 2716 2017/01
- Sargissian, Gabriel Armenia 2715 2019/06
- Alekseenko, Kirill Russia 2714 2019/01
- Moiseenko, Alexander Ukraine 2714 2012/08
- Motylev, Alexander Russia 2711 2020/01
- Ragger, Markus Austria 2711 2015/07
- Grachev, Boris Russia 2710 2012/11
- Meier, Georg Germany 2710 2019/06
- Istratescu, Andrei France 2709 2013/08
- Khairullin, Ildar Russia 2709 2013/07
- Khismatullin, Denis Russia 2709 2016/01
- cShane, Luke J England 2709 2016/08
- Efimenko, Zahar Ukraine 2708 2012/10
- Kokarev, Dmitry Russia 2708 2018/10
- Akopian, Vladimir Armenia 2707 2017/07
- Shirov, Alexei Spain 2707 2019/07
- Popov, Ivan Russia 2706 2016/01
- Bruzon Batista, Lazaro Cuba 2704 2013/10
- Fedorchuk, Sergey A. Ukraine 2704 2017/10
- Socko, Bartosz Poland 2704 2015/11
- Firouzja, Alireza FIDE 2703 2020/01
- Tsydypov, Zhamsaran Russia 2703 2020/04
- Li, Chao b China 2702 2017/01
- Areshchenko, Alexander Ukraine 2701 2013/07
- Najer, Evgeniy Russia 2701 2015/06
- Fridman, Daniel Germany 2700 2017/09
- Iturrizaga, Eduardo Venezuela 2700 2014/07